Detailed and complete responses please A company wnicn nas seven delicate macnin
ID: 2964549 • Letter: D
Question
Detailed and complete responses please
A company wnicn nas seven delicate macnines tnat irequentiy DreaK clown employs twc service people with the sole task of repairing them. Each service person can repair a machine in 2.5 hours on average, with the actual service time being exponentially distributed. A newly repaired machine runs an average of 15 hours before breaking down again; the actual running time is exponentially distributed. Determine the following: (a) the expected number of machines that are operating at any given time. (b) the percentage of time that both service people will be idle, and (c) the percentage of time any given machine will be inoperative (this includes time soent waiting for renair as well as time actually being repaired).Explanation / Answer
a)Probability of machine working at a given time = 15/(15+2.5) = 6/7
=>expected number of machines working at a given time =(6/7)*7 = 6 machines
b)percentage of time both service people are idle = 100*(probability of all machines working)
=>percentage of time both service people are idle = 100*(6/7)^7 = 33.99 percent of time
c)percentage of repair time = (1/7)*100 = 14.285 percent
percentage of waiting time =100*(Probability of more than 1 machine is under repair ) = 100*(1/7)(1- 6c1(1/7)*(6/7)^5 - 6c0*(6/7)^6) = 2.955
total in operative time = 14.285 +2.955 = 17.24 percent of time
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