Question

A critical component on a submarine has an operating lifetime that is exponentially distributed with mean 0.50 years. As soon as a component fails, it is replaced by a new one having statistically identical properties. What is the smallest number of spare components that the submarine should stock if it is leaving for a one-year tour and wishes the probability of having an inoperable unit caused by failures exceeding the spare inventory to be less than 0.02?

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Answer 1

Answer:-

Given that:-

A critical component on a submarine has an operating lifetime that is exponentially distributed with mean 0.50 years. As soon as a component fails, it is replaced by a new one having statistically identical properties.

What is the smallest number of spare components that the submarine should stock if it is leaving for a one-year tour and wishes the probability of having an inoperable unit caused by failures exceeding the spare inventory to be less than 0.02?

Mean = 0.50

Let X(t) be the no .of spare components that the submarine has been used up to time t, and X(t) is a poisson process.

The probability that an inoperable exceeding the spare inventory to be less.than 0.02

Can be determine by

for  

for

for

for

for

So, the smallest n value i 5.