A workstation is used until it fails and then it is sent out for repair. The time between failures, or the length of time the workstation functions until it needs repair, is a random variable T. Assume the times between failures, T1, T2, Tn... of the workstations available are independent random variables that are identically distributed. For , let the number of workstations that have failed be .
(a) If the time between failures of each workstation has an exponential PDF, then what type of process is N (t)?
(b) Assume that you have just purchased 10 new workstations and that each has a 90- day warranty. If the mean time between failures (MTBF) is 250 days, what is the probability that at least one workstation will fail before the end of the warranty period?