A system is built using two independent components, X and Y

MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

A system is built using two independent components, X and Y. The system designer may connect the components either in series (the system works only if both X and Y work) or in parallel (the system works if at least one of X or Y works). Assume

P(X)=r_1

and

P(Y)=r_2

, where

0<r_1,r_2<1

. (i) Define, in the context of reliability analysis, what is meant by a series system and a parallel system. (ii) Derive an expression for the reliability of the series system in terms of

r_1

and

r_2

. (iii) Derive an expression for the reliability of the parallel system in terms of

r_1

and

r_2

. (iv) Compare the two expressions obtained in parts (ii) and (iii) and explain why, for any

0<r_1,r_2<1

, the parallel system is at least as reliable as each individual component, whereas the series system is at most as reliable as the less reliable component.

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