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consider a 4 out of 5 system such that r1=0.96, r2=0.98, r3=0.93, r4=0.99 and r5=0.94. compute...

consider a 4 out of 5 system such that r1=0.96, r2=0.98, r3=0.93, r4=0.99 and r5=0.94. compute system reliability.

Math   Statistics-And-Probability   
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Answer #1

consider a 4 out of 5 system such that r1=0.96, r2=0.98, r3=0.93, r4=0.99 and r5=0.94. compute system reliability.

k out of N system

k = 4, N = 5

Since the component reliabilities are not identical, we have to consider all possible mutual exclusive and exhaustive cases to calculate the system reliability,

The value of k must be at least 4 for success.

For k = 4,

number of mutually exclusive cases = 5C4 = 5

In this case, reliability is,

For k = 5,

number of mutually exclusive cases = 5C5 = 1

In this case, reliability is,

The reliability of the 4 out of 5 system is,

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