Therefore, 2.407 days go by, on average, since Peter has no pending files until the same situation occurs again. (d) What should John think about the way Peter works? Peter generates a daily saving of 3.8 3.476921 = 0.323079 10.18 Files Proceedings Therefore, John should think that Peter's way of working is more efmc.cm inan the standard way of working. m7 Controlling Machinery The control system for a certain machine comprises two independent controls, A and B. This system is activated for every hour the machine operates to check that the machine works according to suitable parameters. The controls have a limited life. Indeed, control A has been replaced 52 times in the last 1,300 h of operation, whereas control B has been substituted 39 times in the same time. Every time the system is activated, apart from controlling the machine, it warns that one (or both) of the controls has failed. The faulty control is replaced before the system is next activated. When one of the two controls is replaced, its reli- ability is lesser because it has not been verified. Specifically, it is considered that when the system is next activated, the reliability of the substituted control is half its normal value. Replacing control A entails a cost of $70 and of $50 for replacing control B. (a) Consider the problem according to a Markov chain (b) What is the hourly cost of the control system? (c) How many hours must pass on average since both controls are replaced at the same time until both fail again at the same time? (d) If 10 h have passed since both controls were changed at the same time and neither has failed since then, with what probability will the system in each state be in after 2 h's time