A particulate monitor has a power supply consisting of two batteries in parallel

Question

A particulate monitor has a power supply consisting of two batteries in parallel. Either battery is adequate to operate the monitor. However, since the failure of one battery places an added strain on the other, the conditional probability that the second battery will fail, given the failure of the first, is greater than the probability that the first will fail. On the basis of testing it is known that 7% of the monitors in question will have at least one battery failed by the end of their design life, whereas in 1% of the monitors both batteries will fail during the design life. (a) Calculate the battery failure probability under normal operating conditions 6 Introduction to Reliablity Engineering b) Calculate the conditional probability that the battery will fail, given that the other has failed.

Explanation / Answer

a)

Let A: first battery fails

event B : second battery fails

P(AUB) =0.07 (given)

P(AnB) =0.01 (given)

P(AuB) =P(A)+P(B) -P(AnB)

0.07 =P(A) +P(B) -0.01

0.07+0.01 =P(A)+P(B)

0.08 =P(A)+P(B)

both batteries are similar,so prob of failing of either is same

So P(A)=P(B)

Hence

0.08 =P(A)+P(A)

0.08 =2P(A)

P(A) =0.08/2

P(A) =0.04

So,P(A)=P(B) =0.04

part b)

P(B|A) =P(BnA)/P(A)

               = 0.01/0.04

               =0.25

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