1. Chapter 6 Time dependent reliability of components and system

2. 6.2 Failure rate time curve

3. 6.3 Reliability and Hazard functions Reliability: (6.1) (6.2) (6.3) Failure rate (instantaneous rate of failure, hazard function or hazard rate): (6.4,6.5)

4. reliability at time t: The distribution function: The reliability of the component:

5. Differentiation, yield 6.4 Modeling of failure Rates

6. and Assuming linear variation:

9. 6.5 Estimation of failure rate from emperical data The estimate reliability function at time t: (6.23) The failure rate can be computed as (6.24) example:6.1

12. 6.6 Mean time before failure (MTBF) Since all system fail after a finite time, we have (6.26)

17. 6.7 Series system

18. Failure time of the series system is The failure time distribution : The probability function of the failure time:

19. 6.7.1 Failure rate of the system Where the failure rate of the system: The reliability can be expressed as:

20. 6.7.2 MTBF of the system

21. 6.8 Parallel System Reliability of parallel system, first seven events

22. 6.8.1 Failure Rate of the system The system failure rate is given by: 6-8-2 MTBF of the system

23. For special case for n=2 6-9 (k,n) systems Where relation is used:

24. Probability distribution function of the system 6.9.1 MTBF of the system Failure time of the system

25. 6.10 Mixed series and parallel system

26. The system failure rate is given by:

27. The reliability R 0 shown in fig. 6-8

28. 6.11 complex systems A B C D E

29. 6.11.1 Enumeration method

30. No component fail 1. ABCDE 0

31. 6.11.2 Conditional Probability method

33. A C D AB A B

34. 6.11.3 Cut set method 1.Identify the minimal cut sets of the system 2.Model the components of each minimal cut set to be in parallel. 3.Assume that the various cut sets are in series 4.Find the reliabilityof the system using the parallel-series model.

37. 6.12 Reliability Enhancement 6.12.1 Series system

39. Constant constrain: That is The cost involved in achieving the new system

40. 6.12.2 parallel system (6.73)

43. For minimum cost: 6.13 reliability allocation- agree method

47. 6.87