The subject of Reliability Theory lies on the interface of Statistics and Engine

Question

The subject of Reliability Theory lies on the interface of Statistics and Engineering and concerns the performance characteristics of engineered systems. Two of the best known system designs are the "series system, " which works as long as all of its components are working, and the parallel system, " which works as long as at least one of its components is working. Suppose such systems have components that work independently, each with probability p. (a) Calculate the probability that a series system with n components will work. (b) Calculate the probability that a parallel system with n components will work.

Explanation / Answer

a) Probability that a series system with n components will work

= Probability that each of the element in the series system works

= p*p*p........... n times

= pn

Therefore pn is the required probability that the series system will work

b) Probability that a parallel system with n components work

= 1 - Probability that the parallel system will not work

= 1 - Probability that each of the n components dont work

= 1 - (1-p)n

Therefore the required probability that the parallel system will work is given as: 1 - (1-p)n

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