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Chapter 6 Time dependent reliability of components and system
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6.2 Failure rate time curve
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6.3 Reliability and Hazard functions
(6.1) (6.2) (6.3) Failure rate (instantaneous rate of failure, hazard function or hazard rate): (6.4,6.5)
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reliability at time t: The distribution function: The reliability of the component:
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Differentiation, yield
6.4 Modeling of failure Rates
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and Assuming linear variation:
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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
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6.6 Mean time before failure (MTBF)
Since all system fail after a finite time, we have (6.26)
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6.7 Series system
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Failure time of the series system is
The failure time distribution : The probability function of the failure time:
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6.7.1 Failure rate of the system
Where the failure rate of the system: The reliability can be expressed as:
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6.7.2 MTBF of the system
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6.8 Parallel System Reliability of parallel system, first seven events
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6.8.1 Failure Rate of the system
The system failure rate is given by: 6-8-2 MTBF of the system
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For special case for n=2 Where relation is used: 6-9 (k,n) systems
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Probability distribution function of the system
Failure time of the system 6.9.1 MTBF of the system
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6.10 Mixed series and parallel system
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The system failure rate is given by:
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The reliability R0 shown in fig. 6-8
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6.11 complex systems A C D B E
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Enumeration method
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No component fail 1. ABCDE 0
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6.11.2 Conditional Probability method
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C A D A B AB
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6.11.3 Cut set method Identify the minimal cut sets of the system
Model the components of each minimal cut set to be in parallel . Assume that the various cut sets are in series Find the reliabilityof the system using the parallel-series model.
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6.12 Reliability Enhancement
Series system
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Constant constrain: That is The cost involved in achieving the new system
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parallel system (6.73)
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For minimum cost: 6.13 reliability allocation- agree method
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6.87
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