Question

The failures of a testing instrument from contamination particles occur at a rate of 0.025 failure per hour. The occurrence of failures appears to satisfy the "memoryless" property.

a) Find the probability that the instrument does not fail in a 4-hour shift.

b) Suppose no failure occurs in the first shift of 4 hours. Find the probability that there is still no failure in the next shift of 4 hours.

Answer 1

This is a simple problem related to poisson's distribtiuon analysis.

We are given with failure rate of 0.025 failures per hour and we need to find the probability of no failure in 4 hour shift.

The poisson paramter () is defined as the total number of events in a unit time.

Thus in the given question

=0.025 /hour

In a poisson distribution ,the probability of occurance of x events is given by

for no failure, it means x=0

Thus we have

or,

2). Now we needno failure in 8 hours thus t=8 hours

keeping values

or at t =8 hours

or ,