Problem 2 N identical components subjected to a test that is

Problem 2 N identical components subjected to a test that is terminated at a predetermined time T. At the end of the test we are told that k of the N components failed during the test, but the failure times are not revealed. Assume that failure times of these components follow the same exponential distribution with a constant failure rate. Use the information provided by this test to estimate the failure rate of these component.

Solution

There are N identical components.

Total time = T

Defective =k

defective unit per time T = k/T per unit time

If we let W the waiting time between two defectives, then we can expect on an average

t = 1/k/T = T/k minute between two defectives

As W is exponentially distributed

pdf is given by

f(W) =