You're a production engineer for a small manufacturing facility that contains three machines (M1, M2, M3) that are arranged in series. That is, raw material enters M, and leaves M3 as a finished part....

Extracted text: You're a production engineer for a small manufacturing facility that contains three machines (M1, M2, M3) that are arranged in series. That is, raw material enters M, and leaves M3 as a finished part. Time between failures (in days) for machine M; is described with random variables T;, which are assumed to follow exponential distributions with the parameters found in the table below. The reliability, R;(t), or the probability that failure occurs after time t, of Mi is calculated as 1 - F;(t). And recall that F;(t) is the cumulative probability distribution for Mi evaluated at time t. a. Calculate the average failure time for the three machines. b. Calculate R;(14), or reliability at 14 days of operation, for each machine. Calculate the system reliability, Rs(14), for this series system (that is, the probability that raw material can enter M, and leave M3, at 14 days of operation). с. M1 М M3 M1 M2 M3 0.026 0.012 0.019