Examples

Reliability: Series, parallel, series

Suppose a process has internal components arranged like this:

Write for the event that component succeeds, and for the event that it fails.

The success probabilities for each component are given in the chart:

1	2	3	4	5
92%	89%	95%	86%	91%

Find the probability that the entire system succeeds.

Solution

(1) Conjoin components 2 and 3 in series.

Compute:

Therefore:

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(2) Conjoin components (2-3) with 4 and 5 in parallel.

Compute for the complement (failure) first:

Flip back to success:

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(3) Conjoin components 1 with (2-3-4-5) in series.

Compute: