1. 4. Dynamic reliability models Objectives Be able to find reliability of series, parallel, stand-by and shared load parallel systems, when the reliabilities of the components change in time Understand and learn how to compute system effectiveness measures, such as operational readiness, availability and maintainability

2. Reliability of series, parallel, standby and shared load parallel systems Series system 1 … n 2 R S (t) = R 1 (t)  …  R n (t) Assume independent components h s (t) = h 1 (t)+…+ h n (t)

3. Constant hazard rate case If Expected time to failure=(λ 1 +… λ n ) -1

4. Parallel system System survives if one component survives 1 2 n

5. Constant hazard rate case If Expected time to failure=

6. Standby systems (perfect switching) 1 2 n … Two components

7. Standby Systems: Three components t t1 t2

8. Constant hazard rate case, identical components

9. System effectiveness measures Operational readiness: probability that system is available at the beginning of the mission Availability: probability that system is operating at some particular time

10. Maintainability: Probability that a failed system will be repaired by time, t

11. Suggested reading Melchers, R., and Beck, A. T., “Time Variant-Reliability,” Engineering Design Reliability Handbook, CRC press, 2004, p. 18-1.