(Solved): 51. Mean Time Between Failures. The mean time between failures (MTBF) is a com- mon metric used to ...

51. Mean Time Between Failures. The mean time between failures (MTBF) is a com- mon metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribu- tion with a mean of 12.7 hours. a. What is the probability that the automated manufacturing system runs for more than 15 hours without a failure? b. What is the probability that the automated manufacturing system runs for eight or fewer hours before failure? c. What is the probability that the automated manufacturing system runs for more than six hours but less than 10 hours before a failure?