Reliability Prediction at Early - DiVA portalltu.diva-portal.org/smash/get/diva2:990750/FULLTEXT01.pdf · extreme values, service life and requirements allocation. There are several

LICENTIATE T H E S I S

Department of Engineering Sciences and Mathematics Division of Product and Production Development

Reliability Prediction at Early Functional Product Development Stages

Jonas Pavasson

ISSN: 1402-1757 ISBN 978-91-7439-489-4

Luleå University of Technology 2012

ISSN: 1402-1757 ISBN 978-91-7439-XXX-X Se i listan och fyll i siffror där kryssen är

Reliability Prediction at arly Functional

Product Development Stages

Jonas Pavasson

Luleå University of TechnologyDepartment of Engineering Sciences and Mathematics

Division of Product and Production Development

Printed by Universitetstryckeriet, Luleå 2012

ISSN: 1402-1757 ISBN 978-91-7439-489-4

Luleå 2012

www.ltu.se

iii

Preface

The research presented in this thesis was conducted in the research area Computer Aided Design, in a project within the Faste Laboratory, Centre for Functional Product Innovation, a VINNOVA (Swedish Governmental Agency for Innovation Systems) Excellence Centre, based at Luleå University of Technology, Sweden.

I wish to thank my industrial collaboration partners Dr. Henrik Strand and Dr. Jonas Larsson at Volvo Construction Equipment, a Partner Company in the Faste Laboratory.

I would also like to thank my supervisor Associate Professor Magnus Karlberg and Professor Lennart Karlsson, Chair of Computer Aided Design at Luleå University of Technology.

I also wish to thank my colleagues at the Division of Product and Production Development, particularly all PhD students in the research area of Computer Aided Design.

To my daughter Fanny, for giving me hope and inspiration, I extend special thanks.

Jonas Pavasson

Luleå, December 2012

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Abstract

A trend among industrial companies is to change business strategies from hardware-oriented to more service-oriented solutions, e.g. functional product business models. Functional products are typically constituted by hardware together with a service support system. For functional product businesses, availability is one critical property upon which the customer and provider must agree. Hence, during functional product development and operation, it is important to enable simulations of functional product availability, which is a function of reliability and maintainability. To more rapidly converge on optimal solutions, simulation-driven design strategies have further been proposed by several researchers. In these strategies, the simulations are used to drive the development rather than simply verify suggested solutions. Measured data or estimated data are often used as input to reliability prediction methods such as fault tree analysis and failure mode and effect analysis. However, when designing new systems, reliability input data may not exist and, hence, prototypes are often manufactured and tested, which requires a significant amount of time.

The objective of the work presented in this thesis is to develop a simulation-driven methodology for how to predict hardware reliability, as a part of functional product availability.

This methodology shall be applied at early concept stages of the functional product development process, where limited component reliability information exists.

The conducted research is based on theories regarding product development methodologies, reliability prediction methods and deterministic simulation methods (e.g. rigid body dynamics). The research presented in this thesis followed a 5-step procedure including as-is study, to-be scenario development (where a future functional business situation is described), method development, method verification (through case studies) and method validation.

During the as-is study, existing reliability methods were evaluated according to suitability in different development stages. Fault tree analysis and probabilistic variation mode and effect analysis were found to give accurate results (since objective input data are used). However, those methods would need further development in order to be used for reliability prediction at early concept stages. Traditional probabilistic variation mode and effect analysis did not result in reliability in terms of a probabilistic quantity. Therefore, the probabilistic variation mode and effect analysis method was further developed and verified through a case study which can be used for probabilistic measures.

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A method based on deterministic simulations to derive component reliability information has been further developed. This method takes different variations into account and through a series of simulations, input data for system reliability (such as fault tree analysis and probabilistic variation mode and effect analysis) can be derived.

Hence, by combining deterministic and probabilistic simulations, hardware system reliability can be predicted, even when limited component reliability information exists. This hardware reliability prediction method is a critical part of a simulation-driven methodology to be used at early stages of functional product development

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Thesis

This licentiate thesis comprises a survey of the following three papers.

Paper A:

Reliability Prediction Based on Variation Mode and Effect Analysis. J. Pavasson, K. Cronholm, H. Strand and M. Karlberg. Journal of Quality and Reliability Engineering International. 2012.

Author contribution: The author of this thesis is the main author of the paper. The author’s contribution to the paper includes a literature review, summary and explanation of the Variation Mode and Effect Analysis (VMEA) method, reliability prediction method development and a case study in collaboration with the co-authors. The author was further responsible for writing the paper, except for the introduction in section 4 and parts of section 4.1.

Paper B:

Variation Mode and Effect Analysis compared to FTA and FMEA in product development. J. Pavasson and M. Karlberg. In proceedings of the 19th AR2TS Advances in Risk and Reliability Technology Symposium. April 12-14, 2011. Nottingham, UK.

Author contribution: The author of this thesis is the main author of the paper. The author’s contribution to the paper includes a literature review, summary and explanation of the Variation Mode and Effect Analysis (VMEA) method, summary and explanation of the Failure Mode and Effect Analysis (FMEA) method, data collection of the compared methods, and an evaluation and analysis of the compared reliability methods in collaboration with the co-author . The author was also responsible for writing the paper, except for section 3 and parts of section 6.

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Paper C:

System Reliability Estimation with input data from Deterministic Simulations. J. Pavasson and M. Karlberg. In proceedings of ASME International Mechanical Engineering Congress & Exposition. November 9-15, 2012. Houston, USA.

Author contribution: The author of this thesis is the main author of the paper. The author’s contribution to the paper includes a literature review, simulation-driven reliability estimation method development and a verifying case study in collaboration with the co-author. The author was further responsible for writing the paper, except for section 2, 3 and parts of section 4 and 5.

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Table of Contents

1 Introduction ................................................................................................... 11

2 Theory ........................................................................................................... 14

2.1 Product Development Methodology .......................................................... 14

2.1.1 Product development process............................................................. 14 2.1.2 Simulation Driven Product Development .......................................... 16 2.1.3 Functional Product Development ...................................................... 17

2.2 Reliability Prediction Methods .................................................................. 17

2.2.1 Variation Mode and Effect Analysis (VMEA) ..................................... 18 2.2.2 Failure Mode and Effect Analysis (FMEA) .......................................... 23 2.2.3 Fault Tree Analysis (FTA) .................................................................. 23

2.3 Deterministic simulations ........................................................................... 25

2.3.1 Rigid Body Dynamics ....................................................................... 25 3 Research Methodology ................................................................................... 26

3.1 As-Is study ................................................................................................ 27

3.2 To-Be scenario development ..................................................................... 28

3.3 Method development ................................................................................ 28

3.4 Method verification ................................................................................... 29

3.5 Method validation ..................................................................................... 29

4 Reliability prediction when availability of input data is limited ......................... 29

4.1 Benchmark and evaluation of reliability methods ........................................ 30

4.2 Reliability prediction strategy development ................................................ 32

4.2.1 Reliability prediction based on probabilistic VMEA ........................... 32 4.2.2 Reliability prediction through combination of deterministic and probabilistic simulations ................................................................................ 36

5 Discussion and Conclusions ............................................................................. 41

6 Future Research ............................................................................................. 41

7 Acknowledgements ......................................................................................... 42

8 References ...................................................................................................... 42

Appended Papers .................................................................................................. 47

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1 Introduction A trend among industrial companies is to change business strategies from hardware-oriented to more service-oriented solutions. One such solution, where the supplier retains the ownership of the hardware throughout the product lifecycle and instead provides and guarantees a function, is called a functional product (FP) business model (Alonso-Rasgado et al., 2004). A functional product is typically constituted by hardware together with a service support system (Alonso-Rasgado et al., 2004). During FP development, it is critical to predict and optimize product functionality to ensure that needed requirements are fulfilled. These requirements are often interconnected and sometimes contradict each other. Virtual Prototyping is used to increase competitiveness, which motivates demands as decreased development cost and shorter project times. Saved resources as time, money and workforces can then be spent on optimization or a new project instead. In functional product businesses availability is one critical property upon which the customer and provider must agree. Therefore, a framework has been derived for prediction of functional product availability to be used both during development and operation (Löfstrand et al., 2011; Löfstrand et al., 2012). In this framework availability is derived by integrating hardware reliability models with support system models (i.e. maintainability models).

The possibility of predicting reliability of hardware, both for components and systems, is important in engineering design. Enabling prediction of reliability makes it possible to prevent failures, for instance, through planned maintenance. The reliability of individual components is superior to the corresponding hardware system reliability (Henley and Kumamoto, 1981). In 1961 Weibull formulated a distribution (the Weibull distribution), which is one of the most commonly used formulas for describing important probabilistic measures in reliability theory, e.g. times to failures, extreme values, service life and requirements allocation. There are several methods for predicting hardware system reliability that consist of many components, i.e. with many failure modes. One commonly used method for predicting reliability of complex hardware systems is Fault Tree Analysis (FTA). FTA is a deductive method where the system state is decomposed into chains of more basic events (faults) of components. The logical interrelationship of how such basic events depend on and affect each other, and thereby cause some system state to occur, is often described analytically in a reliability structure which can be visualized as a tree (Bergman et al., 2010; Andrews et al., 2002). Support systems can be modeled by Petri Nets (Reed et al., 2010), which includes the logical correlation between the components and system and has a top-down approach (Schneeweiss, 1999) or state-space analysis (Markov analysis) (O’Connor, 2002). Failure Mode and Effect Analysis (FMEA) is a commonly used method in the automotive industry. FMEA is categorized as a

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bottom-up approach to identify causes of failure and failure modes (Lönnqvist, 2009). It is realized that many failures are caused by variations (strength, loads, manufacturing tolerances, etc.), resulting in expensive reclamations and dissatisfaction that may lead to lost business. Industries are in need of robust design methodologies that can be used to identify and manage different sources of variation (Arvidsson et al., 2003; Johansson et al, 2006). A relatively new method called Variation Mode and Effect Analysis (VMEA) has been developed (Bergman et al., 2009; Chakhunashvili et al., 2004) to manage variations that significantly contribute to the variability in order to increase the reliability of the design (Bergman et al., 2009). VMEA has been decomposed into three different types: Basic VMEA, Enhanced VMEA and Probabilistic VMEA (Johansson et al., 2006; Chakhunashvili et al., 2009), each of these VMEA methods is suitable in different stages of the product development process, depending on available information. By using the VMEA method it is possible to, with a prescribed reliability, derive safety factors and predict useful life for different applications (Svensson et al., 2009; Johannesson et al., 2009).

Drivelines are lightly damped nonlinear systems with many degrees of freedom and with significant interactions between the subsystems. There are many sources of excitation, such as torsional impact caused by the take-up of backlash in the power train system. Such sources of excitation exist in transmission backlash, in driveline splines and in pinion-to-ring-gear contact in the differential. Abrupt application or release of the throttle in slowly moving traffic or rapid engagement of the clutch can be followed by noise and vibration responses, also referred to as clonk. Walha et al. (2011) investigated the nonlinear dynamic behaviour of an automotive clutch system, including three types of nonlinearity: dry friction path, double stage stiffness and spline clearance. The objective was to identify the dynamic behaviour of mechanical elements (such as: shafts, bearings, gears, flywheel, pressure plate, hub of the clutch) and to reduce vibration. The study showed that eccentricity defect impacts the nonlinear dynamic behaviour of the clutch system and therefore affects the performance of this mechanism. In a drive case study for articulated haulers, Illerhag and Sjögren (2000) investigated how a differential locking in the driveline affects the power delivery to the ground as well as the slip of tires. Coupled nonlinear subsystems of different domains make it difficult to predict and optimize the dynamic behaviour of the complete system. Dynamic simulations of complete machines to optimize the overall performance and related aspects were made by Filla and Palmberg (2003) and Blundell and Harty (2004).

Torsional vibration in the clutch engagement process has a negative impact on light trucks with diesel engines. Centea, Rahnejat and Menday (2001) therefore investigated the effect of various clutch systems and driveline components on its vibration performance. Crowther and Zhang (2005) conducted a numerical study of

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the effect of low-frequency transient vibration on clutch engagement stick-slip and gear backlash in powertrains. Farshidianfar, Ebrahimi and Bartlett (2001) investigated torsional impact in vehicle driveline systems and created a method which can identify the phenomena clonk and shuffle. A field study of the mathematical modelling of gears for dynamic analysis was conducted in a review paper by Özguven and Houser (1988).

Simulations are often conducted to verify proposed designs, i.e. verifying simulations (Roozenburg and Eekels, 1995). However, this simulation strategy can be expensive, time-demanding, and also inhibiting for innovation. Therefore, Simulation Driven Design (SDD) has been proposed as a method where simulations are used as a driver and to guide designers towards optimal solutions rather than to verify suggested solution. Lockwood (2009) stated that the objective of SDD is to converge at optimal solutions as early as possible. Karlberg et al. (2012) conducted a literature review to show the research evolution of SDD and to identify the state of the art in SDD methodology including various definitions, criteria and effects of using SDD approaches.

Measured data or estimated data are often used as input to reliability prediction methods. When designing new hardware systems, such measurement data may not exist and prototypes often need to be manufactured, which may be very time-consuming. In such situations, deterministic simulations could possibly be used to derive the needed input data. By use of simulations, e.g. Simulation Driven Design, concepts can be evaluated by means of reliability in early stages of the product development process, even before a physical prototype is manufactured.

Hence, the objective of the work presented in this thesis is to develop a simulation-driven methodology for how to predict hardware reliability, as a part of functional product availability.

This methodology shall be applied at early concept stages of the functional product development process, where limited component reliability information exists. Further, this methodology should take important variations into account and it should also include combinations of deterministic and probabilistic simulations.

To guide the research work a research question was formulated, i.e.

How shall hardware system reliability, as part of functional product availability, be predicted when limited input data exist?

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2 Theory In this section theories regarding product development methodology, reliability prediction methods and rigid body dynamics are presented.

2.1 Product Development Methodology Traditionally, product development was based on previous solutions that undergo refinement, i.e. a bottom-up working process. Evaluation and improvement was typically carried out by use of physical prototypes, i.e. trial and error. This type of working process is often resource-demanding and expensive.

The market today faces increased demands on customer needs, quality, shorter product lifecycles and increased competition (Persson, 2001). The products have a higher degree of complexity and contain various technologies that demand increased efficiency during the product development process. Therefore, to better meet customer needs, companies have been forced to streamline the product development process by introducing integrated collaboration between engineering design, industrial design, production, marketing, etc., i.e. a top-down process. The possibility of a low product development cost is increased by the use of computer-aided software to evaluate the concepts before a physical prototype is built. To obtain a satisfactory result it is important to allow creativity on a detailed level in a more strictly defined product development process (Persson, 2001). Drivers of product development are divided into three different areas, i.e., technology push-, market pull- and society-driven development. Technology push development is based on the use of new technology, often in a more long-term perspective. Market pull development is based on market needs and competing products, usually in a short-term perspective. The third type is society-driven development, which is based on laws and regulations, due to aspects regarding the environment, e.g. fuel-efficient cars decrease the greenhouse effect.

2.1.1 Product development process There is no overall theoretical product development process which holds for all products. Hubka and Eder (1988) used two different axes for descriptive and prescriptive product development methods. The first is focusing on product feature and the second on the design process, as shown in the Design Science map, see Figure 1.

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Figure 1. Main Categories of Design Science Statements, based on Hubka

and Eder (1988)

Pahl and Beitz (1995) and Olsson (1978 and 1985) have documented methodologies to support the product development process. These methodologies are based on empirical prescriptive design methods describing the steps and which activities should be implemented during a product development process. Similar prescriptive methods have been proposed by Wheelwright and Clark (1992) Hubka and Eder (1992), Pugh (1990), Ullman (1992), Roozenburg and Eekels (1995) and Ulrich and Eppinger (2004). Authors within this research field are using different terminology, but the product development process is similar and is roughly divided into following stages:

Product specification

Concept generation Concept evaluation and selection Detail design and product layout

Production adjustment

The usefulness and applicability of product development methods is continuously discussed. Product development methods have their advantages and disadvantages, depending on when and who is performing the operation in the product development process. The development cost increases the later the product changes are performed and this applies to all the different proposed product development processes. For designers or users of different methodologies it is reasonable on the

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basis of experience-based judgment to apply and mix parts from different methods that best fit the activity.

The work in this thesis is based on Ulrich and Eppinger’s (2004) product development process, and the process is divided into following parts, see Figure 2.

Figure 2. Product Development Process, based on Ulrich and Eppinger

(2004)

Concepts are generated, evaluated and selected during the product development process, see Figure 3.

Figure 3. Concept selection, based on Ulrich and Eppinger (2004)

2.1.2 Simulation Driven Product Development In a traditional engineering process the simulations are often conducted to verify designs that have already been proposed, i.e. verifying simulations (Roozenburg and Eekels, 1995). Engineers are developing products by testing and iterating prototypes towards a desired performance of the design (Lockwood, 2009). However, this simulation strategy can be expensive, time-demanding, and also inhibiting for innovation. Therefore, Simulation Driven Design (SDD) has been proposed as a

ConceptDevelopment

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Testing and Refinement

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Concept generation

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method where simulations are used as a driver and to guide designers towards optimal solutions rather than to verify suggested solution. Lockwood (2009) stated that the objective of SDD is to converge at optimal solutions as early as possible. Karlberg et al. (2012) conducted a literature review to show the research evolution of SDD and to identify the state of the art in SDD methodology including various definitions, criteria and effects of using SDD approaches. Löfstrand et al. (2010) claimed that the modelling and simulation SDD approach minimises the cost of each concept and allows simulation of a number of different concepts before the actual work is carried out.

2.1.3 Functional Product Development A trend among industrial companies is to change business solutions from hardware-oriented to more service-oriented solutions. One such solution, where the supplier retains the ownership of the hardware throughout the product lifecycle and instead provides and guarantees a function, is called the functional product business model (Alonso-Rasgado et al., 2004). A functional product (FP) is typically constituted by hardware, software and a service support system. Due to the complexity of the development process for a functional product, there is a need to communicate and share information during the process (Lindström et al., 2012). A framework has further been derived for a functional product development process to manage the FP development (Lindström et al., 2012). This framework includes development of hardware, software, service support system and management of operation. Selling a function whereby the provider still owns the hardware and the customer pays for a function require a life-,cycle perspective for the provider, including design and development, support and maintenance, competence, risk management, finance, etc. To manage the risks involved there is a need for the provider to predict product availability versus cost to be able to sell the function. A function must also be monitored to extract data in real-time, so the provider can deliver an agreed level of availability to the customer and also find root cause if problems occur (Karlsson et al., 2012). In functional product businesses availability is one critical property that the customer and provider must agree upon. Therefore, a framework has been derived for prediction of functional product availability to be used both during development and operation (Löfstrand et al., 2011; Löfstrand et al., 2012). In this framework, availability is derived by integrating hardware reliability models with support system models (i.e. maintainability models).

2.2 Reliability Prediction Methods Reliability can generally be expressed as a measure of the frequency of hardware system or component failures i.e., the probability of a hardware system or component to perform its intended functions under stated conditions for a specified period of

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time. Hence, the mathematical expression for reliability, tetR , where is the

(constant) hazard or failure rate and t is the length of the period, which is assumed to start from time zero.

Reliability can be interpreted in several ways (Bergman et al., 2010; Andrews et al., 2002):

The idea that a hardware system or component is fit for a purpose with respect to time

The capacity of a hardware system or component to perform as designed The resistance to failure of a system or component The ability of a hardware system or component to perform a required

function under stated conditions for a specified period of time The probability that a functional unit will perform its required function for a

specified interval under stated conditions The ability of a hardware system or component to fail, without major

consequences

Reliability engineering relies on statistics, probability theory and reliability theory. In reliability engineering, different techniques, such as reliability prediction, Weibull analysis, thermal management, reliability testing and accelerated life testing are used. These techniques can be used in different phases in the product development process, depending on available information, reliability requirement, expenses, etc.

Availability is a measure of the probability that the repairable system or subsystem is operating at a specified time, i.e. the proportion of time a system is in a functioning condition. Availability is a ratio of the expected value of the uptime of a system divided by the sum of the expected values of up- and downtime, A=E[Uptime]/ (E[Uptime]+ E[Downtime]). Expected up- and downtime can also be expressed as, E[Uptime] = Mean Time Between Failure (MTBF) which is a measure of reliability and E[Downtime] = Mean Time To Repair (MTTR) which is a measure of maintainability.

Hence, availability is a function of reliability and maintainability. A framework has been derived for prediction of functional product availability to be used both during development and operation (Löfstrand et al., 2011; Löfstrand et al., 2012). In this framework, availability is derived by integrating hardware reliability models with support system models (i.e. maintainability models).

2.2.1 Variation Mode and Effect Analysis (VMEA) VMEA is a deductive method of managing effects of variations during product development. VMEA can be divided into three different levels:

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1. Basic VMEA, which is used in the early design stages, where information about the variation is vague, and the aim is to compare and evaluate different concepts.

2. Enhanced VMEA, which is used later in the design stages, where more information about the sources of variation is known.

3. Probabilistic VMEA is used in late design stages, where detailed and statistical information about sources of variation is available.

In VMEA, product characteristics that are of particular interest from a variation standpoint are selected and are usually referred to as Key Product Characteristics (KPCs). The KPC can be compared to the top event in a fault tree. Each KPC is decomposed into a number of sub-KPCs that are affected by variations, i.e. Noise Factors (NF). An Ishikawa cause-and-effect chart can be used to illustrate how NFs and sub-KPCs are related to the corresponding KPCs, see Figure 4.

Figure 4. Ishikawa cause and effect chart

Note that the logical interrelationships between the Sub-KPCs and the KPC (And gate, Or gate, Exclusive or gate, etc.) are excluded.

Basic VMEA and Enhanced VMEA (B/E VMEA) are based on subjective ratings, made on a 1-10 scale both for the sub-KPC and the NF. The result from the B/E VMEA is a Variation Risk Assessment and Prioritization (VRPN). VRPN for the j:th NF of the i:th sub-KPC (1) 222

ijijiNFijVRPN

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where 2i is the KPC sensitivity to the sub-KPC, 2

ij the sub-KPC sensitivity to

the NF and 2ij the NF variation size. Then, the VRPN for the i:th sub-KPC

(2)

These VRPNs can be used to derive which sources of variation are most important for the KPC studied.

Probabilistic VMEA (Prob. VMEA), on the other hand, is a method based on quantitative data from test results or other available measurements and allows a higher degree of objectivity. The probabilistic VMEA method aims at systematically assessing factors that affect KPCs, i.e. the response variable that is affected by the variation (Johansson et al., 2006; Chakhunashvili et al., 2004). Hence, according to (Bergman et al., 2009), the different types of VMEA can be used in diverse stages of the product development process, see Figure 5.

Figure 5. Usability of different VMEA method in diverse stages in the

product development process

Probabilistic VMEA is divided into four steps: causal breakdown of KPCs, sensitivity assessment, variation size assessment and variation risk assessment and prioritization.

Causal breakdown of KPCs

The first step in probabilistic VMEA concerns decomposition of KPCs into a number of affecting sub-KPCs. The characteristic of a sub-KPC derives from the product, parts of the product or the manufacturing process. The sub-KPCs’ characteristics are usually known, controllable and are affected by one or more NFs. There are two types of NFs: dissipation between manufactured products (unit-to-unit variation), and different behaviour between used products (in-use variation). The NFs that emerge from the second type can be divided into causes from external or internal sources. External sources are, for instance, operating or user variations, while internal

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sources are related to the product itself, e.g. wear and degradation. The KPC causal breakdown can be visualized in a cause-and-effect chart to clarify the contribution of variation, e.g. an Ishikawa diagram. The KPC is usually expressed analytically as a transfer function, KPCsubfY .

Sensitivity assessment

In the second step of probabilistic VMEA, sensitivity coefficients are determined. In order to enable relative measures of the NFs, the target function is derived as the

natural logarithm of the transfer function, i.e. ixgYQ ln where ix includes

all the NFs. Using natural logarithm is practical in engineering applications, where uncertainties often are judged in percentage of variation. The sensitivity coefficients

ixc for each variable ix that are influencing the target function (KPC) are

determined analytically by the partial derivative of the target function, i.e.

ix x

gci

. (3)

Variation size assessment

In the third step of probabilistic VMEA, the standard deviation ix for each variable

ix is derived. If the variable ix contains more than one NF, the standard deviation

can be determined by use of the Gauss approximation formula, which requires

expected values and variance for all included NFs. If the variable ix contains only

one NF, the logarithmical standard deviation (relative measure) can be derived directly. Note that if measured data are not available, a suitable distribution is assumed (when only min and max values are available, a uniform distribution is often a suitable first choice) to predict the standard deviation for that NF.

Variation Risk Assessment and Prioritization (VRPN)

In the fourth step of probabilistic VMEA, the variation contribution ix for each

variable ix and total variation contribution tot for the KPC are calculated to

determine the VRPN, which is a measure of the variation contribution. If insufficient measured data are available to accurately derive the standard deviations

ix a correction factor variable ixt is estimated by use of some suitable distribution

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(chi-square, t-distribution, etc.). The sensitivity coefficient ixc is derived from the

sensitivity assessment in probabilistic VMEA (step two), and the standard deviation

ix derives from the variation size assessment conducted in step three. Hence, for

each variable ix , the variation contribution

iiii xxxx tc (4)

and the total variation contribution

222 ...21 ixxxtot . (5)

The individual variation contributions for each variable and the total variation contribution are compiled.

Safety factor from VMEA

By use of probabilistic VMEA it is possible to derive a safety factor pSF as the ratio

between the low quantile of design parameters pD and the median of design

parameters 5.0D (Bergman et al. 2009), i.e. the selected KPC

5.0D

DSF p

p (6)

where p is the probability of failure. Eq. (6) can be rewritten so that

totp zDD

p eeSF 5.0lnln

(7)

where z is a random variable with a suitable distribution function according to the

chosen probability p, and tot is the total contribution of variation. Hence, when

probabilistic VMEA is used the reliability is prescribed and then a safety factor can be predicted. In design situations several parameters can be involved with different variations, meaning that the same safety factor can be obtained from many different sets of parameter data.

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2.2.2 Failure Mode and Effect Analysis (FMEA) In FMEA, information about the consequences and effects of the failures is usually collected through interviews with experienced people, from different divisions, with different knowledge, i.e. cross-functional groups (Holmberg et al., 1997; Britsman et al., 1993). FMEA is performed to identify causes of failures affecting the reliability of the product, i.e. the product’s function, failure, causes of failure and consequences of failure. FMEA is often conducted to clarify the correlation between causes of failure on component level and corresponding causes of failure on system level, and to obtain arrangement to avoid causes of failure or reduce the consequences of failure. The accuracy of the result is dependent on the amount of information and how detailed the information is.

Noise factors of parameters affect the reliability of the product (Hasenkamp et al., 2009). To enable identification of sources of noise and to be able to study the influence of noise factors, FMEA has been further developed into two major methods where causes of failure are replaced with noise factors. The first method is called Design Failure Mode and Effect Analysis (D-FMEA) and is used to analyse the failure mode for the design, while the second method is Process Failure Mode and Effect Analysis (P-FMEA).

One result from FMEA is a Risk Priority Number (RPN), which is based on subjective ratings, often on a 1-10 graded scale. The RPN is calculated as the product of the three criteria: potential causes Po , failure mode S and effect of failure Pd ,

i.e.

(8)

Note that the logical interrelationships are excluded.

2.2.3 Fault Tree Analysis (FTA) Fault tree analysis (FTA) is a deductive method, i.e. a general system state is postulated and decomposed into chains of more basic events (faults) of components (Fault Tree Handbook, U.S. Nuclear Regulatory Commission, 1981). The logical interrelationship of how such basic events depend on and affect each other, and thereby cause some system state to occur, is often described analytically in a reliability structure which can be visualized as a tree, see Figure 6. The reliability structure is composed by events interlinked with gates which enable the derivation of analytical mathematical expressions to evaluate the hardware system reliability. One basic assumption in FTA is that the component failures occur independently of each other (Bergman et al., 2010; Andrews et al., 2002).

PdSPoRPN

24

SystemFailure

Component 1Failure

Component 2Failure

Component 3Failure

Component 4Failure

Component 5Failure

Component 6Failure

Figure 6. FTA tree

For each failure mode, besides the reliability structure, the components failure rate are required (this assumes that the component has a constant failure rate and that failure times are given by the exponential distribution); these failure rates correspond to the useful life part of the bathtub curve, see Figure 7.

Figure 7. Bathtub curve

Time

Ageing failures

Increasing Failure Rate

Failure Rate

Initial failures Decreasing Failure Rate

Useful life

Low ”constant” Failure Rate

25

Hence, in order to retrieve the data necessary to conduct FTA, knowledge about existing failure modes and their causes is required. This might not be a problem when upgrading existing hardware systems. On the other hand, when developing completely new solutions, failure mode data and failure rates may not be available; therefore, in such situations estimations are often used. Even for existing hardware systems, all the required data are seldom available, in which case interviews must be conducted, which may require some time (and may also introduce a risk of retrieving incorrect data). For large hardware systems, since one fault tree is needed for each failure mode, it may be time consuming to derive the fault tree itself (since the reliability structure might be quite complex).

2.3 Deterministic simulations At early concept stages there is often a lack of component reliability information. Measured data or estimated data are often used as input to reliability prediction methods. When designing new hardware systems, such measurement data may not exist and therefore, prototypes often need to be manufactured. In such situations, deterministic simulations e.g. strength calculations, fluid dynamics, rigid body dynamics, etc., can be used to derive the needed input data and concepts can be evaluated by means of reliability in early stages of the product development process, i.e., before a physical prototype is manufactured.

2.3.1 Rigid Body Dynamics Rigid body dynamics is the study of motion of rigid bodies under the influence of forces. A rigid body is a system of particles whose distances from one another are fixed, i.e. non-deformable bodies (Inman, 2009). The general motion of a rigid body consists of a combination of translations (parallel motion in three directions) and rotations (circular motion in three directions).

The location of a mass point m can be specified relative to a fixed coordinate system by a position vector with Cartesian components (x,y,z) and the vector force which acts on the mass points has corresponding components (Fix,Fiy,Fiz). Newton's second law states that the rate of change of the linear momentum of a rigid body with constant mass m is equal to the sum of all acting external forces Fi i.e.,

(9)

where v is the rigid body velocity and a is the acceleration.

N

ii

N

ii

N

ii FmaF

tvmF

tmv

111

26

Example of a system with one degree of freedom (translation in x direction)

Where k is the spring constant and c is the damping acting on the body.

thus,

where is the body’s velocity.

According to Newton's second law, the equation of motion for the rigid body can be expressed,

(10)

More generally, eq. (10) can be expressed in matrix notation, i.e., . Simulations of the dynamic behaviour in a hardware system can be used to estimate load on components which then can be used to derive component failure rates, as input to reliability prediction methods e.g. FTA.

3 Research Methodology The research presented in this thesis followed a 5-step procedure: as-is study, to-be scenario development, Method development, Method verification and Method validation.

k c

x(t)

F(t)

m

m

tFkxxcxm

tF

xckxx

tFxkxcxM }{}{}{

27

3.1 As-Is study Initially, an as-is study was conducted to gain information about research development in the field as well as the industrial situation. A state-of-the-art analysis was therefore conducted, whereby existing research work regarding functional product development, simulation-driven design, reliability prediction, etc. was reviewed. In particular, the reliability prediction methods VMEA, FMEA and FTA, were evaluated in terms of requirements, limitations and possibilities in the context of product development (see paper B).

To get an overview of the as-is situation at the industrial partner company, information was collected through documentation, archival records and interviews with company staff regarding the following topics:

The company product development process

Existing durability calculations – which formulas and equations are used, developed in-house solutions

Reliability – what is the base for reliability prediction? Availability – what is the base for availability prediction? Rig tests – hardware system tested in controlled environment

Field tests – construction of vehicle testing in working environment Extended field tests – construction of vehicle tested by customer, additional

measurements are added to the vehicle

Component testing – single hardware or subsystem tested in controlled environment

Computer-based simulations – subsystem and complete vehicle, how can the result be used, particularly in the early phases?

Load/Strength model – in-house developed method for stress-strength calculation, and the beginning of a reliability prediction model

The Case Study Research Design and Methods approach (Yin 2009) was used to conduct the interviews and other methods, e.g. archival analyses to collect data. The Case Study Research Design and Methods approach is suitable for understanding a real-life phenomenon in depth. However, such understanding depends on the contextual conditions (Yin 2009), e.g. how the customer is using the vehicle and why the durability is different between vehicles from diverse area of use. The collected data were further reduced and analysed according to the methodology suggested by Miles and Huberman (1994), i.e. collected data were arranged in different arrays and categorized in matrix.

28

The as-is study was explanatory and descriptive. It was further carried out by means of qualitative methods, like interviews, and quantitative methods such as collection of information from databases.

3.2 To-Be scenario development In order to reveal critical research challenges a visionary to-be scenario was developed. This scenario includes a hypothesis based on deductive conclusions from the as-is study to derive a simulation-driven methodology for how to predict hardware reliability to be applied at early concept stages of the product development process where limited component reliability information exists.

Since the Faste Laboratory partner company is moving towards more flexible service contracts and increased range of soft offers, i.e. functional products, a to-be scenario in relation to the partner company exploitation plan was developed. In this to-be scenario mobility was used for the functional product business offer. Mobility was defined as the possibility to transport some amount of different material per time unit. In the scenario, the partner company owns the hardware and is responsible for delivering mobility at an agreed-upon availability. Hence, the partner company is responsible for all the service, software and hardware needed to provide the mobility with a certain agreed-upon availability.

In the scenario, a simulation-driven methodology, including both deterministic and probabilistic simulation models and methods which are used to converge at optimal solutions as rapidly as possible, has been developed. A model of the complete system exists which combines these methods and enables the partner company to develop mobility with known availability already at early functional product development stages.

3.3 Method development By analysing the gap between the as-is situation and the to-be scenario, it was found that certain methods, including simulation models and tools, needed to be developed. Hence, in this licentiate thesis work, two methods were developed for reliability prediction (as part of the FP availability prediction proposed by Löfstrand et al., 2011), including component variations when a limited amount information exists.

1st method development: Probabilistic VMEA is traditionally used to derive a safety factor for an assembled hardware system. However, traditional probabilistic VMEA could not be used to evaluate reliability. Hence, probabilistic VMEA was further developed to enable the possibility of predicting hardware system reliability while still including variations of relevant properties (see Paper A).

29

2nd method development: At early concept stages there is often a lack of component reliability information (failure rates). Hence, a method based on deterministic simulations, has been developed from which input data for reliability estimations can be derived (see Paper C).

3.4 Method verification Two case studies have been carried out to verify the hypothesis and the proposed methods (as part of the simulation-driven methodology). One case study concerned the developed method for reliability prediction by use of the probabilistic VMEA method (see Paper A) and the other case study concerned the method where deterministic simulations are used to conduct input data (failure rates) for FTA (see Paper C).

3.5 Method validation The methodology and methods need to be validated through tests on existing hardware systems. There are a number of validation strategies which can be deployed:

Rig tests o Fatigue and wear, if any errors occur, a new strength calculation

or component testing is performed o Development of new components o Confirmation

Machine tests o Confirmation for durability

Component testing Field tests

o Confirmation for durability o The Extended field test (customer)

Conformation for durability Note that validation is outside the scope of this licentiate thesis.

4 Reliability prediction when availability of input data is limited

The possibility of predicting reliability of hardware, both for components and systems, is important in engineering design. By predicting reliability it is possible to prevent failures, for instance, through planned maintenance. Today, it is acknowledged that many failures are caused by variations, e.g. strength, loads, manufacturing tolerances, etc., resulting in expensive reclamations and dissatisfaction that may lead to lost business. Industries are in need of design methodologies that can

30

be used to identify and manage different sources of variation when limited input data is available.

4.1 Benchmark and evaluation of reliability methods There are several methods for improving the prediction of reliability. Variation Mode and Effect Analysis is a relatively new such methodology. The objective of this research work was to show how Variation Mode and Effect Analysis differs from Fault Tree Analysis and Failure Mode and Effect Analysis in terms of requirements, limitations and possibilities in the context of product development.

In Table 1, different properties important for the product development have been compiled for each of the methods. The Data Collection Method concerns how the in-data are collected, whereas Usefulness Area shows how the results can be used. In the Level of Accuracy FTA is used as a reference level to which the other methods are compared. In the Product Development (PD) stage, suitable PD stages at which the methods may be applied are proposed. In Logical Connection, it is stated whether or not the method takes the logical connection between component and hardware system failure into account.

For completely new solutions to be developed, FMEA and basic and enhanced VMEA are suitable for early PD stages, due to the methods’ subjective ratings. Probabilistic VMEA is suitable after concept evaluation and FTA would be suitable in PD stages after concept selection. For upgrading development projects, both FTA and probabilistic VMEA can probably be used from the start of the PD process, since at least some of the needed data may be available (reliability structure from previous analyses, failure rates from field measurements, measured standard deviations, etc.). Based on this benchmark, probabilistic VMEA and FTA were the most suitable methods for reliability prediction, due to the objective ratings.

31

Table 1. Comparison between methods

FMEA FTA B/E VMEA

Prob. VMEA

Data Collection Method

- Interviews from cross-functional groups


- Reliability from assemblies modelled in CAD system

-Measurements from rig- and field tests (failure rates)



- Tolerances from drawings

- Measurements from rig- and field tests

(standard deviation)

Usefulness Area - Identify failure modes

- Identify causes and consequences of failures

-RPN

- Derive reliability of hardware system

- Identify causes and consequences of failures

- Identify, assess and manage unwanted variation

-VRPN

- Derive safety factor

- Identify, assess and manage variation contribution

-VRPN

Level of Accuracy

- Less than FTA

- Reference Level

- Less than FTA

- Same as FTA

Product Development Stage

- All PD stages

- After concept selection

- All PD stages

- After concept evaluation

Explicit Logical Interrelationship

- No - Yes - No - No

32

4.2 Reliability prediction strategy development The possibility of predicting reliability of hardware, both for components and systems, is important in engineering design, since many failures result in substantial impact on safety or functional requirements. However, there is a need for methodologies for reliability prediction where variations are considered, especially for use during evaluation of concepts in early product development stages. There is further a need for methods to create input data for reliability predictions such as FTA and probabilistic VMEA.

4.2.1 Reliability prediction based on probabilistic VMEA Probabilistic VMEA can be used to, with a prescribed reliability, derive safety factors in different applications (see section 2.2.1). However, there exist no reports on how to derive the reliability based on probabilistic VMEA. The objective of the presented research was therefore to show how to derive hardware system reliability based on probabilistic VMEA. In contradiction to previous research work where reliability is prescribed, the proposed method can be used to predict reliability. In design situations, several parameters can be involved with different variations, meaning that the same safety factor can be obtained from many different sets of parameter data. In this thesis a complementary method is proposed whereby the reliability is directly derived for a set of parameter data. For a known set of parameter data, the SF can be derived directly from the transfer function given in eq. (7), i.e.

(11)

With a known safety factor the random variable

(12)

The reliability can then be derived directly from the chosen distribution function i.e., = ( ). By this method, the safety factor is derived directly from the definition and then, given a set of parameter data, the reliability can be predicted by the normal distribution function.

case study

To verify this reliability prediction method and to show how different sources of variations affects the reliability, a case study of a wheel loader automatic transmission clutch shaft was conducted, see Figure 8.

LoadAppliedStrengthSF

tot

SFz ln

33

Figure 8. Automatic transmission clutch shaft

Torque transferred through the clutch is transmitted via multiple discs, where the limiting factor of the magnitude of the torque is friction at the discs. In this model the load is the transferred torque through the clutch shaft and the strength is the capacity of the included parts in the clutch. The clutch is applied by use of hydraulics and the return is achieved with mechanical pull-off springs in series. When the clutch is applied the springs will cause a counter force.

The case study was divided into five steps: causal breakdown of KPCs, sensitivity assessment, variation size assessment, variation risk assessment and prioritization (see section 2.2.1) and the proposed step Reliability prediction based on probabilistic VMEA.

In this case study the transferred torque, Y, was the main KPC. The first step regerded Causal breakdown of KPCs, to decompose the KPC into a number of affecting Sub-KPCs (Applied Load and Strength) and noise factors (NF) affecting the Sub-KPCs , see Table 2. By eq. (11) the KPC was further expressed analytically as a transfer function,

lossin

eff

TTNrkPA

KPCsubKPCsubfY 21, (13)

34

Table 2. KPC, sub-KPCs and NFs

Variable Unit Structure

Declaration of variables

Mean value

Standard deviation

Y [-] KPC Coefficient of ratio between load and strength

LoadApplied [-] Sub-

KPC Transferred torque

Strength

[-] Sub-KPC

Strength of the included components

[-] NF Coefficient of friction on the disc kit

0.11 0.00577

[m] NF Motion of piston 0.00417 0.00000005

inT [Nm] NF Torque in to clutch 2682 147.2

lossT [Nm] NF Loss of torque in clutch 100 5.78

effr [m] NF Effective radius of the discs in the kit in the plate clutch

0.088 0.00254

P [Pa] NF Hydraulic pressure in the cylinder

1659470 11493

A [m2] NF Nominal area on the top of the piston in the cylinder

0.02151 0.00000877

k [N/m] NF Coefficient of spring 116852 6746

N [-] NF Number of discs in the kit of the plate clutch

20 0

In the second step, Sensitivity assessment, each sensitivity coefficient was determined. In order to enable relative measures of the NFs, the target function was derived as the natural logarithm of the transfer function, i.e.

ixgYQ ln (14)

where ix includes all the NFs, see Table 3. The sensitivity coefficients ixc for each

variable ix influencing the target function were determined analytically by the partial

derivative of the target function, i.e. ix xgci

, see Table 3.

35

Table 3. Sensitivity coefficients

Sensitivity coefficient Value NF

1xc 1 )ln(1 kPAx

2xc 1 )ln(2x

3xc 1 )ln(3 effrx

4xc 1 )ln(4 Nx

5xc -1 )ln(5 lossin TTx

In the Variation size assessment step, for each of the variables 51 xx the standard

deviation ix was assessed by suitable methods. In this case study, available data

included: drawings with associated tolerances for components, measured data of actuating hydraulic pressure from rig test, measured data of output transmission torque from rig test, coefficient of friction, transmission ratio, and effective radius and losses.

In the Variation Risk Assessment and Prioritization (VRPN), eq. (4) and (5) was used to

derive the variation contribution ix for each variable ix and total variation

contribution tot for the KPC, see Table 4. The correction factor, ixt , was in this

case study 1 for each variable ix .

Table 4. Compilation of the variation contribution

Type of scatter and uncertainty

Scatter Uncertainty Total

Strength 0.0604 -

1x 0.0071

-2x 0.0526

-3x 0.0289

-4x 0

Applied Load 0.0047

-5x 0.0047

Total tot 0.0047 0.0604 0.0606

The variation contribution was summarized to a total variation contribution. The variation contribution for each of the included variables for the Strength and Applied

36

load separately is summarized (see the rightmost column in Table 3 and for each of the included variables for Scatter and Uncertainty is also summarized (see bottom row in Table 3). By this procedure, it was possible to discover the origin of the highest degree of variation contribution.

Combining eq. (11) and (13) together with the mean values given in Table 2, = 2.67. By this SF together with the total contribution of variation tot given in

Table 4, the random variable z from the normal distribution function can be derived, i.e.

21.16lnexp zSFzzSFtot

tot (15)

Reliability prediction based on probabilistic VMEA

With a known safety factor and random variable the reliability was derived directly from the normal distribution function, i.e.,

(16)

The reliability prediction, i.e. probability of failure for the automatic transmission clutch shaft, was derived to R=1.0, when evaluated with 300 digits.

In the clutch shaft case study the input torque inT was measured only for first gear in

forward direction, which is a simplification. In order to have a more accurate prediction of the reliability coupled to transferred torque, all gears (forward and reverse) should be included in the analysis. Another way of improving the accuracy is to use data from field tests rather than from rig tests whenever possible. The wear on the discs is not included in the model, which hence leads to a reliability prediction which is higher than the real hardware system reliability. Further, note that the stress-strength model used is time-independent; therefore, the reliability prediction can be seen as a snapshot in time.

4.2.2 Reliability prediction through combination of deterministic and probabilistic simulations

Existing reliability prediction methods require measured or estimated input data which can be difficult to retrieve. The objective is, therefore, to derive a simulation-driven method, including variation management, for how to combine deterministic simulations with Fault Tree Analysis, to predict hardware system reliability when measured data is not available.

duezfRz u

22

21

37

Simulation-driven method

The focus in this research is on how to derive the failure rates through simulations, given that the reliability structure is known. The accuracy of the input data to the FTA requires valid deterministic simulation models with low uncertainty in the preprocessing parameters and solving parameters. The proposed simulation-driven method was divided into five steps, see Figure 9.

Figure 9. Proposed simulation-driven method

Case study

The case study was conducted on a rotor bearing model, see Figure 10, and the corresponding fault tree consists of two failure modes both coupled to bearing failure, see Figure 11.

38

Figure 10. Rotor bearing model

Bearing clearance was the only parameter variation in this model and the clearance was generated randomly based on the normal distribution, see Table 5.

Table 5. Parameters of rotor system SHAFT ROTOR

Density (kg/m^3)

7800 Shaft position (m) Node 3

Young’s Modulus (GPa)

200 Mass (kg) 2000

Length (m) 1 Polar mass moment of inertia (kgm^2)

300

Radius (m) 0.1 Transversal mass moment of inertia (kgm^2)

600

PEDESTALS LOAD Shaft Position (m)

0 0.8

Rotor Unbalance (m) 1e-3

type Radial bearing with clearance

Gravity (m/s^2) 10

Isotropic Stiffness (N/m)

1e11

1e11

Spin Speed (Hz) 20

MVL Clear (m) 0.0001

STD Clear (m) 0.00001

39

In order to derive the failure rates for each of the bearings the bearing load for each set of parameters generated in the randomization step must be estimated. Therefore, rotor dynamical simulations for each set of parameters were conducted.

Figure 11. Fault tree of rotor system

When the load on the bearing was known, the durability value L10h for each failure mode and failure distribution L10m, see Figure 12, was derived (Harris and Kotzalas, 2007), i.e.

(15)

and

(16)

and = (17)

L10 represents the basic rating life (at 90% reliability) [millions of revolutions], L10h the basic rating life (at 90% reliability) [operating hours], C the basic dynamic load rating [kN], P the equivalent bearing load [kN], n the rotational speed/spin speed [r/min], p the exponent of the life equation, L10m the rating life (at 90% reliability) [millions of revolutions], L10mn the fraction rating lives (at 90% reliability under constant conditions) [millions of revolutions] and Un the lifecycle fraction under the condition (percentage of operation)

=

= 10 60

40

Figure 12. Failure distribution rear bearing

When the failure distribution is known the failure rate can be calculated

(Andrews et al., 2002), i.e.

(18)

(19)

(20)

where Nf is the cumulative failures, N is the total failures, t is operating hour, dt the histogram time block size, failure rate at the rear bearing and failure rate at the front bearing. The fault tree consists of two failure modes, see in Figure 11, the probability of failure (Andrews et al., 2002),

(21)

and, hence the reliability,

(22)

Eq. (22) gives the estimated hardware system reliability R(t) = e , which is valid until 12,000 operating hours. Deterministic simulations were used to derive failure rates as input data to fault tree analysis for reliability estimations. Since the proposed method only requires information regarding variation distributions and fault

= ( + ) ( )( )

bilit

( ) = 1 + 1 1 1

(2( ) = 1 Q(t) = + 1 + 1 1

0

5 10

41

mechanics, it is appropriate for use during evaluation of concepts in early product development stages when limited measured data are available.

5 Discussion and Conclusions This licentiate thesis comprises a survey of three publications. By comparing existing reliability prediction methods it can be stated that probabilistic VMEA and FTA are suitable for reliability prediction to be included in a SDD methodology. In contradiction to VMEA, FTA includes the logical relationship between component failure and hardware system failure (reliability structure). This reliability structure can be important to include when evaluating different hardware systems. Although reliability, through the developments presented in this thesis, can be predicted by use of probabilistic VMEA, it still suffers from limitations regarding the need for analytically expressed transfer functions. However, probabilistic VMEA takes relevant variations into account, which is important when designing robust hardware systems.

It can be concluded that deterministic simulations (such as rigid body dynamics) can be used to derive input data to be used for probabilistic reliability prediction methods such as FTA and probabilistic VMEA. Hence, by combining deterministic and probabilistic simulations, hardware system reliability can be predicted even when limited component reliability information exists. This hardware reliability prediction method is a critical part of a simulation-driven methodology to be used at early stages of functional product development processes.

6 Future Research The methods presented in this thesis need further development regarding challenges such as convergence, accuracy, simulation settings, etc. and they also need to be validated. When developing completely new hardware systems, the reliability structure may not exist. Hence, methods for how to derive the reliability structures from concept design protocols (e.g. solid models) must be developed.

In a future scenario the industrial company owns the equipment and is responsible for providing mobility. To reach that scenario, the proposed hardware reliability prediction method should be combined with support system reliability prediction methods in order to derive functional product availability.

42

7 Acknowledgements This work was conducted at the Faste Laboratory, Centre for Functional Product Innovation, a VINNOVA (Swedish Governmental Agency for Innovation Systems) Excellence Centre, based at Luleå University of Technology, Sweden.

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Karlberg, M., Löfstrand, M., Sandberg, S. and Lundin, M., State of the Art in Simulation Driven Design, International Journal of Product Development, 2012. Karlsson, L., Lindström, J. and Löfstrand, M., Functional Products – Goodbye to the industrial age, June 2012 in: Ericsson Business Review. 18, 2, s.21-24. 4 s. Lindström, J., Löfstrand, M., Karlberg, M. and Karlsson, L., A development process for Functional Products: hardware, software, service support system and management of operation. International Journal of Product Development, 2012. Lindström, J., Karlsson, L., Löfstrand, M. and Karlberg, M., Functional Product development: what information should be shared during the development process? International Journal of Product Development, 2012. Lockwood, A.J., Simulation-Driven Product Development: Will Form Finally Follow Function, 2009. Löfstrand, M., Reed, S., Karlberg, M., Andrews, J., Karlsson, L. and Dunnett, S., Modelling And simulation of functional product system availability and support costs. International Journal of Product Development, 2012. Löfstrand, M., Andrews, J., Karlberg, M. and Karlsson, L., Functional product system availability: simulation-driven design and operation through coupled multi-objective optimisation. International Journal of Product Development, 2011. Löfstrand, M. and Isaksson, O., A process modelling and simulation approach for business Decision support in pre-conceptual product design. International Journal of Product Development, 2010. Lönnqvist, Å., Including Noise Factors in Design Failure Mode and Effect Analysis (D- FMEA) -A Case Study at Volvo Car Corporation. Robust design methodology for reliability, ed. B. Bergman, et al.2009, West Sussex: Wiley. Miles, M.B. and Huberman, A.M., (1994) Qualitative Data Analysis: An Expanded Sourcebook, SAGE publications, second edition, ISBN 0-8039-5540-5 OĆonnor, P.D.T., D. Newton, and R. Bromley, Practical reliability Engineering 2002, West Sussex: Wiley. Olsson, F., Principkonstruktion, Institutionen för Maskinkonstruktion, LTH, Lund, 1978. Olsson, F., Primärkonstruktion, Institutionen för Maskinkonstruktion, LTH, Lund, 1985.

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Pahl, G. and Beitz, W., Engineering Design: A Systematic Approach, 2nd edition, Springer- Verlag, London, 1995. Persson, J.G., Balancing Structured Design Processes and Innovative New Product Development, Proc. 10thIAMOT Conference on Management of Technology, Lausanne, Switzerland, 2001. Pugh, S., Total Design: Integrated Methods for Successful Product Engineering, Addison- Wesley, Wokingham, 1990. Reed, S., Andrews, J., Dunnett, S., Karlberg, M., Karlsson, L. and Löfstrand, M., Modelling service support system reliability. in IFAC IMS’10 workshop. Lisbon, Portugal. 2010. Robust design methodology for reliability, ed. B. Bergman, 2009, West Sussex: Wiley. Roozenburg, N.F.M. and Eekels, J., Product Design: Fundamentals and Methods, John Wiley and sons, Chichester, 1995. Schneeweiss, W.G., Petri Nets for reliability Modeling1999, Hagen: LiLoLe-Verlag Gmbh. Ullman, D.G., The Mechanical Design Process, McGraw-Hill, New York, 1992. Ulrich, K.T. and Eppinger, S.D.,Product Design and Development, McGraw-Hill, Singapore, 2004. Walha, L., Driss, Y., Khabou, M.T., Fakhfakh, T. and Haddar, M., Effects of eccentricity defect on the nonlinear dynamic behavior of the mechanism clutch-helical two stage gear, Mechanism and machine theory 46 (2011), no. 7, 986-997. Weibull, W., Fatigue testing and the analysis of results, Pergamon Press, New York, 1961. Wheelwright, C. and Clark, K., Revolutionising Product Development – Quantum Leaps in Speed, Efficiency and Quality, the Free Press, New York, USA, 1992. Yin, R.K., Case Study Research – Design and Methods, fourth edition, SAGE Publications, USA, 2009. Özguven, N.H. and Houser, D. R., (1988) Mathematical models used in gear dynamics – a review. Journal of Sound and Vibration, 121(3), pp 383-411.

46

47

Appended Papers

Reliability Prediction Based on Variation Modeand Effect AnalysisJonas Pavasson,a*† Kent Cronholm,b Henrik Strandc and Magnus Karlberga

The possibility of predicting the reliability of hardware for both components and systems is important in engineering design.Today, there are several methods for predicting the reliability of hardware systems and for identifying the causes of failureand failure modes, for example, fault tree analysis and failure mode and effect analysis.

Many failures are caused by variations resulting in a substantial effect on safety or functional requirements. To identify, toassess and to manage unwanted sources of variation, a method called probabilistic variation mode and effect analysis(VMEA) has been developed. With a prescribed reliability, VMEA can be used to derive safety factors in different applications.However, there are few reports on how to derive the reliability based on probabilistic VMEA, especially for transmissionclutch shafts.

Hence, the objective of this article was to show how to derive system reliability based on probabilistic VMEA. In particular,wheel loader automatic transmission clutch shaft reliability is investigated to show how different sources of variationaffect reliability.

In this article, a new method for predicting system reliability based on probabilistic VMEA is proposed. The method isfurther verified by a case study on a clutch shaft. It is shown that the reliability of the clutch shaft was close to 1.0 and thatthe most significant variation contribution was due to mean radius of the friction surface and friction of the disc. Copyright ©2012 John Wiley & Sons, Ltd.

Keywords: VMEA; reliability engineering; clutch shaft; engineering design

1. Introduction

The possibility of predicting the reliability of hardware for both components and systems is important inengineering design. Enabling the prediction of reliability makes it possible to prevent failures, for instance, throughplanned maintenance.

Today, there are several methods for predicting system reliability, which consists of several components. One commonly usedmethod for predicting the reliability of complex hardware systems is the fault tree analysis.1,2 Support systems can be modelledby Petri Nets,3 which include the logical correlation between components and systems, and have a top–down approach4 or astate–space analysis (Markov analysis).5

The failure mode and effect analysis (FMEA) is a commonly used method in the automotive industry.6 FMEA is categorised as abottom–up approach to identify the causes of failure and failure modes. In FMEA, information about the consequences and effectsof the failures is usually collected through interviews with experienced people, from different divisions, with different knowledge, thatis, cross-functional groups.7

Noise factors of parameters affect the reliability of the product.8 To enable the identification of sources of noise and to be able tostudy the influence of noise factors, FMEA has been further developed into two major methods where the causes of failure arereplaced with noise factors. The first method, called design FMEA, is used to analyse the failure mode for the design. The secondmethod, called process FMEA, is used to analyse the failure mode for a process.6,9

Today, it is realised that many failures are caused by variations (strength, loads, manufacturing tolerances, etc.), resulting in expensivereclamations and dissatisfaction that may lead to lost business. Industries are in need of robust design methods that can be used toidentify and manage different sources of variation.10,11 Therefore, a quite new method called variation mode and effect analysis (VMEA),which is a top–down method of identifying and managing sources of variation, has been developed.12,13 The VMEA method can be

aDivision of Product and Production Development, Computer Aided Design, Luleå University of Technology, Luleå, SwedenbVehicle Dynamics Department, Royal Institute of Technology, Stockholm, SwedencVolvo Construction Equipment, Eskilstuna, Sweden*Correspondence to: Jonas Pavasson, Division of Product and Production Development, Computer Aided Design, Luleå University of Technology, Luleå, Sweden.†E-mail: [email protected]

Copyright © 2012 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2012

Research Article

(wileyonlinelibrary.com) DOI: 10.1002/qre.1420 Published online in Wiley Online Library

used to systematically identify, assess and manage variations, which in this method is expressed by noise factors (NF),11 affecting thekey product characteristics (KPCs) early in the product development process. One important benefit of using VMEA is to managevariations that significantly contribute to the variability of the KPCs to increase the reliability of the design.13 VMEA has beendecomposed into three different types: basic VMEA, enhanced VMEA and probabilistic VMEA.11,14 In 2009, Chakhunashvili et al.14

concluded that each of these types of VMEA is suitable in the different stages of the product development process, dependingon available information. In 2011, Pavasson and Karlberg15 compared VMEA with the fault tree analysis and FMEA by the use-fulness in product development.

By using the VMEA method, it is possible to derive safety factors and predict useful life for different applications, with aprescribed reliability.16,17 To use reliability as an evaluation parameter during product development, it should be possible toinstead predict reliability. However, there are few reports on how to derive reliability based on VMEA, especially for transmissionclutch shafts.

Hence, the objective of this article was to show how to derive system reliability based on probabilistic VMEA. In particular, wheelloader automatic transmission clutch shaft reliability is investigated to show how different sources of variation affect reliability.

VMEA can be used when the transfer function, that is, the relationship between the KPCs and the factors affecting them, isunknown or when the analytical expression of the transfer function is known. The result of the VMEA can then serve as a basis fordesigning components for improved reliability.

2. The VMEA method

Unwanted variation is a severe problem in the industry where the variation might have a substantial effect on safety, compliance withgovernmental regulations, final cost or functional requirements, and so on.12,13 A common approach to illustrate the input variables,the factors that affect the input variables and the response variable is to use a P-chart18 (see Figure 1).

The P-chart shown in Figure 1 illustrates the relationship between the input variable signal factors and the output variableresponse. This relationship is disturbed by several NFs from different sources of variation. Control factors are used to mitigate theeffects of the NFs, that is, to make the response as close as possible to the signal factors.

In the early stages of product development, before conducting a VMEA, information about customer needs is required. Thecustomer needs are usually expressed in subjective terms and are thereby not suitable for the VMEA method.13 However, customerneeds can be translated into correlated product characteristics (PCs). Quality function deployment19 is commonly used to translateneeds into PCs (see Figure 2). Then, PCs that are of particular interest from a variation standpoint are selected. These are called KPCs.Each KPC is usually decomposed into several sub-KPCs that are affected by variations, that is, NFs. One way of illustrating how NFs andsub-KPCs are related to the corresponding KPC is to use an Ishikawa cause-and-effect chart (see Figure 3).

The cause-and-effect chart shown in Figure 3 is a two-level version including the KPC, the affecting sub-KPC and the NFs. All theabovementioned methods are commonly used in preface to VMEA and are usually conducted in cross-functional teams.

Figure 1. P-chart

Figure 2. Translation into objective PC

J. PAVASSON ET AL.


2.1. Description of VMEA

VMEA can be divided into three different types:14,17

1. Basic VMEA, which is used in the early design stages where the information about the variation is vague and the aim is tocompare and evaluate different concepts.

2. Enhanced VMEA, which is used later in the design stages where more information about the sources of variation is known.3. Probabilistic VMEA, which is used in late design stages where detailed and statistical information about sources of variation

is available.

Basic VMEA and enhanced VMEA are based on subjective ratings, made on a 1 to 10 scale similar to the FMEAmethod. Probabilistic VMEA,on the other hand, is amethod based on quantitative data from test results or other availablemeasurements, allowing greater objectivity. Theprobabilistic VMEAmethod aims to systematically assess factors that affect KPCs, that is, the response variable that is affected by the variation.

The working process of the probabilistic VMEA (which is used in the work reported in this article) consists of four steps: causalbreakdown of KPCs, sensitivity assessment, variation size assessment and variation risk assessment and prioritisation (VRPN).14

2.1.1. Causal breakdown of KPCs. The first step in probabilistic VMEA concerns the decomposition of KPCs into several affectingsub-KPCs. The characteristic of a sub-KPC derives from the product, the parts of the product or the manufacturing process. Thecharacteristics of sub-KPCs are usually known, controllable and affected by one or more NFs. There are two types of NFs: dissipationbetween manufactured products (unit-to-unit variation) and different behaviour between used products (in-use variation). The NFsthat emerge from the second type can be divided into causes from external or internal sources. External sources are, for instance,operating or user variations, whereas internal sources are related to the product itself, for example, wear and degradation. TheKPC causal breakdown can be visualised in a cause-and-effect chart to clarify the contribution of variation. The KPC is usuallyexpressed analytically as a transfer function, Y= f(sub-KPC).

2.1.2. Sensitivity assessment. In the second step of probabilistic VMEA, sensitivity coefficients are determined. To enable relativemeasures of the NFs, the target function is derived as the natural logarithm of the transfer function, that is, Q= ln(Y) = g(xi), wherexi includes all the NFs. Using natural logarithm is practical in engineering applications, where uncertainties often are judged inpercentage of variation. The sensitivity coefficients cxi for each variable xi that are influencing the target function (KPC) are determinedanalytically by the partial derivative of the target function, that is,

cxi ¼@g

@xi(1)

2.1.3. Variation size assessment. In the third step of probabilistic VMEA, the standard deviation sx i for each variable xi is derived. If thevariable xi contains more than one NF, the standard deviation can be determined using the Gauss approximation formula, which requiresexpected values and variance for all included NFs. If the variable xi contains only one NF, the logarithmical standard deviation (relativemeasure) can be derived directly. Note that if the measured data are not available, a suitable distribution is assumed (when only minand max values are available, a uniform distribution is often a suitable first choice) to predict the standard deviation for that NF.

2.1.4. Variation risk assessment and prioritisation. In the fourth step of probabilistic VMEA, the variation contribution txi for eachvariable xi and the total variation contribution ttot for the KPC are calculated to determine the VRPN. If not enough measured data

Figure 3. Ishikawa cause-and-effect chart

J. PAVASSON ET AL.


are available to accurately derive the standard deviation sx i , a correction factor variable txi is estimated using some suitabledistribution (chi-square, t-distribution, etc.).

The sensitivity coefficient cxi is derived from the sensitivity assessment in probabilistic VMEA (step two), and the standard deviationsxi derives from the variation size assessment conducted in step three. Hence, for each variable xi, the variation contribution is

tx i ¼ cx ij jtx i :sx i (2)

and the total variation contribution is

ttot ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit2x1 þ t2x2 þ . . .þ t2xi

q(3)

The individual variation contributions for each variable and the total variation contribution are compiled.

3. Reliability prediction based on probabilistic VMEA

By using probabilistic VMEA, it is possible to derive a safety factor SFp as the ratio between the low quantile of design parameters Dp

and the median of design parameters D0.5,17 that is, the selected KPC

SFp ¼ Dp

D0:5(4)

where p is the probability of failure. Equation (4) can be rewritten so that

SFp ¼ e lnDp� lnD0:5ð Þ ¼ e z�ttotð Þ (5)

and then

SFp ¼ ez�ttot (6)

where z is a random variable with a suitable distribution function according to the determined probability p and ttot is the totalcontribution of variation. Hence, when probabilistic VMEA is used, the reliability is prescribed and then a safety factor can be predicted.In design situations, several parameters can be involved with different variations, meaning that the same safety factor can beobtained from many different sets of parameter data.

In this article, a complementary method is proposed where the reliability is directly derived for a set of parameter data. For aknown set of parameter data, the SF can be derived directly from the transfer function, that is,

SF ¼ Strength

Applied load(7)

With a known safety factor, the random variable

z ¼ ln SFð Þttot

(8)

With a known z, the reliability is derived directly from the chosen distribution function. As an example, for a normal distribution(often used as an approximation)

R ¼ f zð Þ ¼Z z

�1

1ffiffiffiffiffiffi2p

p e�u2=2 du: (9)

4. Verifying case study

To verify the reliability method described in Section 3 and to show how different sources of variation affect the reliability, a case studyof a wheel loader automatic transmission clutch shaft has been used.

Torque transferred through the clutch is transmitted via multiple discs, where the limiting factor of the magnitude of the torque isfriction at the discs. In this model, the load is the transferred torque through the clutch shaft and the strength is the capacity ofthe included parts in the clutch. The system used in this study is a lubricated disc clutch (see Figure 4). The clutch is applied usinghydraulics, and the return is achieved with mechanical pull-off springs in series. When the clutch is applied, the springs will causea counter force.

The clutch shaft is analysed following the probabilistic VMEA method described in Section 2.1, combined with the proposedreliability prediction method described in Section 3.

J. PAVASSON ET AL.


4.1. Causal breakdown of KPCs

For this case study, the ratio between applied load (transferred torque) and strength of the included components in the clutch shaft ischosen as KPC. Hence, the transfer function

Y ¼ Strength

Applied load(10)

This KPC can further be decomposed into the two sub-KPCs applied load and strength, each one affected by NFs according to thecause-and-effect chart shown in Figure 5.

Figure 4. Sketch over the clutch

Figure 5. Cause-and-effect chart of KPC, sub-KPCs and NFs

J. PAVASSON ET AL.


The KPC, the sub-KPCs and the NFs with mean values and standard deviations are further listed in Table I. Here, m, Tin, Tloss, P and kare derived from empirical data, whereas d, reff, A and N are derived from drawings.

For the clutch shaft, the relationship between the sub-KPCs and the parameters affecting them is given by mathematical models.Maximal torque Tf that can be transferred through a friction clutch with N surfaces is given by

Tf ¼ reff �m�FN�N (11)

where reff is the mean radius of the friction surface, m is the friction coefficient and FN is the actuation force (normal force).Mean radius (effective radius) is calculated using the following equation:

reff ¼ R1 þ R2

2(12)

R1 and R2 are shown in Figure 6.As mentioned earlier, the clutch used in this study is actuated using hydraulics and return is achieved by mechanical springs.

Normal force is then calculated according to

FN ¼ Fpressure � Fspring (13)

where Fpressure and Fspring are presented as follows:

Fpressure ¼ P�A (14)

Fspring ¼ k�d (15)

Combining Equations (13)–(15) into Equation (11) gives the first sub-KPC

Table I. KPC, sub-KPCs and NFs

Variable Unit Structure Declaration of variables Mean SD

Y – KPC Coefficient of ratio between load and strengthApplied Load – Sub-KPC Transferred torqueStrength – Sub-KPC Strength of the included componentsm – NF Coefficient of friction on the disc kit 0.11 0.00577d m NF Motion of piston 0.00417 0.00000005Tin Nm NF Torque into clutch 2682 147.2Tloss Nm NF Loss of torque in clutch 100 5.78reff m NF Effective radius of the discs in the kit in the plate clutch 0.088 0.00254P Pa NF Hydraulic pressure in the cylinder 1659470 11493A m2 NF Nominal area on the top of the piston in the cylinder 0.02151 0.00000877k N/m NF Spring stiffness 116852 6746N – NF Number of discs in the kit of the plate clutch 20 0

Figure 6. Effective radius of the disc

J. PAVASSON ET AL.


Strength ¼ sub-KPC1 ¼ P�A� k�dð Þm�reff �N (16)

which is the maximum torque that can be transmitted through the clutch. The second sub-KPC in this model is the applied load,that is,

Applied load ¼ sub-KPC2 ¼ Tin � Tloss (17)

where Tin is the input torque and Tloss is the torque losses in the clutch.Combining Equations (16) and (17) into Eq. (10) gives the transfer function

Y ¼ f sub-KPC1; sub-KPC2ð Þ ¼ P�A� k�dð Þm�reff �NTin � Tloss

(18)

4.2. Sensitivity assessment

Let Equation (18) undergo the logarithmic transformation, which hence gives the target function

ln Yð Þ ¼ lnP�A� k�dð Þ m�reff �N

Tin � Tloss

� �(19)

which leads to

ln Yð Þ ¼ ln PA� kdð Þ þ lnmþ lnreff þ ln Nð Þ � ln Tin � Tlossð ÞThe target function, with NFs embedded in variables x1� x5, is as follows:

Q ¼ ln Yð Þ ¼ g x1; x2; x3; x4; x5ð Þ ¼ x1 þ x2 þ x3 þ x4 � x5 (20)

where

x1 ¼ ln P�A� k�dð Þ (21)

x2 ¼ ln mð Þ (22)

x3 ¼ ln reffð Þ (23)

x4 ¼ ln Nð Þ (24)

x5 ¼ ln Tin � Tlossð Þ (25)

The sensitivity coefficients cxi are given by the partial derivative of the target function Q with respect to each of variables x1� x5given in Equation (20), that is, cxi ¼ @g=@xi . The sensitivity coefficients are shown in Table II.

4.3. Variation size assessment

For each of variables x1� x5, the standard deviation sx i has to be assessed. In this case study, available data included the following:

• Drawings with associated tolerances for including components.• Measured data of actuating hydraulic pressure from rig test.• Measured data of output transmission torque from rig test.• Coefficient of friction, transmission ratio, effective radius and losses.

Table II. Sensitivity coefficients

Sensitivity coefficient Value

cx1 1cx2 1cx3 1cx4 1cx5 �1

J. PAVASSON ET AL.


Variables x1 and x5 are influenced by more than one NF. Therefore, the standard deviation is derived by the use of the Gaussapproximation formula,20 which requires expected valuesmj

�and corresponding variance Varbmjc, that is, the squared standard devia-

tion s2mj, where subscripts m1 = P, m2 = A, m3 = k, m4 = d, m5 = Tin and m6 = Tloss. In this case study, mean values,mj

�, are known, which is

therefore used instead of expected values.For the variable x1, Equation (21) together with data given in Table I gives

�x1 � ln �P��A� �k��d� � ¼ 10:47 (26)

and the Gauss approximation formula with independent variables gives that

Var x1½ � ¼ Var ln PA� kdð Þ½ � �X4

j¼1

V mj

� � @x1@m�j

� �2

¼ Var Pð Þ�A

�P��A� �k��d� �2

þ

Var Að Þ�P

�P�A� �k�d

� �2

þ Var kð Þ ��d�P�A� �k�d

� �2

þ Var dð Þ ��k�P�A� �k�d

� �2

¼ 0:0000501

(27)

Equations (26) and (27) give the standard deviation

sx1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVar x1½ � ¼

p0:00708 (28)

For the variable x5, Equation (25) together with data given in Table I gives

�x5 � ln �T in � �T lossð Þ ¼ 7:856 (29)

and the Gauss approximation formula with independent variables gives that

Var x5½ � ¼ Var ln Tin � Tlossð Þ½ � �X6

j¼5

V mj

� � @x5@m�j

� �2

¼ Var Tinð Þ 1�T in � �T loss

� �2

þVar Tlossð Þ �1�T in � �T loss

� �2

¼ 0:0000221

(30)

Equations (29) and (30) give the standard deviation

sx5 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVar x5½ � ¼

p0:00470 (31)

Variables x2, x3 and x4 consist of only one NF; hence, the Gaussian approximation is not needed. In this case, min and max valuesare based on empirical data and drawings used; hence, the logarithmic standard deviation sxi was predicted by assuming a uniformdistribution, that is,

sx2 ¼ln mmaxð Þ � ln mminð Þffiffiffiffiffi

12p ¼ 0:0526 (32)

sx3 ¼ln reffmaxð Þ � ln reffminð Þffiffiffiffiffi

12p ¼ 0:02889 (33)

sx4 ¼ln Nmaxð Þ � ln Nminð Þffiffiffiffiffi

12p ¼ 0 (34)

Note that when large amounts of empirical tolerance data exist, the probability for those parameters to exceed the tolerance rangeis low. However, when tolerances are based on drawing values, the probability for those parameters to exceed the range is uncertain.

4.4. Variation risk assessment and prioritisation

When measured data are used, the tabular value from the statistical t-distribution that derives from the 97.5% t-quantile (t0.025) isoften a suitable choice. The insecurity from the ta-factor estimation is compensated by reducing the number of input sources, thatis, degrees of freedom, v, by one unit.

tx i ¼ta v � 1ð Þta 1ð Þ (35)

where t0.025(1) = 1.96 when the number of degrees of freedom is greater than 120.Hence, in the case of a large number of input sources, the correction factor variable txi gets close to 1.In this case study, a large number of input sources where used to assess the VRPN number for variable xi, that is, the t-correction

factor txi=1. The sensitivity coefficients cxi given in Table II and the standard deviation sxi by combining Equations (28), (31)–(34) intoEquation (2) give the variation contribution tx1 � tx5. Using the variation contribution tx1 � tx5 as input to Equation (3) further gives the

J. PAVASSON ET AL.


total variation ttot. The individual variation contributions (in this case, the same as the standard deviation) and the total variationcontribution are given in Table III.

In this work, the variation in the transferred torque (applied load) is denoted scatter. Uncertainties from tolerances in the drawingsare denoted uncertainties, that is, the variation of the included components in the strength variable. The variation contribution issummarised to a total variation contribution. The variation contribution for each of the included variables for the strength and appliedload separately is summarised according to Equation (3) (see the rightmost column in Table III). The variation contribution for each ofthe included variables for scatter and uncertainty is also summarised according to Equation (3) (see bottom row in Table III). The sumof the strength and the applied load variations will be equal to the sum of the scatter and the uncertainty variations, which is also thetotal variation of the system. By this procedure, it is possible to discover the origin of the highest degree of variation contribution.

4.5. Reliability prediction based on probabilistic VMEA

Equation (18) together with the data of the mean value given in Table I gives

SF ¼ Strength

Applied load¼ P�A� k�dð Þm�reff�N

Tin � Tloss¼ 2:67 (36)

Equation (8) together with the total contribution of variation ttot given in Table III gives

SF ¼ exp z�ttotð Þ⇒z ¼ ln SFð Þttot

⇒z ¼ 16:21 (37)

Combining Equation (37) into Equation (9) (the normal distribution) gives R= 1.0 for the clutch shaft when evaluated with 300digits, that is, a probability of failure.

5. Conclusion

In this article, a method for predicting reliability based on probabilistic VMEA has been proposed. In contradiction to previousresearch work where reliability is prescribed, the proposed method can be used to predict reliability. By this method, the safety factoris derived directly from the definition, and then given a set of parameter data, the reliability can be predicted by the normaldistribution function. To verify this method, a case study of a wheel loader automatic transmission clutch shaft was conducted. Itwas shown that variables x2 (friction of the disc) and x3 (mean radius of the friction surface) give the largest contribution to variationsof the reliability. It was further shown that the reliability of the specific case is close to 1.0.

Some of the standard deviations were derived using data from drawings together with a uniform distribution. Hence, whenmeasured data are available, the accuracy of the derived standard deviations may be improved.

In the clutch shaft case study, the input torque Tin wasmeasured only for first gear in forward direction, which is a simplification. To have amore accurate prediction of the reliability coupled to transferred torque, all gears (forward and backward direction) should be included in theanalysis. Another way of improving the accuracy is to use data from field tests rather than from rig tests whenever possible. The wear of thediscs is not included in the model, which hence leads to a reliability prediction, which is higher than the real system reliability. Further, notethat the stress–strength model used is time independent, and hence the reliability prediction can be seen as a snapshot in time.

From an engineering perspective, the upgraded probabilistic VMEA presented in this article can be used to identify, to assess andto manage different variations to increase the system reliability. This can be used not only for existing products but also for productdevelopment situations. Deriving system reliability for completely new solutions with probabilistic VMEA requires information aboutcomponents included and standard deviations of properties. Hence, for completely new solutions (where little preexisting data areavailable), probabilistic VMEA is suitable in the later part of the product development process. On the other hand, for upgrading

Table III. Compilation of the variation contribution

Type of scatter and uncertainty Scatter Uncertainty Total

Strength 0.0604tx1 0.0071tx2 0.0526tx3 0.0289tx4 0

Applied load 0.0047tx5 0.0047

Totalttot 0.0047 0.0604 0.0606

J. PAVASSON ET AL.


existing systems, probabilistic VMEA can probably be used from the start of the product development process because at least someof the needed data may be available (reliability structure from previous analyses, failure rates from field measurements, measuredstandard deviations, etc.).

Acknowledgements

This work was conducted at the Faste Laboratory, Centre for Functional Product Innovation, a VINNOVA (Swedish GovernmentalAgency for Innovation Systems) Excellence Centre, based at Luleå University of Technology, Sweden.

The authors would further like to acknowledge Volvo Construction Equipment in Eskilstuna for their collaboration and support andfor providing data for the case study.

References1. Bergman B, Klefsjö B. Quality from Customer Needs to Customer Satisfaction. Studentlitteratur: AB, 2010.2. Andrews JD, Moss TR. Reliability and Risk Assessment. Professional Engineering Publishing: London, 2002.3. Reed S, Andrews J, Dunnett S, Karlberg M, Karlsson L, Löfstrand M. Modelling service support system reliability, IFAC IMS’10 workshop, 2010, p.^pp.4. Schneeweiss WG. Petri Nets for Reliability Modeling. LiLoLe-Verlag Gmbh: Hagen, 1999.5. OĆonnor PDT, Newton D, Bromley R. Practical Reliability Engineering. Wiley: West Sussex, 2002.6. Lönnqvist Å. Including noise factors in design failure mode and effect analysis (D-FMEA) - a case study at volvo car corporation. In Robust Design

Methodology for Reliability, Bergman B et al. (ed.). Wiley: West Sussex, 2009.7. Holmberg G, Lönnkvist Å. Säkra Produkter. Industrilitteratur AB: Stockholm, 1997.8. Hasenkamp T, Arvidsson M, Gremyr I. A review of practices for robust design methodology. Journal of Engineering Design 2009; 20(6):645–657.9. Britsman C, Lönnqvist Å, Ottosson SO. Handbok I Fmea, Failure Mode and Effect Analysis. Industrilitteratur: Stockholm, 1993.

10. Arvidsson M, Gremyr I, Johansson P. Use and knowledge of robust design methodology: A survey of swedish industry. Journal of Engineering Design2003; 14(2):129–143.

11. Johansson P, Chakhunashvili A, Barone S, Bergman B. Variation mode and effect analysis: A practical tool for quality improvement. Quality andReliability Engineering International 2006; 22(8):865–876.

12. Robust Design Methodology for Reliability, Bergman B et al. (ed.). Wiley: West Sussex, 2009.13. Chakhunashvili A, Johansson PM, Bergman BLS. Variation mode and effect analysis. Proceedings of the Annual Reliability and Maintainability

Symposium 2004; 364–369.14. Chakhunashvili A, et al. Robust product development using variationmode and effect analysis. Robust DesignMethodology for Reliability, Bergman B et al.

(ed.). Wiley: West Sussex, 2009.15. Pavasson J, Karlberg M. Variation mode and effect analysis compared to FTA and FMEA in product development. 19th AR2TS Advances in Risk and

Reliability Technology Symposium, 2011, pp. 252–260.16. Svensson T, De Maré J, Johannesson P. Predictive safety index for variable amplitude fatigue life. Robust Design Methodology for Reliability,

Bergman B et al. (ed.). Wiley: West Sussex, 2009.17. Johannesson P, Svensson T, Samuelsson L, Bergman B, Maré JD. Variation mode and effect analysis: An application to fatigue life prediction. Quality

and Reliability Engineering International 2009; 25(2):167–179.18. Phadke MS. Quality Engineering Using Robust Design. Prentice Hall: New York, 1989.19. Griffin A, Hauser JR. The voice of the customer. Marketing Science 1993; 12:1–27.20. Hald A. Statistical Theory with Engineering Applications. John Wiley & Sons, Inc: New York, 1952.

Authors' biographies

Jonas Pavasson is a PhD student at the Division of Product and Production Development, Computer Aided Design at Luleå University ofTechnology, Sweden. His research interests include simulation-driven design, that is, how to use simulations as a driver rather than as averifier, and reliability engineering.

Kent Cronholm is a PhD student at the Vehicle Dynamics Department at KTH, Royal Institute of Technology, Stockholm. His researchinterests include load data acquisition and evaluation.

Henrik Strand has been working since 1998 at Volvo Construction Equipment with bearing-related issues. He had his PhD from KTHin 2005. The title of his dissertation thesis was ‘Design, Testing and Analysis of Journal Bearings for Construction Equipment’.

Magnus Karlberg is an associate professor in Computer-Aided Design at Luleå University of Technology and was born in 1976.Karlbergs research interests include simulation-driven design, that is, how to use simulations as a driver rather than as a verifier,rotordynamics, nonlinear dynamics such as impact systems and reliability engineering. As an example, Karlbergs research has beenapplied in the product development process of fibre refiners, which is a machine that grind wood chips into slender fibres to beused for example in panel board production.

J. PAVASSON ET AL.


Variation Mode and Effect Analysis compared to FTA and FMEA in Product Development

Jonas Pavasson, Magnus Karlberg Division of Computer Aided Design, Luleå University of Technology, Sweden

Universitetsområdet, Porsön, SE-97187, Luleå, Sweden

AbstractThe possibility of predicting reliability of hardware, both for components and systems, is important in engineering design. By predicting reliability it is possible to prevent failures, for instance, through planned maintenance. There are several methods for improving the prediction of reliability. Variation Mode and Effect Analysis is a relatively new such methodology. The objective of this paper is to show how Variation Mode and Effect Analysis differs from Fault Tree Analysis and Failure Mode and Effect Analysis in terms of requirements, limitations and possibilities in the context of product development. Comparison of these methods has shown that they are useful in different stages of the product development process. Further, depending on the type of development project, e.g. whether it be a completely new solution or an upgrade, different methods are suitable.

1. IntroductionThe possibility of predicting reliability of hardware, both for components and systems, is important in engineering design. Prediction of reliability enables prevention of failures, for instance, through planned maintenance. The reliability of individual components is superior to the corresponding system reliability [1]. 1961, Weibull [2] formulated a distribution (the Weibull distribution) which is one of the most commonly used formulas for describing important probabilistic measures in reliability theory e.g., times to failures, extreme values, service life and requirements allocation. Today, there are several methods for predicting system reliability that consist of several components. One commonly used method for predicting reliability of complex hardware systems is Fault Tree Analysis (FTA) [3, 4]. Support systems can be modelled by Petri Nets [5], i a deductive method (top-down approach) which includes the logical correlation between the components and system [6], or state-space analysis (Markov analysis) [7]. Failure Mode and Effect Analysis (FMEA) is a commonly used method which is used extensively in the automotive industry [8]. FMEA is an inductive method (bottom-up approach) to identify causes of failure and failure modes. Today, many failures are caused by variations [9] (strength, loads, manufacturing tolerances, etc.), resulting in expensive reclamations and dissatisfaction that may lead to loss of customers [10]. Therefore, a method called Variation Mode and Effect Analysis (VMEA), which is a deductive method of identifying and managing sources of variation, has been developed [11]. The VMEA method has been decomposed into three different levels [12]: Basic VMEA, Enhanced VMEA and Probabilistic VMEA. So far, few studies have compared VMEA to traditional tools like FTA and FMEA by means of usefulness in product development. Hence, the objective of this paper is to show how VMEA differs from FTA and FMEA in terms of

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requirements, limitations and possibilities in the context of product development (PD).

2. Variation Mode and Effect Analysis VMEA is a deductive method and can be divided into three different levels[12]:

1. Basic VMEA is used in the early design stages, where information about the variation is vague and the aim is to compare and evaluate different concepts.

2. Enhanced VMEA is used later in the design stages, where more information about the sources of variation is known.

3. Probabilistic VMEA is used in late design stages, where detailed and statistical information about sources of variation is available.

Product characteristics that are of particular interest from a variation standpoint are selected and are usually referred to as Key Product Characteristics (KPCs). The KPC can be compared to the top event in a fault tree. Each KPC is decomposed into a number of sub-KPCs that are affected by variations, i.e. Noise Factors (NF). One way of illustrating how NFs and sub-KPCs are related to the corresponding KPCs is to use an Ishikawa cause-and-effect chart, see Figure 1.

Figure 1. Ishikawa cause and effect chart

Note that the logical interrelationships between the Sub-KPCs and the KPC (And gate, Or gate, Exclusive or gate, etc.) are not expressed in a logic diagram by the VMEA method. Basic VMEA and Enhanced VMEA (B/E VMEA) are based on subjective ratings, made on a 1-10 scale both for the sub-KPC and the NF. The result from the B/E VMEA is a Variation Risk Assessment and Prioritization (VRPN). VRPN for the j:th NF of the i:th sub-KPC

(1) 222ijijiNFij

VRPN

253

where 2i is the KPC sensitivity to the sub-KPC, 2

ij the sub-KPC

sensitivity to the NF and 2ij the NF variation size. Then the VRPN for the

i:th sub-KPC

. (2) n

jNFKPCsub iji

VRPNVRPN1

These VRPNs can be used to derive which sources of variation are most important for the KPC studied.

Probabilistic VMEA (Prob. VMEA), on the other hand, is a method based on quantitative data from test results or other available measurements and allows greater objectivity. The probabilistic VMEA method aims to systematically assess factors that affect KPCs i.e., the response variable that is affected by the variation [11]. Hence, according to [8], the different types of VMEA can be used in diverse stages of the product development process, see Figure 2.

Figure 2. Diverse stages in the product development process [8]

The working process of the probabilistic VMEA consists of four steps: causal breakdown of KPCs, sensitivity assessment, variation size assessment and variation risk assessment and prioritization.

2.1 Causal breakdown of KPCsKPCs can usually be decomposed into a number of affecting sub-KPCs. The characteristic of a sub-KPC derives from the product, parts of the product or the manufacturing process. The sub-KPCs’ characteristics are usually known, controllable and are affected by one or more NFs. There are two types of NFs: dissipation between manufactured products (unit-to-unit variation), and different behaviour between used products (in-use variation). The NFs that emerge from the second type can be divided into causes from external or internal sources. External sources are, for instance, operating or user variations, while internal sources are related to the product itself e.g., wear and degradation. The KPC causal breakdown can be visualized in a cause-and-effect chart to clarify the contribution of variation. The KPC is usually expressed analytically as a transfer function. In order to enable relative measures of the NFs, the target function ixfY is derived as the natural

254

logarithm of the transfer function [8] where the NFs are included in the variables .ix

ix

2.2 Sensitivity assessmentThe second VMEA step is to determine the sensitivity coefficients for each variable . The sensitivity coefficients for the sources of variation that are influencing the target function (KPC) are determined analytically by the partial derivative of the target function.

2.3 Variation size assessment In the third VMEA step, the standard deviations

ix for each variable are

derived. If the variable contains more than one NF, the standard deviation is determined by use of the Gauss approximation formula, which requires mean values and standard deviations for all included NFs. If the variable contains only one NF, the logarithmical standard deviation (relative measure) can be derived directly. Note that if measured data are not available, uniform distributions are used to predict the standard deviation for that NF.

ix

ix

ix

2.4 Variation Risk Assessment and Prioritization (VRPN) In the fourth VMEA step the variation contribution

ix for each variable and total variation contribution

ix

tot for the KPC are calculated to determine the VRPN. To calculate this spread of variation the t-correction factor variable

ixt is estimated (often the tabular value from the statistical t-distribution that derives from the 97.5% t-quantile). The insecurity from the -factor estimation is compensated by reducing the number of input sources i.e., degrees of freedom, by one unit. Hence, in the case of a large number of input sources, the factor gets close to 1. The sensitivity coefficient

t

tixc is derived from

sensitivity assessment in VMEA step two, and the standard deviation ix

derives from the variation size assessment in step three. Hence, for each variable , the variation contribution isixx1

(3) ixixixix tc

and the total variation contribution is

(4) .

222 ...21 ixxxtot

For a specific group of customers, an identified uncertainty with implicit random distribution (aleatory uncertainty) is denoted as scatter.Uncertainties from e.g., tolerances in the drawings (epimistic uncertainty), are simply denoted as uncertainties. The variation contribution is summarized to a total variation contribution.

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2.5 Safety factor from VMEA By traditional probabilistic VMEA it is possible to derive a safety factor pSFas the ratio between the low quantile of design parameters and the median of design parameters [8] i.e., the selected KPC

(5)

5.0DD

SF pp

where p is the probability of failure. Eq. (3) can be rewritten so that

(6) totpp zDDSF explnlnexp 5.0

and then

(7) totzp eSF

where z is the normal random variable according to the determined probability p and tot is the total contribution of variation. Hence, in traditional VMEA reliability is prescribed, and then a safety factor can be predicted.

3. Fault Tree Analysis Fault tree analysis (FTA) is a deductive method i.e., a general system state is postulated and decomposed into chains of more basic events (faults) of components [13]. The logical interrelationship of how such basic events depend on and affect each other, and thereby cause some system state to occur, is often described analytically in a reliability structure which can be visualized as a tree. The reliability structure is composed by events interlinked with gates which enable the derivation of analytical mathematical expressions to evaluate the system reliability. One basic assumption in FTA is that the component failures occur independently of each other. For each failure mode, besides the reliability structure, the failure rate of the components is required (this assumes that the component has a constant failure rate and that failure times are given by the exponential distribution). Hence, in order to retrieve the data necessary to conduct FTA, knowledge about existing failure modes and their causes are required. This might not be a problem when upgrading existing systems. On the other hand, when developing completely new solutions, failure mode data and failure rates may not be available; therefore, estimations have to be used. Even for existing systems, all required data is seldom available, in which case interviews must be conducted, which may require some time (and may also introduce a risk of retrieving incorrect data). For large systems, since one fault tree is needed for each failure mode, it may take a long time to derive the fault tree itself (since the reliability structure might be quite complex).

256

4. Failure Mode and Effect Analysis In FMEA, which is an inductive method, information about the consequences and effects of the failures is usually collected through interviews with experienced people, from different divisions, with different knowledge i.e., cross-functional groups [14]. FMEA is performed to identify causes of failures affecting the reliability of the product [15] i.e., the product’s function, failure, causes of failure and consequences of failure. FMEA is often conducted to clarify the correlation between causes of failure on component level and corresponding causes of failure on system level, and to obtain arrangement to avoid causes of failure or reduce the consequences of failure. The accuracy of the result is dependent on the amount of information and how detailed the information is.To enable identification of causes of failures and to be able to study the influences of failures, FMEA has been further developed into two major methods. The first method is called Design- Failure Mode and Effect Analysis (D-FMEA) and is used to analyse the failure mode for the design, while the second method, Process- Failure Mode and Effect Analysis (P-FMEA), is used to analyse the failure mode for a process [4, 8, 16]. One result from FMEA is a Risk Priority Number (RPN), based on subjective ratings, often on a 1-10 scale. The RPN is calculated by the mathematical product of the three criteria: potential causes Po , failure mode and effect of failure , hence

SPd

. (8) PdSPoRPN

Note that the logical interrelationships between the component failure and the system failure are not expressed in a logic diagram.

5. Comparison between VMEA, FTA and FMEA In Table 1, different properties important for the product development have been compiled for each of the methods considered in this paper. The DataCollection Method concerns how the in-data are collected, whereas Usefulness Area shows how the results can be used. In the Level of AccuracyFTA is used as reference level to which the other methods are compared. In Product Development Stage, suitable PD stages at which the methods may be applied are proposed. In Logical Connection, it is stated whether or not the method takes the logical connection between component and system failure into account.

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FMEA FTA B/E VMEA

Prob. VMEA

Data Collection Method

- Interviews from cross-functionalgroups

- Interviews from cross-functionalgroups- Reliability fromassembliesmodelled in CAD system -Measurements from rig- and field tests (failure rates)

-Interviewsfromcross-functionalgroups

- Interviews from cross-functionalgroups- Tolerances from drawings - Measurements from rig- and field tests (standarddeviation)

Usefulness Area - Identify failuremodes - Identify causes and consequences of failures-RPN

- Derive reliability of hardwaresystem- Identify causes and consequencesof failures

- Identify, assessandmanageunwantedvariation-VRPN

- Derive safety factor- Identify, assess and managevariationcontribution -VRPN

Level of Accuracy - Less than FTA

- Reference Level

- Less than FTA

- Same as FTA

ProductDevelopmentStage

- All PD stages

- After conceptselection

- All PD stages

- After concept evaluation

Explicit Logical Interrelationships

- No - Yes - No - No

Table 1. Comparison between methods

6. Discussion and Conclusions In this paper VMEA is compared to FTA and FMEA in the context of product development. Requirements, limitations and possibilities of these methods are summarized in Table 1. Both FMEA and FTA can be used to identify causes of failures. FMEA is often used to identify failure modes, to rate consequences of specific failures and to subjectively derive a risk and priority number. VMEA is used, instead, to identify, assess and manage unwanted variation to increase the reliability of systems. Analogous to FMEA, in basic and enhanced VMEA a Variation Risk Assessment and Prioritization number can be derived subjectively. With probabilistic VMEA it is possible to quantitatively (i.e. more objectively) analyse how each included variation contribution affects, for instance, some safety factor based on a prescribed reliability. It can be concluded that, among the methods included in this paper, the logical interrelationships between component and system failure are expressed explicitly only in FTA. Hence, FTA gives additional possibilities of increasing the accuracy and managing the mathematics involved in reliability prediction. Although probabilistic VMEA does not explicitly include the logical interrelationships, it may include in-data

258

from products in use and rig tests, as is the case for FTA. In addition, VMEA also includes the variation contribution of each included property, which hence will increase the accuracy. The methods analysed in this paper are, due to different requirements, limitations and possibilities, suitable in different stages of the product development process. The results from FMEA, FTA and VMEA are somewhat complementary and are useful during the whole PD process. For completely new solutions to be developed, FMEA, basic and enhanced VMEA are judged to be suitable for early PD stages (such as concept design), since those methods require fewer in-data, which can be collected by interviews. FMEA, basic and enhanced VMEA have a lower level of accuracy, which is acceptable in early PD stages. Probabilistic VMEA does not require the reliability structure but rather the included components and standard deviations of properties and is hence suitable after concept evaluation. Due to the increased data need requirements, FTA would be suitable in PD stages after concept selection, so that it is possible to retrieve the reliability structure. Note that, for upgrading development projects, both FTA and probabilistic VMEA can probably be used from the start of the PD process, since at least some of the needed data may be available (reliability structure from previous analyses, failure rates from field measurements, measured standard deviations, etc.).

7. Acknowledgments This work was conducted at the Faste Laboratory, Centre for Functional Product Innovation, a VINNOVA (Swedish Governmental Agency for Innovation Systems) Excellence Centre, based at Luleå University of Technology, Sweden.

References1. E. Henley and H. Kumamoto, Reliability engineering and risk assessment,

Prentice Hall, New York, 1981. 2. W. Weibull, Fatigue testing and the analysis of results, Pergamon Press,

New York, 1961. 3. J. D. Andrews and T. R. Moss, Reliability and risk assessment,

Professional Engineering Publishing, London, 2002. 4. B. Bergman and B. Klefsjö, Kvalitet från behov till användning,

Studentlitteratur, Lund, 1991. 5. S. Reed, J. Andrews, S. Dunnett, M. Karlberg, L. Karlsson and M.

Löfstrand, Modelling service support system reliability, IFAC IMS’10 workshop, 2010, p.^pp.

6. W. G. Schneeweiss, Petri nets for reliability modeling, LiLoLe-Verlag Gmbh, Hagen, 1999.

7. P. D. T. OĆonnor, D. Newton and R. Bromley, Practical reliability engineering, Wiley, West Sussex, 2002.

8. B. Bergman, J. de Maré, S. Lorén and T. Svensson, Robust design methodology for reliability, Wiley, West Sussex, 2009.

9. M. Arvidsson, Use and knowledge of robust design methodology: A survey of Swedish industry, Journal of Engineering Design 14 (2003), no. 2, 129-143.

259

10. P. Johansson, Variation mode and effect analysis: A practical tool for quality improvement, Quality and reliability engineering international 22 (2006), no. 8, 865-876.

11. A. Chakhunashvili, Variation mode and effect analysis, Proceedings of the Annual Reliability and Maintainability Symposium (2004), 364-369.

12. P. Johannesson, Variation mode and effect analysis: An application to fatigue life prediction, Quality and reliability engineering international 25 (2009), no. 2, 167-179.

13. http://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr0492/#pub- info [22 November 2010]

14. G. Holmberg and Å. Lönnkvist, Säkra produkter, Industrilitteratur AB, Stockholm, 1997.

15. T. Hasenkamp, A review of practices for robust design methodology, Journal of Engineering Design 20 (2009), no. 6, 645-657.

16. C. Britsman, Å. Lönnqvist and S. O. Ottosson, Handbok i fmea, failure mode and effect analysis, Industrilitteratur, Stockholm, 1993.

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1 Copyright © 2012 by ASME

Proceedings of the ASME 2012 International Mechanical Engineering Congress & ExpositionIMECE2012

9-15 November 2012, Houston, Texas, USA

IMECE2012-87490

SYSTEM RELIABILITY ESTIMATION WITH INPUT DATA FROM DETERMINISTIC SIMULATIONS

Jonas PavassonLuleå University of Technology

Luleå, Sweden

Magnus KarlbergLuleå University of Technology

Luleå, Sweden

ABSTRACTThe possibility of estimating reliability of hardware,

both for components and systems, is important in engineering design, since many failures result in substantial impact on safety or functional requirements. Existing reliability estimation methods require measured or estimated input data which can be difficult to retrieve. The objective of this paper is therefore to derive a simulation-driven method, including variation management, for combining deterministic simulations with Fault Tree Analysis, to estimate system reliability when measured data is not available.The research work started with a literature survey followed by description of a typical as-is situation and definition of a to-be scenario. Then, a simulation-driven method was derived and verified by a case study. In particular, the system used for the case study was modeled and simulated as a transient dynamical system to derive information about loads on components. It was found that deterministic simulations can be used to produce relevant input data for fault tree analysis. The derived simulation-driven system reliability estimation method includes variation management and can be used for evaluation of concepts in the early stages of product development when limited measurement data is available.

1 INTRODUCTIONThe possibility of estimating reliability of hardware, both

for components and systems, is important in engineering design, since many failures result in substantial impact on safety or functional requirements resulting in expensive reclamations and dissatisfaction that may lead to loss of income.The reliability of individual components is superior to the corresponding system reliability [1]. In 1961, Weibull [2]formulated a distribution (the Weibull distribution) which is one

of the most commonly used formulas for describing important probabilistic measures in reliability theory, e.g. times to failures, extreme values, service life and requirements allocation.Today, there exist several methods for predicting the reliability of hardware systems and for how to identify causes of failure and failure modes, e.g. Fault Tree Analysis (FTA) [3, 4] and Failure Mode and Effect Analysis (FMEA) [4, 5]. In FTA and FMEA, information about the consequences and effects of failures and failure modes is usually collected through interviews with experienced people, from different divisions, with different knowledge, i.e. cross-functional groups [6]. Fault tree analysis (FTA) is a deductive method, i.e. a general system state is postulated and decomposed into chains of more basic events (faults) of components [7]. The logical interrelationship of how such basic events depend on and affect each other, and thereby cause some system state to occur, is often described analytically in a reliability structure which can be visualized as a tree. Since many failures are caused by variations (strength, loads, manufacturing tolerances, etc.), industries are in need of robust design methodologies that can be used to identify and manage different sources of variation [8, 9]. Therefore, a method called Variation Mode and Effect Analysis (VMEA) hasbeen developed. VMEA is a top-down method for identification and management of sources of variation [10, 11]and reliability prediction of hardware systems [12]. FTA, FMEA and VMEA can be used in different phases of the product development process, depending on whether the developed system is completely new or is an upgraded system [13].Ruppert and Bertsche [14] proposed a method for combiningqualitative reliability analysis with quantitative methods. They further integrated reliability analysis with a computer-aided design (CAD) process throughout all stages of product development for a limited number of system components. The


failure behavior of the mechanical parts was determined using a three-parametric Weibull distribution and a practical application of a Boolean serial model and fault tree analysis (FTA) [14].Design for reliability and built-in reliability, i.e. effective measures to create robust designs and manufacturing processes,can be achieved through modeling of failure processes and proactive work early in product development. A statistical virtual experimental design has been developed, based on finite element models of key structures in systems, including the geometrical and materials variables comprising the system and a fatigue prediction model. Information for process development or improvement derived from the virtual experiment is embedded in a Monte Carlo simulation to assess the impact of uncertainty and variability [15]. A similar methodology has been developed to predict the reliability of a product at an early stage in the development process [16]. This methodology integrates Finite Element Models (FEM) with statistical methods such as Design of Experiments (DOE) and Response Surface Models (RSM) that generate the input parameters used in Finite Element Analysis. Failure probability was calculated by using Monte Carlo simulationsBearing models have been developed to determine the vibration response of general rotor-bearing systems, enabling identification of sets of parameters resulting in undesirable vibrations due to bearing nonlinearity [17]. Models and methods for estimation of bearing fatigue limit stress [18] and defect-propagation models for remaining utility estimation of defect bearing have also been developed [19].Today, measured data or estimated data is often used as input to such reliability prediction methods. However, when designing new systems, such measurement data may not exist. Hence, in order to conduct measurements to retrieve such data a prototype needs to be manufactured, which often requires a significant amount of time. In such situations, deterministic simulations could possibly be used to derive the needed input data, which is the scope for this paper. By use of simulations, concepts can be evaluated by means of reliability in early stages of the product development process, i.e. before a physical prototype is manufactured. Variations in raw material properties, production outcome and assembling tolerances, etc. result in system variations which must be managed.

Hence, the objective is to derive a simulation-driven method, including variation management, for combining deterministic simulations with Fault Tree Analysis, to estimate system reliability when measured data is not available.

The hypothesis is that component failure rate can be estimatedby use of deterministic simulations and used as input data to Fault Tree Analysis. The result from the Fault Tree Analysis can then serve as a basis for designing components and systems for improved reliability.

2 RESEARCH APPROACHThe research presented in this paper began with a literature

review regarding reliability estimation methods, variation management and methods for how to derive information needed for such analyses. To further highlight gaps that must be overcome and to guide the research work, a typical as-is situation was described and a to-be scenario was developed forecasting a possible future situation. Based on this to-be scenario, a new simulation-driven method is proposed, wherebydeterministic simulations are used to provide necessary information to probabilistic reliability methods, hence enabling estimation of reliability for new concepts where failure data islacking. To verify the suggested method a case study of a rotor dynamical example was conducted.

3 AS-IS SITUATION AND TO-BE SCENARIOToday, FTA is a commonly used method for evaluation of

hardware reliability. For each failure mode, besides the reliability structure, the failure rate of the components is required (this assumes that the component has a constant failure rate and that failure times are given by the exponential distribution). Hence, in order to retrieve the data necessary to conduct FTA, knowledge about existing failure modes and their causes is required, i.e. logical relationships thst cause faults to propagate from components to system level.

3.1 AS-IS SITUATIONWhen upgrading existing systems, FTA is usually not a problem, since the failure modes and failure rates of the old system are often documented and can to some extent be transferred to the upgraded system. On the other hand, when developing completely new solutions, failure mode data and failure rates may not be available; today, this is often managed through estimations. Even for existing systems, all required data is seldom available, in which case interviews often are conducted, which may require some time (and may also introduce a risk of retrieving incorrect data). For large systems, since one fault tree is needed for each failure mode, it may be time consuming to derive the fault tree itself (since the reliability structure might be quite complex).

3.2 TO-BE SCENARIOIn a future scenario, when performing FTA of completely new concepts, i.e. where little or no data for such analyses exists, as much required information as possible is derived through simulations. Commonly, the design of hardware systems is carried out by use of some computer-aided design (CAD) software. In this to-be scenario the reliability structure, including all relevant failure modes, is automatically generated from the assembly structure designed in the CAD software. In this scenario, the assembly structure serves as a base to preprocess simulation models from which transient loads on the components included in the reliability structure can be estimated. There are several variation sources between the design stage of the product development process and the finally manufactured hardware (tolerances in raw material properties,


tolerances in drawings, variations during manufacturing, etc.). Such variations are in this scenario accounted for in thedeterministic transient simulations, which then give component failure rates. With a known reliability structure and coupled component failure rates regular FTA can finally be conducted to derive the hardware system reliability.

4 SIMULATION-DRIVEN RELIABILITY ESTIMATION METHOD

In order to reach the to-be scenario described in section 3.2, there are several enablers needed. In this paper, the focus is on how to derive the failure rates through simulations, given that the reliability structure is known. In order for such simulations to provide added value, compared to as-is methods, the accuracy of the input data to the FTA must increase. This requires valid deterministic simulation models with low uncertainty in the preprocessing parameters and solving parameters.

The proposed simulation-driven method can be divided into five steps, see Fig. 1.

Figure 1. Proposed simulation-driven method

No series produced products are identical. On the contrary, such products always include variations in geometry, material properties, strength, ductility, load intensity, etc., each with some variation distribution function. During the Parameter Variation step of the proposed simulation-driven method variations, i.e. distribution functions in the manufactured product are traced.In order to derive the information needed for FTA, deterministic models coupled to each failure mode are developed, e.g. finite element models, multi body dynamical models, fluid dynamical models, etc.The variation distributions are then mapped to the deterministic model preprocessing parameters. Then, based on these distributions, several sets of parameters are randomly

generated, i.e. each set of parameters representing one possible manufactured system. If the number of significant variations is large, some suitable method for selecting the most important ones can be deployed, e.g., design of experiments, etc.All the different models are then solved numerically for every set of parameters to derive the transient loads on each component. Known load on the components, together with strength, enables derivation of the component durability. Durability is an aspect of reliability, related to the ability of a component to withstand the effects of time, travelled distance, operating cycles/hours, etc. One component can have several failure modes due to different causes of failure, e.g. due to fatigue, overload, wear, corrosion, etc. Durability is usually expressed as a minimum time before the occurrence of wear-out failures. Hence, in the third step of the proposed method, for each deterministic model (each set of preprocessing parameters) the durability of each failure mode is derived usingthe transient loads and the component strength. For every failure mode, the durability of every deterministic model is listed and hence, when the number of models is large enough, the failure rates can be determined. If no failure modes that corresponds to initial failures and ageing failures exist, these failure rates corresponds to the useful life part of the bathtub curve, see Fig. 2.

Figure 2. Bathtub curve

Finally, when the failure rates and the fault tree are known, a regular FTA can be conducted in order to derive the system reliability.

5 CASE STUDYTo verify the proposed reliability estimation method a case study on rotating machinery was conducted. This machine is an overhung rotor system supported on two roller bearings mounted on two pedestals. For simplicity reasons, it is assumed that the corresponding fault tree consists of two failure modes,both coupled to bearing failure. If one bearing fails the system fails, giving the fault tree shown in Fig. 3.A complete simulation on this system should include all failure modes for the system, e.g. shaft fracture, rotor fatigue, loss of


torque, etc. Deterministic models and simulations coupled to each failure mode should then have to be performed to derive the failure rates needed for the FTA to derive the system reliability.

Figure 3. Fault tree of rotating machinery

Variation PropertiesIn this paper, for simplicity reasons, it is assumed that all system properties are constants except for the bearing clearance, which is assumed to have a normal distribution withmean value (MVL) 0.1 mm and a standard deviation (STD) of 0.01 mm.

Deterministic ModelingIn order to determine the transient loads acting on the bearings a rotor dynamical model was developed, see Fig. 4.

Figure 4. The rotor bearing model

In this simplified model, the shaft was meshed by 2 Euler beam elements with the degrees of freedom x, y, and at each node (while a more accurate model probably would have required more elements). Hence, the system has 3 nodes and 12 degrees of freedom, where node 1 is the leftmost node in Fig. 4 where the rear bearing is positioned. The front bearing is positioned in node 2, i.e. at the middle node in Fig. 4 and Disc 1 (the rotor) is positioned at node 3, i.e. at the rightmost node in Fig. 4 The xy-plane is perpendicular to the rotational symmetric z-axis, is rotation around the x-axis and rotation around the y-axis. In the model, gravity is applied in y-direction (volume load) and the rotor is subjected to rotational load with spin speed frequency due to a mass unbalance (See Unbal. 1 in Fig. 4), i.e. the rotor mass is positioned a short distance away from

the rotor center. Parameters of the Shaft, Rotor, Pedestals and load of the rotor system model are given in Table 1, i.e. preprocessing parameters.

Table 1. Parameters of rotor systemSHAFT ROTORDensity (kg/m^3)

7800 Shaft position (m)

Node 3

Young’s Modulus (GPa)

200 Mass (kg) 2000

Length (m) 1 Polar mass moment of inertia (kgm^2)

300

Radius (m) 0.1 Transversal mass moment of inertia (kgm^2)

600

PEDESTALS LOADShaft Position (m)

00.8

Rotor Unbalance (m)

1e-3

type Radial bearing with clearance

Gravity (m/s^2) 10

Isotropic Stiffness (N/m)

1e111e11

Spin Speed (Hz) 20

MVL Clear (m)

0.0001

STD Clear (m) 0.00001

Proportional damping is used, i.e. the damping matrix 10 , which results

in a range of damping ratio between 0.25% and 14% when considering all vibration modes (when the clearance vanishes). In this scenario it is assumed that all parameters shown in Table 1 are held constant except for the clearance.

RandomizationIn this case it is assumed that only the clearances in the roller bearings are subjected to variations. Here, 2000 sets of parameters (in this case clearance) are generated randomly based on the normal (Gaussian) distribution. A normal distribution is often used as a first approximation to describe real valued random variables that cluster around a single meanvalue. The distribution for the clearance in the rear bearing and the front bearing are shown in Fig. 5.


Figure 5. Clearance distribution in bearings

Failure Rate EstimationIn order to derive the failure rates for each of the bearings the bearing load for each set of parameters generated in the randomization step must be estimated. Therefore, rotor dynamical simulations for each set of parameters were conducted through a fourth-order Runge Kutta algorithm with a time step of 1 10 s. Figure 6 shows the vibration orbit in the rear bearing at 20 Hz spin speed.

Figure 6. Vibration orbit in the rear bearing at 20 Hz spin speed

The vibrations result in radial forces on the bearing that affect the durability. Figure 7 shows the radial force on the rear bearing at 20 Hz spin speed.

Figure 7. Radial force on rear bearing at 20 Hz spin speed

When the load on the bearing is known, the durability value L10h for each failure mode is derived by using the affected load and component strength for the bearing. L10h (basic rating life at 90% reliability, operating hours) is a measure of the durability for a population of components or system of components, in the form of rating life/ hours in use. L10h is a time measure at which 10% of components or systems of components have failed. Failure rate is the frequency of component or system components failures, commonly expressed in failures per hour. The failure rate of a component or system of components usually depends on time, with the rate varying over the lifecycle of the system. In this case study, the spin speed is constant, giving an opportunity to express the rating life in terms of operating hours or number of revolutions. In this case study the rating life formula of a bearing is used for durability calculation, i.e.

(1)

and

(2)

where

L10 represents the basic rating life (at 90% reliability) [millions of revolutions], L10h the basic rating life (at 90% reliability) [operating hours], C the basic dynamic load rating [kN], P the equivalent bearing load [kN], n the rotational speed/spin speed[r/min] and p the exponent of the life equation [20].

In this case study the bearings are of type SKF NU 1040 MA with properties according to Table 2. NU 1040 MA is a single-row cylindrical roller bearing provided by the bearing manufacturer SKF. [21].


Table 2. Properties for L10h calculationBEARINGTYPE

SKF NU 1040 MA

C [kN] 380e6P [kN] Radial force derived from the rotor dynamical model n [r/min] 1200p[-] 10/3

Since the bearing load varies significantly with time load,spectrums for each set of parameter are generated.

Figure 8. Bearing load spectrum for the rear bearing

Figure 8 shows the load histogram at the rear bearing for one of the 2000 different sets clearances. The x-axis shows load (divided in blocks) and y-axis shows load level distribution within each load block.

Heavy and medium loads have a larger impact on component durability than small loads. Therefore, it is important to capture shock and peak, even if the occurrence of these loads can be rare and is limited to a few revolutions. Within each block the bearing load is averaged to a constant value, Pn, and lifecycle fraction under the condition is based on percentage of operation, Un, during the same block.

The bearing life estimation for durability calculation undervariable operating condition,

(3)

is used in this case study where

L10m represents the SKF rating life (at 90% reliability) [millions of revolutions], L10mn the fraction SKF rating lives (at 90% reliability under constant conditions) [millions of revolutions] and Un the lifecycle fraction under the condition (percentage of operation) [20].

The bearing load spectrum shown in Fig. 8 combined with Eq. (1), (2) and (3) gives the bearing durability value L10mh, rating life (at 90% reliability) [operating hours]. At L10mh, 10% of the components with that particular clearance combination have failed. Hence, some model for when these and the other 90% of components fail could be applied, thereby giving more statistical data to be used for failure rate calculations. However, for simplicity reasons in this case study, the L10mh is directly used as a measure of one component failure. Figure 9 shows the L10mh failure distribution at the rear bearing from the 2000 simulations.

Figure 9. Number of L10 failures at different times for rear bearing

Figure 10 shows the L10mh failure distribution at the rear bearing from the 2000 simulations.

Figure 10. Number of L10 failures at different times for front bearing

When the failure distribution is known (see Fig. 9) the failure rate

(4)

where Nf is the cumulative failures, N is the total failures, t is operating hour and dt the histogram time block size [4]. Figure 11 shows the estimated failure rate function for the rear bearing and Fig. 12 the estimated failure rate function for the front bearing.

(3


Figure 11. Failure rate rear bearing

Figure 12. Failure rate front bearing

The rear bearing carries less load than the front bearing, which therefore has a higher failure rate. The front bearing limits the durability, hence the system reliability until 12000h (see fig. 12) is of interest. In this time span the constant failure rates

(5)

(6)

are assumed for the rear ( and the front bearing .

FTAThe fault tree consists of two failure modes, shown in Fig. 3, both coupled to bearing durability failure. The probability of failure

(7)

for the fault tree in this case study, hence the reliability

(8)

Combining Eqs. (5) and (6) into Eqs. (7) and (8) then gives the system reliability for the case study

(9)

Eqs. (5) and (6) into Eq. (9) gives the estimated system reliability , which is valid until 12000 operating hours.

CONCLUSIONSIn this paper, a five-step simulation-driven method

combining deterministic models and probabilistic methods for estimating system reliability has been proposed based on a to-be scenario. In this method, variation properties (distribution, standard deviation, etc.) are randomized and then considered in deterministic models.

Through the case study, it was found that deterministic simulations can be used to generate failure rates to be used in fault tree analysis for reliability estimations. The proposed method takes different variations into account, e.g. due to manufacturing, differences in raw material, assembling, etc. Since the proposed method only requires information regarding variation distributions and fault mechanics, it is appropriate for use during evaluation of concepts in early product development stages when limited measured data is available. Hence, it is plausible that the proposed method can limit testing procedures during product development.

ACKNOWLEDGMENTSThis work was conducted at the Faste Laboratory, Centre for Functional Product Innovation, a VINNOVA (SwedishGovernmental Agency for Innovation Systems) Excellence Centre, based at Luleå University of Technology, Sweden.

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Reliability Prediction at Early - DiVA portalltu.diva-portal.org/smash/get/diva2:990750/FULLTEXT01.pdf · extreme values, service life and requirements allocation. There are several

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