Question

1. You, the resident industrial engineer, are evaluating a new milling machine. The sales rep states the machine will break down once every 1000 hours of operation. However, you talk to an engineer who estimated it will break down once every 500 hours of operation. You also have testing data collected for 1000 hours. During these tests, the machine broke down two times.

What is the probability of your test results if the sales rep is correct?

Answer 1

Given that the sales rep is correct, the machine is expected to break down once every 1000 hours of operation. Therefore the mean waiting of break down here is given to be 1000 hours. The waiting time for break down is therefore modelled here as:

as mean is reciprocal of parameter for exponential distribution.

The mean number of failures is given here to be 1 per thousand hours. Therefore the probability of 2 failures in the first 1000 hours is computed using Poisson distribution function here as:

Therefore 0.1839 is the required probability here.