Recall the model of the manufacturing system in Prob. 1.22 with five machines that are sub...

Recall the model of the manufacturing system in Prob. 1.22 with five machines that are subject to breakdowns, and s repairmen. Suppose that the shop has not yet been built and that in addition to deciding how many repairmen to hire, management has the following two decisions to make:

(a) There is a higher-quality “deluxe” machine on the market that is more reliable, in that it will run for an amount of time that is an exponential random variable with mean 16 hours (rather than the 8 hours for the standard machine). However, the higher price of these deluxe machines means that it costs the shop $100 (rather than $50) for each hour that each deluxe machine is broken down. Since deluxe machines work no faster, the shop will still need five of them. Assume also that the shop cannot purchase some of each kind of machine, i.e., the machines must be either all standard or all deluxe.

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(b) Instead of hiring the standard repairmen, the managers have the option of hiring a team of better-trained “expert” repairmen, who would have to be paid $15 an hour (rather than the $10 an hour for the standard repairmen) but who can repair a broken machine (regardless of whether it is standard or deluxe) in an exponential amount of time with a mean of 1.5 hours (rather than 2 hours). The repairmen hired must be either all standard or all expert.

Use the coding in Table 12.28 to perform a full 2³ factorial experiment, replicate n = 5 times, and compute 90 percent confidence intervals for all expected main and interaction effects. Each simulation run is for 800 hours and begins with all five machines in working order. Make all runs independently. What are your conclusions?

TABLE 12.28 Coding chart for the generalized machine-breakdown model