4 the Assessment and Control of Product Reliability

CHAPTER - FOUR THE ASSESSMENT AND CONTROL OF PRODUCT RELIABILITY

In todays technological world, nearly everyone depends upon the continued functioning of a wide array of complex machinery and equipment for their everyday health, safety, mobility and economic welfare.

ReliabilityReliability is a question of whether a product can be bought with confidence and used for a long time with confidence.Reliability is thus a quality characteristic, and achieving it is a quality assurance activity.This means that well-planned reliability tests must be carried out at every step of new-product development from the design stage onward, for parts, subassemblies and the complete product.

Historically, reliability became a problem for the following four reasons:Products (for example, telephone cables) began to require longer lifetimes)Conditions of use became harsherNew-product development times became shorterThe number of products using very large numbers of parts increased

From the viewpoint of the consumer or user, we can start by dividing reliability into the following three types:Reliability before purchase: this is the reliability of a particular company, i.e, whether customers regard its products as always good and believe they can buy them with confidence.

Reliability at time of purchase: whether a product is good at the time it is purchased, and whether its characteristics are initially satisfactory.Reliability after purchase: whether a product can be used for a long time with peace of mind.

Reliability TerminologyIntrinsic reliability, Ri, is reliability built into an item through design, manufacturing, testing, and other processesQuantitatively, it is the targeted or predicted value of the reliability set at the design stage, or the reliability characteristic value obtained from the results of reliability tests.

Mean time between failures, MTBF, is the average operating time between successive failures.Initial or early failure is failure occurring at a relatively early stage after first use as a result of design or manufacturing faults or unsuitability for the environment in which the product is used.

Random or chance failure is sporadic breakdown that occurs between the initial failure stage and the wear-out failure stage.Wear-out failure is breakdown that increases with time as a result of fatigue, wear, or deterioration.

Useful life is the period for which a product can be usefully used before the failure rate rises to an unacceptable level and economic operation is no longer possible.Gradual failure is failure in which characteristics deteriorate gradually with time and can be predicted by inspection or monitoring.

Sudden failure is breakdown that occurs unexpectedly and cannot be predicted by inspection or observation.Maintainability is the probability of the maintenance of an item being completed under specified conditions during a certain period of time.

Failure is the loss of ability of an item to perform a specified function.Failure rate is the frequency of failure of an item during a continuous period where the item has functioned normally up to a certain point in time.Redundancy is the provision of extra structural elements or means of achieving a specified function to ensure that the overall system does not fail even if one of the components fails.

Parallel redundancy is redundancy in which all structural elements are functionally connected in parallel.Stand-by redundancy is redundancy in which redundant constituent elements are held on stand-by until switched on when the primary constituent element fails.

Quality versus ReliabilityThe everyday usage term quality of a product is loosely taken to mean its inherent degree of excellence. In industry, this is made more precise by defining quality to be conformance to requirements at the start of use.

Quality is a snapshot at the start of life and reliability is a motion picture of the day-by day operation. Time zero defects are manufacturing mistakes that escaped final test. The additional defects that appear over time are reliability defects or reliability fallout.

Statistical Aids to ReliabilityBathtub CurveA plot of the failure rate over time for most products yields a curve that looks like a drawing of a bathtubThe initial region that begins at time zero when a customer first begins to use the product is characterized by a high but rapidly decreasing failure rate

This region I known as the Early Failure Period (also referred to as Infant Mortality Period, from the actuarial origins of the first bathtub curve plots). This decreasing failure rate typically lasts several weeks to a few months.

Next, the failure rate levels of and remains roughly constant for (hopefully) the majority of the useful life of the product. This long period of a level failure rate is known as the Intrinsic Failure Period (also called the Stable Failure Period) and the constant failure rate level is called the Intrinsic Failure Rate. Note that most systems spend most of their life times operating in this flat portion of the bathtub curve.

Finally, if units from the population remain in use long enough, the failure rate begins to increase as materials wear out and degradation failures occur at an ever increasing rate. This is the Wearout Failure Period.

Users are concerned with the length of time that a product will run without failure. For repairable products, this means that the time between failures is a critical characteristic

Exponential Formula for ReliabilityThe distribution of time between failures indicates the chance of failure free operation for the specified time period.

Where Ps = R = probability of failure-free operation for a time period equal to or greater than te=2.718t=a specified period of failure-free operation = mean time between failures, or MTBF (the mean of the TBF distribution)

= failure rate (the reciprocal of )

Mean Time between Failure MTBFThe MTBF is the mean (or average) time between successive failures of a product

The Relationship between Part and System ReliabilityIt is often assumed that system reliability (i.e, probability of survival Ps) is the product of the individual reliabilities of the n parts within the system. Ps=P1P2..Pn

If it can be assumed that each part follows the exponential distribution, thenFurther, if t is the same for each part:

Reliability or Survival FunctionThe Reliability Function R(t), also known as Survival Function S(t), is defined by: R(t) = S(t) = the probability a unit survives beyond time t.Since a unit either fails, or survives, and one of these two mutually exclusive alternative must occur, we have

R(t) = 1-F(t), F(t) = 1-R(t) Calculations using R(t) often occur when building up from single components to subsystems with many components. For example, if one microprocessor comes form a population with reliability function R(t) and two of them are used for the CPU in a system, then the system CPU has a reliability function given by

Failure (or hazard) rate The failure rate (or hazard rate) is defined by h(t) and calculated fromthe instantaneous (conditional) failure rate

Since h(t) is also equal to the negative of the derivative of the , we have the useful identity:If we let

be the Cumulative Hazard Function, we then have F(t) = 1-e-H(t). Two other useful identities that follow from these formulas are:

It is also sometimes useful to define an average failure rate over any interval (T1,T2) that ''averages" the failure rate over that interval. This rate, denoted by AFR (T1,T2).The formulas for calculating AFR's are:

Redundancy is the existence of more than one element for accomplishing a given task, where all elements must fail before there is an overall failure to the system. In parallel redundancy two or more elements operate at the same time to accomplish the task, and any single element is capable of handling the job itself in case of failure of the other elements. When parallel redundancy is used, the over all reliability is calculated as follows:

Where Ps = reliability of the systemP1= reliability of the individual elements in the redundancy'n = number of identical redundant elements

Reliability as a Function of Applied Stress and StrengthAn individual component is satisfactory if its strength is greater than the stress applied to it. For the same design, strength will vary from component to component.

If normality is assumed, the probability of a difference greater than 0 can be estimated by finding the area under the curve.Example: Suppose the following estimates apply to a part:

StrengthApplied stressAverage60,000 Kg/cm246,000 Kg/cm2Standard deviation 3,000 Kg/cm2 5,500 Kg/cm2

The Average difference = 60,000 - 46,000 = 14,000From Table, the area greater than 0 is 0.9875. Thus, the reliability is 98.75 percent.

Availability"Availability" is sometimes a more appropriate measure than reliability. Whereas reliability is a measure of performing without failure, availability recognizes both reliability and maintainability:Time availability is the percentage of operating time that an equipment is operational. This is usually computed as

Where MTBF = means time between failuresMRT = mean repair time

Equipment availability is the percentage of equipments which will be available for use after t hours of operation due to the combined effect of units which did not fail and failed units which were restored to service within a specified maximum downtime.Mission availability is the percentage of missions of time t which will not have any failure which cannot be restored within a specified maximum downtime

There are five key areas of effort affecting the achievement of a reliable end item. They are design, production, measurement and test, maintenance, and field operation.Notwithstanding this there are several common methods used to achieve a reliable design. Prior to designing for reliability, standards of reliability must be established; that is some benchmarks of reliability required should be set

There is no economic sense in designing one component to last for 1,000hours when another that it is depends upon cannot possibly last beyond ten hours.The design should be as simple as possible. Error rate is directly proportional to complexity. The greater the number of components we have the greater the chance of failure

"Maintainability" and "serviceability" are important considerations in designing for reliability. Ease of maintenance and service contributes to higher field reliability. The easier and faster necessary maintenance becomes, the longer an item of known reliability may remain in effective service

Reliability Measurement and TestsConsidering the definition of reliability, it is evident that reliability testing is merely an extension of functional, environmental, and life testing. Functional testing involves a testing involves a test to determine if the product will function at time zero.

An environmental test is a functional test with the added condition of some environmental stress such as a temperature, pressure, vibration, or other extreme. A life test is to determine the mean life of a product. Combine the three types of test together and the result is a reliability test

Maintenance and ReliabilityApproximately twice the original cost of complex equipment is expended each year to support the equipment. Much of this cost is the result of upkeep and maintenance. The total reliability of the equipment in the field is a function of design, maintenance, and field operation reliability; that is,

An item with high maintainability is one which is easy to keep in operation; one with low maintainability is exactly the opposite. Modular design (design for replacement of entire sub-systems) is one example of designing for ease of maintenance

Field Operation ReliabilityThere are three important variables which have major effect on reliability at operation; the environment, the functional interactions between the various sub-systems within the entire system, and the conditions imposed by the operator of the system.