It is generally known that redundancy at the component level is more effective t

Question

It is generally known that redundancy at the component level is more effective than redundancy at the system level in improving the overall system reliability using the same number of components. Consider two alternative configurations consisting of three redundant components A, B, and C as shown below. Assume that all components have the same reliability of 0.99. In both cases, find the overall system reliability and make a recommendation as to which of the two approaches should be used.

Explanation / Answer

here reliabilty of left system P(R) =P(at least one of top and bottom row works)

=1-P(none of both will work) =1-P(top row will not work*bottom row will not work)

=1-((1-top row will work)*(1-bottom row will work)

=1-((1-0.993)(1-0.99)3 ) =0.999118

reliabilty of right system =P(first block works*second block works *third block works)

=P((at least A or B works)*(at least A or B works)*(at least A or B works))

=P((1-P(both does not work)*(1-P(both does not work)*(1-P(both does not work)

=(1-0.01*0.01)*(1-0.01*0.01)*(1-0.01*0.01) =0.9997

therefore right system is more reliable   

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