A laboratory has η test locations for life testing a particular type of electronic equipment….

A laboratory has η test locations for life testing a particular type of electronic equipment. To conserve time, it is decided to place an item in each test location and test all η items simultaneously. As soon as an item fails, it is immediately replaced by a new item and the system is observed until the di  failure occurs. Suppose that the failure times are exponentially distributed. Let S be the random variable representing the time to cessation of testing. Show that S is sufficient for the failure rate A. Derive the distribution of S and give an exact 9 5% confidence interval for λ when η = 25, d = 5, and the fifth failure occurs 407 hours after the start of the experiment.