Reliability[1]

Reliability

What is Reliability?

“Probability that a system or product will perform in a satisfactory manner for a given period of time when used under specified operating condition”Reliability is an integral part of how the company develops products and production systems

Plan for it - Design for it - Do it (and verify) - Learn from it (and get even better)

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Reliability Definition vs. the “Real World”Reliability is the probability that an item can perform its intended function for a specified interval under stated conditions following prescribed procedures.

There are “Real World” conflicts with this textbook definition that we need to keep in mind…

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Reliability Definition vs. the “Real World”◦ Probability – Customers expect a probability of

1, “It Works”

◦ Intended Function – The product may be used in unintended ways and still be expected to work

◦ Under Stated Conditions – The product may be operated outside of the stated conditions and still be expected to work

◦ Prescribed Procedures – Customers may not have the required tools or skill level and may not follow procedures and still expect the product to work

Customers are looking for Quality over Time

Reliability vs. Quality (Glesner,

Kececioglu, et al.)

Reliability Assuranceis the ability of a system or component to perform its required functions under stated conditions, for a specified period of time.

Quality Assuranceis a set of activities whose purpose is to demonstrate that a product meets all quality requirements.

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Reliability - 4 main elements

1. Probability – numerical representation - number of times that an event occurs (success) divided by total number trials

2. Satisfactory performance – criteria established which describe what is considered to be satisfactory system operation

3. Specified time – measure against which degree of system performance can be related - used to predict probability of an item surviving without failure for a designated period of time

4. Specified operating conditions expect a system to function - environmental factors, humidity, vibration, shock, temperature cycle, operational profile, etc.

Reliability - 4 main elements…

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Managing ReliabilityReliability Engineering A systems approach to planning for,

designing in, verifying, and tracking the reliability of products throughout their life to achieve reliability goals.

Failu

re R

ate

Early Life

Useful Life Wearout

“Bathtub Curve”

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Reliability Tools

◦Quality Function Deployment

◦Life Cycle Cost

◦Corrective and Preventive Action

◦Awareness of Reliability Prediction, Maintainability Analysis, FMEA, DOE, Reliability Testing, Field Data Collection and Analysis

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Basic Reliability Terms Failure - A failure is an event when an item is not available to

perform its function at specified conditions when scheduled or is not capable of performing functions to specification.

Failure Rate - The number of failures per unit of gross operating period in terms of time, events, cycles.

MTBF - Mean Time Between Failures - The average time between failure occurrences. The number of items and their operating time divided by the total number of failures. For Repairable Items

MTTF - Mean Time To Failure - The average time to failure occurrence. The number of items and their operating time divided by the total number of failures. For Non-repairable Items

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Basic Reliability Terms Maintainability - A characteristic of design, installation and

operation, usually expressed as the probability that an item can be retained in, or restored to, specified operable condition within a specified interval of time when maintenance is performed in accordance with prescribed procedures.

MTTR - Mean Time To Repair - The average time to restore the item to specified conditions.

Maintenance Load - The repair time per operating time for an item.

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Basic Reliability Terms Overall Equipment Effectiveness - A measure of a production

system’s ability to meet requirements for availability, efficiency, and yield. This represents the system’s ability to operate, at specified production rate, to specified quality standards, when needed.

Availability - A measure of the time that a system is actually operating versus the time that the system was planned to operate.

Efficiency - A measure of the actual production rate that a system produces product versus the specified production rate of the system.

Yield - A measure of the portion of product that meets defined product quality specifications versus the total amount of product produced.

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Overall Equipment Effectiveness

Overall Equipment Effectiveness is a measurement of a production system’s ability to meet requirements for availability, throughput, and quality. It is a percentage calculation that represents the portion of the time that the system is operating, at specified production rate, to specified quality standards versus the time that the system was planned to operate.

OEE = Availability x Efficiency x Yield

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Overall Equipment Effectiveness

OEE = Availability x Efficiency x Yield

Availability = Uptime / (Uptime + Downtime) 

Efficiency = Design Cycle Time / Actual Cycle Time 

Yield = Good Parts / Total Parts

How is the

Production System performing?

Is it running?

At design rate?

Are the parts good?

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What Would You Try To Improve?

75%95%90%64% =

98%75%90%66% =

98%95%75%70% =

98%95%90%85% =

YieldEfficiencyAvailabilitySystem

Effectiveness

75%95%90%64% =

98%75%90%66% =

98%95%75%70% =

98%95%90%85% =

YieldEfficiencyAvailabilityOEE

Basic Calculations

0

1

0 0

0

( )ˆ, ( )

( ) ( )ˆ ˆ( ) , ( ) ( )( )

n

ifi

f sr

s

tn t

MTTF f tn n t

n t n tt R t P T t

n t t n

Suppose n0 identical units are subjected to a test. During the interval (t, t+∆t), we observed nf(t) failed components. Let ns(t) be the surviving components at time t, then the MTTF, failure density, hazard rate, and reliability at time t are:

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Basic Definitions Cont’dThe unreliability F(t) is

( ) 1 ( )F t R t

Example: 200 light bulbs were tested and the failures in 1000-hour intervals are

Time Interval (Hours) Failures in the interval

0-10001001-20002001-30003001-40004001-50005001-60006001-7000

1004020151087

Total 200

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Calculations

Time

Interval

Failure Density

( )f t x 410

Hazard rate

( )h t x 410

0- 1000

1001- 2000

2001- 3000

……

6001- 7000

3

1005.0

200 10

3

402.0

200 10

3

201.0

200 10

……..

3

70.35

200 10

3

1005.0

200 10

3

404.0

100 10

3

203.33

60 10

……

3

710

7 10

Time Interval (Hours)

Failures in the

interval

0-10001001-20002001-30003001-40004001-50005001-60006001-7000

1004020151087

Total 200

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Failure Density vs. Time

1 2 3 4 5 6 7 x 103

Time in hours 19

×10

-

4

Hazard Rate vs. Time

1 2 3 4 5 6 7 × 103

Time in Hours

20

×10

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Calculations

Time Interval Reliability ( )R t

0- 1000

1001- 2000

2001- 3000

……

6001- 7000

200/ 200=1.0

100/ 200=0.5

60/ 200=0.33

……

7/ 200=0.035

Time Interval (Hours)

Failures in the

interval

0-10001001-20002001-30003001-40004001-50005001-60006001-7000

1004020151087

Total 200

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Reliability vs. Time

1 2 3 4 5 6 7 x 103

Time in hours

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Exponential Model Cont’d

1MTTF

2

1Variance

12Median life ( ln )

Statistical Properties

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6 Failures/hr5 10

MTTF=200,000 hrs or 20 years

Median life =138,626 hrs or 14 years

Reliability Function

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0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

1.2

Time

Reliability