Reliability

1
Reliability

• Topics
• FR()
• FR(N)
• MTBF
• Reliability engineering

2
Reliability

• Definition
• The probability of a product performing without
  failure a specified function under given
  conditions for a specified period of time
• In two formats
• Probability that system will perform on a given
  trial
• 99.999 for telephone system (Five-9 system)
• Frequency of successful performances of a system
  in a given number of attempts.
• 10,000 operating hours
• Three dimensions
• Probability
• frequency of successful uses out of a certain
  number of attempts
• Likelihood of an item lasting a given amount of
  time
• Failure
• A situation in which an item does not perform as
  intended
• Operating conditions
• How the product should be used?
• What is normal operating conditions

3
Failures

• Definition
• Very clear in simple system, for example, light
  bulb
• No longer produces light
• Not very clear in other systems, for example,
  automobile tire
• Catastrophic failure? Blowout? Useful life?
• It is a good idea to use prescribed operating
  conditions
• Some products have different reliability at
  different condition.
• For example, some light bulb designed specially
  for outdoor!!

4
Introduction

• Why thing fails?
• Design failure
• Because a characteristics of demand was overlook
  and miscalculated
• A production line cannot cope with the demands
  placed upon it
• Facilities failure
• All the facilities of the operation are liable to
  break down
• Such as machine, equipment, building and fitting
• Staff failure
• Error - are mistakes in judgment
• Violation - contrary to defined procedures
• Supplier failure
• Delivery, quality of incoming goods and service
• Customer failure
• Misuse of the products
• Misuse of service which the operation has created
  for
• Inattention or incompetence

5
Measuring failure

• There are 3 ways to measure failure
• Failure rate - how often a failure occur (i.e.
  FR(), FR(N))
• Reliability - the chance of a failure occur
  (MTBF)
• Availability - the amount of available useful
  operating time
• MTBF / (MTBFMTTR)
• Failure rate (FR)
• calculated as the number of failures over a
  period time
• FR (N) number of failures x 100 / operating
  time
• FR() number of failures x 100 / total number
  of products tested

6
Measuring failure

• Example 1
• To compute the value of FR, suppose that 10 units
  are tested over 100 hours periods. Four units
  failed with one unit each failing after 6, 35, 65
  and 75 hours, the remaining six units performed
  satisfactory until the end of the test.
• FR(N) 4/ 776
• 0.0052 failure per hour
• Total operation hours 6x1001x61x351x651x75
  776

7
Measuring failure

• Example 2
• A batch of 50 electronics components is tested
  for 2000 yours. Four of the components failed
  during the test as follows
• Failure 1 occurred at 1200 hours
• Failure 2 occurred at 1450 hours
• Failure 3 occurred at 1720 hours
• Failure 4 occurred at 1905 hours
• Answer
• FR() no. of failure / number tested 4/50
  8
• Alternatively, FR(N) can be calculated
• 1 component was not operating 2K-1.2k 800hrs
• 1 component was not operating 2K-1.45k 550hrs
• 1 component was not operating 2K-1.72k 280hrs
• 1 component was not operating 2K-1.905k 95hrs
  (total 1725 hours)
• FR (N) number of failure / operating time
  4/98275 0.000041 per hour

8
MTBF

• An alternative measures of failure of a component
  system is MTBF
• Defined as the average length of time between
  failures of a product or component
• MTBF is the reciprocal of failure rate (FR(N))
• MTBF operating hours / number of failure (unit
  hours)
• Example 3
• In the previous example with electronics
  components, the FR(N) was 0.000041. What is its
  MTBF?
• MTBF 1/F(N)) 1/ 0.000041 24390 hours
• That is a, a failure can be expected once every
  24390 hours on average

9
Availability

• Availability is the probability that a system is
  operating satisfactorily at any point in them
  when used under stated conditions.
• It is the degree to which the operation is ready
  to work
• An operation is unavailable if it has either
  failed or is being repaired following failure
• Availability MTBF / (MTBFMTTR)
• MTTR the mean time to repair, which is the
  average time taken to repair the operation, from
  the time it fails the time it is operation again
• What is the causes of unavailability?
• Planned maintenance
• Change over

10
Example 4

• A company which designs and produces display
  poster for exhibition. Currently, the MTBF of a
  printer is 70 hours and its mean time to repair
  is 6 hours. What is the availability?
• Ans
• MTTR6, MTBF70
• A 70 / (70 6) 0.92
• Next we compute the number of failure per
  operating hour
• FR(N) No of failure / total operating time
• Where total time 1000 hours x 20 units
• 20000 units hours
• Non-operating time at (1000-200) 1st, (1000-600)
  2nd 8004001200 unit hours
• Operating time Total time - non-operating time
• 20x1000 -1200 18800 unit hours
• FR(N) 2 / 18800 0.0011 failure/unit hours
• MTBF 1 1 9430 hours
• FR(N) 0.0011

11
Example 5

• 20 air conditioning systems designed for use by a
  company in NASA space shuttles were operated for
  1000 hours. Two of the system failed during the
  test One after 200 hours and the other 600
  hours. Find the FR(), FR(N) and MTBF
• Solution
• FR() No of failure x 100
• No of units tested
• 2/20 10
• FR(N) No of failure / total operation hours
• 2 / (18x1000 800 400) 2/19200 0.00104
  / per hour
• MTBF 9,600 hours

12
Reliability Prediction

• System of components may be configured in
• Series
• Parallel
• Of mixed combination
• Series Systems
• All components must function or the system will
  fail
• The reliability of the system is the product of
  the individual reliabilities, that is
• Rs R1 x R2 x R3 x Rn
• Example
• A personal computer is compose of the CPU, modem,
  and printer with reliability of 0.997, 0.98 and
  0.95 respectively. The overall reliability of the
  system is given by
• Rs 0.997 x 0.98 x 0.975 0.953

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Example (service industry)

• The HSBC Bank processes Loan application through
  3 clerks set up in series
• R1 R2 R3
• 0.9 0.8 0.99 Rs
• Rs R1 x R2 x R3
• 0.8 x 0.9 x 0.94
• 0.713
• 71

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Reliability Prediction (2)

• Parallel system
• The system will operate as long as one component
  functions
• The additional components are redundant
• In this kind of system, failure of an individual
  component is less critical than in series system
• Redundant is often build into system to improve
  the reliability
• Rs Rm Rb (1- Rm ) R(main)
  R(backup)xFail(main)
• Where Rs reliability of the system
• Rm reliability of the main sub-system
• Rb reliability of the stand-by sub-system
• (1- Rm ) probability that the main sub-system
  will fail
• For example
• 0.8 0.8 (1-0.8) 0.8 0.160.9696
• Note the reliability has been increased from 80
  to 96

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Reliability Prediction (3)

• Alternatively, the reliability of the system can
  be written as
• Rs 1- (1- Rm )(1- Rb ) 1 - Fail(main)xFail(back
  up)
• Rs 1- 1- Rm - Rb Rm Rb Rm Rb - Rm Rb
  Rm Rb (1- Rm )
• If there are more than one backup components, the
  equation can be written as
• Rs 1- (1- R1 )(1- R2 ) ( 1 - R3 ) (1 - Rn )
• If all components have identical reliability
• Rs 1 - (1-R)n

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Reliability Prediction (4)

• For example
• The computers on the space shuttle were designed
  with built-in redundancy in case of failure. Five
  computers were designed in parallel. Thus, if the
  reliability of each computer is 0.99. What is the
  combined reliability Rs.
• Rs 1- (1-0.99)5
• Rs 0.9999999999

17
Reliability Prediction (4)

• The HSBC is disturbed that the loan process has a
  reliability of only 71. Therefore the bank
  decides to provide redundancy for first 2 clerks
• 1st 0.9
• 2nd 0.8
• R1 R2
• 0.9 0.8
• R1 R2 R3 Rs
• 0.9 0.8 0.99
• Rs R1 R1(1-R1) x R2 R2(1-R2) x R3
• 0.9 0.9x0.1 0.80.8x0.2 x 0.99 0.99 x
  0.96 x 0.99 0.9409

18
Reliability Engineering

• Objective Capability of the system
• Good reliability strategy protects both
  Performance its Investment
• The reliability tactics are
• improving reliability of individual components
• The No. of components in a SERIES increase, the
  reliability of the whole system decrease very
  quickly.
• Each individual part may have its own unique rate
  of reliability. Thus, it is very difficult to use
  reliability curve to predicts its reliability.
• decrease number of individual components
• An alternative way is to decrease number of
  stages. A simple design can always make the
  system easier to debug and maintain
• providing redundancy
• To increase the reliability of the system
• The resulting reliability is the Probability of
  the first component working PLUS the probability
  of the back up component working X the
  probability of needing the back up component

19
Reliability life characteristic concepts

• If we were to run a piece of equipment to
  failure, repair it, and repeat the process over
  and over again
• recording the failure time for each run, we would
  have a set of data that would indicate the
  failure rate for that equipment
• When we plot failure rate against time, we often
  see a pattern of failure known as a bathtub curve
• Early-stage failure Expected normal life of the
  product End-of-life failure

Failure rate
time
20
Reliability life characteristic concepts (2)

• Early-stage failure
• Characterized by high failure rates early in the
  life cycle.
• These failures are usually the result of design,
  manufacture, or use errors and are usually
  correctable given a good quality system
• Expected normal life of the product
• At this stage, there is a constant pattern and
  relatively low failure rate.
• Failures in this stage usually result from design
  limitations, changes of the environment, and
  damage caused by day-to-day use or maintenance.
• Training in the proper use and maintenance of the
  equipment can minimize accidents. To reduce
  failure rate in this stage, would generally
  require redesign of the product
• End-of-life failure
• Failure occurs when the product exceeds its
  intended normal life expectancy.
• Due to variations, some units fails early and
  some units fail beyond their life expectancy
• Failure are mostly the result of daily wear and
  stress on equipment.
• Many company desire to run equipment to failure
• There are risks associated with it
• When continue to use these about-to-fail
  equipment, company may produce products
  out-of-specification
• An unexpected failure may lead to undesirable and
  uncontrollable consequence (e.g. stop of
  production)
• Preventive maintenance program will allow
  controlled replacement of old or worn equipment
  before a catastrophic failure occur

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Summary

• The basic unit of measure for reliability is the
  product failure rate FR
• The FR measures the percentage of failures among
  the total No. of products tested called FR()
• FR () Number of failure X 100
• No of units tested  
• OR
• The No of failure during a period of time called
  FR(N)
• FR (N) Number of failure
• No of unit hour of operating time  
• The most common term in reliability analysis is
  Mean Time Between Failure(MTBF)
•   MTBF _ 1___
• FR (N)
• Availability MTBF / (MTBFMTTR)

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Summary

• Two ways to improve overall system reliability
• Increase individual components
• Decrease number of components
• Add redundancy
• Rs Rm Rb (1- Rm )
• Three stages in bathtub curve
• Early-stage failure
• Expected normal life of the product
• End-of-life failure