1. Wan Mohd Faizal Bin Wan Abd Rahim
Reliability
Wan Mohd Faizal Bin Wan Abd Rahim

2. Definition of Reliability
“Reliability is the probability that a product will perform its intended function satisfactorily for a prescribed life under certain stated environmental conditions.”
“Kebarangkalian sesuatu produk itu berfungsi dengan memuaskan untuk jangkahayat tertentu dibawah keadaan persekitaran yang telah ditetapkan.”

3. Definitions
Failure: Situation in which a product, part, or system does not perform as intended.

4. A product that “works” for a long period of time is a reliable one.
Since all units of a product will fail at different times, reliability is a probability.

5. There are four factors associated with reliability: Numerical value.
Intended function.
Intended Life
Environmental conditions
Next

6. Numerical Value (Nilai Berangka)
The numerical value is the probability that the product will function satisfactory during particular time.
Kebarangkalian bahawa produk akan berfungsi dengan sempurna disepanjang waktu tertentu.

7. Example
A value of 0.93 would represent the probability that 93 of 100 products would function after a prescribed period of time and 7 products would not function after prescribed period of time.
Back

8. Intended function (fungsi ditentukan)
Product are designed for particular applications and are expected to be able to perform those applications.
Produk direkabentuk untuk aplikasi tertentu dan dijangka berupaya untuk melakukan aplikasi tersebut.

9. Example (lift cable & screwdrier)
An lift cable is expected to lift a certain design load,it is not excepted to lift a load that exceeds the design specification.
The screwdriver is designed to turn screw, not open paint cans.
Back

10. Intended Life (Hayat Ditentukan)
How long the product expected to last. Product life is specified as a function of usage, time or both.
Beberapa lama sesuatu produk itu boleh berfungsi dengan sempurna.Hayat produk adalah fungsi masa, kegunaan atau kedua-duanya.

11. Example (tire)
The life of automobile tires is specified by different values, such as 36 months (time) or 70,000 km (usage), depending on the construction of the tire.
Back

12. Environmental Conditions.(Keadaan Persekitaran)
A product that is designed to function under certain conditions. Environmental conditions also include the storage and transportation aspects of the product.
Produk yang direkabentuk untuk berfungsi dibawah keadaan persekitaran tertentu.

13. Example
A product design to function indoors, such as sofa, cannot be excepted to function reliably outdoors in the sun, wind, and precipitation.
Back

14. Achieving Reliability
System Reliability
Design
Production
Transportation
Maintenance
Next

15. 1. System Reliability
As products become more complex (have more components), the chance that they will not function increases.
The method of arranging the components affects the reliability of the entire system.
Components can be arranged in:
series
parallel
combination

16. Series
A series system is one in which all of the components must be operating for the entire system to operate.
When components are arranged in series, the reliability of the system is the product of the individual components (multiplicative theorem).

17. Each of the component in a system has a reliability of Ri
Each of the component in a system has a reliability of Ri. There are n components. The system has a reliability of Rs. To determine Rs, we calculate

18. Contoh
Sebuah sistem peluru berpandu mempunyai 4000 komponen. Keboleharapan setiap komponen amatlah tinggi. Katakan Ri = untuk i = 1…4000. Maka keboleharapan sistem ini ialah
Rs = (0.9999)4000 = 0.67
Jika bilangan komponen boleh dikurangkan kepada separuh, maka keboleharapan sistem ini ialah
Rs = (0.9999)2000 = 0.82

19. Example
Rs = (RA)(RB)(RC)
= (0.955)(0.750)(0.999)
= 0.716

20. Example

21. As the number of component increase in the series, the system reliability decreases.
The system reliability is always less than its lowest value.

22. Parallel
Reliability can be increased by placing certain component in parallel.
When a component does not function, the product the product continues to function using another component until all parallel components do not function.
A system consisting of n component in parallel will fail only if all n components fail.

23. If the probability of failure of a component is Fi = 1 – Ri , the unreliability, Fp of the parallel system can be determined as
Conversely, the reliability of the parallel system, Rp, is given by

24. Example
Katakan satu sistem mengandungi 3 komponen dalam keadaan selari yang setiap satu mempunyai keboleharapan Apakah keboleharapan sistem ini?
Rp = 1 - (1 – 0.65)3
= 1 – 0.353
= 0.957

25. Rs = 1-(1-RI)(1-RJ)
= 1-( )( )
= 0.960

26. Example

27. As the number of components in parallel increases, the reliability increases.
The reliability for a parallel arrangement of components is geater than the reliability of the individual components.

28. Combination System
Most complex products are a combination of series and parallel arrangements of components.

29. parallel
Back

30. 2. Design The fewer the number of components, the greater reliability.
The most important aspect of reliability is the design. It should be as simple as possible.
The fewer the number of components, the greater reliability.
Example
If a system has 50 component in series and each component has a reliability of 0.990, the system reliability is
Rs = = 0.605
If the system has 20 omponents in series, the system reliability is
Rs = = 0.818

31. Having a backup component
Having a backup component. When the primary component does not function, another component is activated.
By overdesign. The use of large safety factors can increase the reliability of a product.
Example
A 1-in. rope may be substituted for a ½ - in. rope even though the ½ -in. would have been sufficient.

32. Maintenance. Product that are easy to maintain will likely receive better maintance. In some situations it may be more pratical to eliminate the need for maintenance (oil impregnated bearing).
Environmental conditions such as dust, temperature, moisture, and vibration can be the cause of an unreliable product. The designer must protect the product from these conditions.
Back

33. 3. Production
The production process is the second most important aspect of reliability.
Emphasis should be placed on those components which are least reliable.
Production personnel can take action to ensure that the equipment used is right for the job and investigate new equipment as it becomes available.
Production personnel can experiment with process conditions and parameter to determine which conditions produce the most reliable product.
Back

34. Transportation
The third aspect of reliability is the transportion of the product to the customer.
No matter how well the design or how carefully produced, the actual performance of the product by customer is the final evaluation.
The reliability of the product at the point of use can be greatly affected by the type of handling the product receives in transit.
Good packaging techniques and shipment evaluation are essential.
Back

35. Maintance
While designer try to eliminate the need for customer maintenance, there are many situations where it is not pratical or possible.
In such cases, the customer should be given ample warning.
Maintenance should be simple and easy to perform.
Back

36. STATISTICAL ASPECTS OF RELIABILITY

37. Distribution Applicable to Reliability
Types of continuous probability distributions used in reliability studies are:
exponential
normal
Weibull
Their frequency distribution as function of time.

38. Reliability Curve
Reliability curves for the exponential, normal and Weibull distribution.
Area under curve

39. Failure-Rate Curve
Failure-rate is important in describing the life-history curve of a product.
Normal
Weibull
Exponential

40. Failure rate
Failure rate can be estimated by three types:
Time terminated without a replacement situation.
Time terminated with replacement
Failure terminated

41. Time terminated without a replacement situation
Where:
λest = failure rate, which is the probability that a unit will fail in stated unit of time or cycles.
r = number of test failures
t = test time for a failed item
n = number of item tested
T = termination time

42. Example r = number of test failures = (4)
t = test time for a failed item = ( )
n = number of item tested = (9)
T = termination time = (22)
Back

43. Time terminated with replacement.
Where:
r = number of test failures
t = test time for a failed item

44. r = number of test failures = (6)
t = test time for a failed item = (50x15)
Back

45. Failure terminated
Di mana:
r = number of test failures
t = test time for a failed item

46. r = number of test failures = 6
t = test time for a failed item
=( )

47. Mean life or Mean Time Between Failure (MTBF)
For the exponential distribution and for the Weibull distribution when β, the shape parameter, equals 1, there is a constant rate.
When the failure rate is constant, the relationship between mean life and failure rate.
(for constant failure rate)
Where,
θ = mean life or Mean Time Between Failures (MTBF)
λ = failure rate

48. Example 1, λ = 0.025
Example 2, λ = 0.008
Example 3, λ =

49. Life-History Curve
The curve, sometimes referred to as the “bathtub” curve, is comparison of failure rate with time.
It has three distinct phases:
the debugging phase
chance failure phase
wear out phase

50. Typical Forms of Failure
Early failure (debugging phase) due to design faults, poor quality components, manufacturing faults, installation errors, operator & maintenance errors
Useful life(chance failure phase)has a low, constant failure rate
Wear-out failure parts approach the end of life
Time
Failure Rate
Early
Failure
Useful
Life
Wear-out

51. Debugging phase
Which also called the burn in or infant-mortality phase.
Characterized by marginal and short life parts that cause a rapid decrease in the failure rate.
the debugging phase may be part of testing activity prior to shipment for some product.

52. Chance Failure Phase
Shown in figure as a horizontal line, making the failure rate constant.
Failures occur in a random manner due to the constant failure rate.
Reliability studies and sampling plans are, for the most part, concerned with the chance failure phase.
The lower the failure, the better the product.

53. Wear-out-Phase
Depicted by a sharp rise in the failure rate.
Normal distribution is the one that best describes the wear-out phase.
Part approach the end of life.

54. Example Problem 8
Turn to page. 180

55. Normal Failure Analysis (wear out phase)
The normal curve is applicable to the wear-out phase.
However, the integral ∫f(t)dt, is the area under the curve to the left of time, t, and is obtained from Appendix Table A.

56. Thus, equation becomes,
Where
Rt = reliability at time t
P(t) = probability of failure or area of the normal curve to the left of time t.

58. Exponential Failure Analysis (chance failure phase)
The exponential distribution used to describe the constant failure rate (chance failure phase).
Can calculate the reliability using the formula:
Where
t = time or cycles
θ = mean life

60. Weibull Failure Analysis
The Weibull distribution can be used for the debugging phase (β < 1), chance failure phase (β = 1), and the wear-out phase (β > 1)
Where:
β = Weibull slope
θ = mean life

62. OC Curve Construction
The Operating Curve (OC).

63. Langkah pembinaan OC curve untuk ujian keboleharapan
Tentukan purata hayat (mean life), θ.
Tentukan kadar kegagalan (failure rate), λ=1/θ.
Tentukan jangkaan purata bilangan kegagalan, nTλ.
Dimana n = sample size, T = time of test.
Tentukan nilai probability of acceptance, Pa menggunakan jadual taburan Poisson (nilai kumalatif).
Susun nilai langkah 1-4 dalam jadual.
Kemudian lakarkan kurva OC dengan Probability of acceptance, Pa melawan mean life, θ

64. Contoh
Bina kurva OC untuk plan persampelan di mana n = 12, T = 800 h, c = 2, .
Tentukan purata hayat, θ. Untuk contoh pengiraan θ = 8000 h.
Tentukan kadar kegagalan (failure rate), λ=1/θ = 1/8000 =
Tentukan jangkaan purata bilangan kegagalan, nTλ = 12(800)(1/8000) = 1.2
(Dalam Jadual Poisson nTλ adalah nP0
Tentukan nilai probability of acceptance, Pa = 0.879

66. Susun nilai langkah 1-4 dalam jadual.

67. Kemudian lakarkan kurva OC dengan Probability of acceptance, Pa melawan mean life, θ

68. Life and Reliability Testing Plan
Since reliability testing requires the use of the product and sometimes its destruction. The type of test and the amount of testing is usually an economic decision.
Testing is normally done on the end product, however, components and parts can be tested if they are presenting problems.
Testing usually done in the laboratory, every test should be made to simulate the real environment.

69. There are three types of life test:
Failure-Terminated
Time-Terminated
Sequential

70. Failure-Terminated
These life test sample plans are terminated when a preasigned number of failures occurs to the sample.
Acceptance criteria for the lot are based on the accumulated item test times when the test is terminated.

71. Time-Terminated
This type of life-test sampling plan is terminated when sample obtains predetermined test time.
Acceptance criteria for the lot are based on the number of failures in the sample during the test time.

72. Sequential
This type of life-testing plan is sequential life-test sampling plan whereby neither the number of failures nor the time reqiured to reach a decision are fixed in advance.
Decisions depend on the accumulated results of the test.
The sequential life-test plan have the advantage that the expected test time and the expected number of failures required to reach a decision as to lot acceptability are less than the failure-terminated or the time-terminated types.

73. Test are based on one or more of the following characteristics:
Mean life – the average life of the product.
Failure rate – the percentage of failure rate per unit time or number of cycles.
Hazard rate – the instantaneous failure rate at specified time. This varies with age except in the special case of a constant failure rate wherein the failure rate and hazard rate are the same.
Reliable life – the life beyond which some specified portion of the items in the lot will survive.

74. Table 11.2 gives summary of some of the life-testing and reliability plans.

76. Life and Reliability Testing Plan
Example
Handbook H108 – US Department of Defence.
Gives sampling procedures and tables for life and realibility testing.

77. Availability and Maintainability
Availability is a time-related factor that measures the ability of a product or service to perform its designed function.
The product or service is available when it is in the operational state, which includes active and standby use.
Availability can be quantified by the ratio:

78. Maintainability
Maintainability is the ease with which preventative and corrective maintenance on a product or service can be achieved.
The best times to improve maintainability is in the design phase of a product or service.
Maintainability uses a number of different figures of merit such as
mean time to repair,
mean time to service,
repair hours per 1000 number of operating hours,
preventative maintenance cost and
downtime probability.