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The Avery Co$.$ factory has been having a maintenance problem with the control panel for one of its production processes. This control panel contains four identical electromechanical relays that have been the cause of the trouble. The problem is that the relays fails fairly frequently, thereby forcing the control panel $($and the production process it controls$)$ to be shut down while a replacement is made. The current practice is is to replace the relay only when they fail. The average total cost of doing this has been $$3\mathrm{.}19$ per hour. To attempt to reduce this cost, a proposal has been made to replace all four relays whenever any one of them fails to reduce the frequency with which the control panel must be shut down. Would this actually reduce the cost?

The pertinent data are the following. For each relay, the operating time until failure has approximately a uniform distribution from $1,000$ to $2,000$ hours. The control panel must be shut down for one hour to replace one relay or for two hours to replace one relay or for two hours to replace all four relays. The total cost associated with shutting down the control panel and replacing relays is $$1,000$ per hour plus $$200$ for each new relay.

Use simulation on a spreadsheet to evaluate the cost of the proposal and compare it to the current practice. Use ASPE $($or Microsoft Excel in general$)$ to perform $1,000$ trials $($where the the end of each trial coincides with the end of a shutdown of the control panel$)$ and determine the average cost per hour.

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