Chapter 6 Time dependent reliability of components and system
6.2 Failure rate time curve
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)
reliability at time t: The distribution function: The reliability of the component:
Differentiation, yield 6.4 Modeling of failure Rates
and Assuming linear variation:
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
6.6 Mean time before failure (MTBF) Since all system fail after a finite time, we have (6.26)
6.7 Series system
Failure time of the series system is The failure time distribution : The probability function of the failure time:
6.7.1 Failure rate of the system Where the failure rate of the system: The reliability can be expressed as:
6.7.2 MTBF of the system
6.8 Parallel System Reliability of parallel system, first seven events
6.8.1 Failure Rate of the system The system failure rate is given by: MTBF of the system
For special case for n=2 6-9 (k,n) systems Where relation is used:
Probability distribution function of the system MTBF of the system Failure time of the system
6.10 Mixed series and parallel system
The system failure rate is given by:
The reliability R 0 shown in fig. 6-8
6.11 complex systems A B C D E
Enumeration method
No component fail 1. ABCDE 0
Conditional Probability method
A C D AB A B
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.
6.12 Reliability Enhancement Series system
Constant constrain: That is The cost involved in achieving the new system
parallel system (6.73)
For minimum cost: 6.13 reliability allocation- agree method
6.87