Hatmobile Hatman protects the Gotburg City at night. Busy fighting against various scheming forces, he is looking to hire a mechanic with analytics foundation to take care of his favourite Hatmobile. The engine in Hatmobile fails frequently, and the exact probability of failure depends on the engine's age, as follows: If the engine fails while Hatman is driving Hatmobile at night, the engine must be replaced on an emergency basis. This means the Hatmobile is out of commission for the rest of the day, putting residents in Gotburg City in danger. Depending on how badly Hatmobile is damaged, the replacement cost is uniformly distributed between $5,000 and $10,000. In this case, you start the next day with a fresh engine. Day of Use Chance of Engine Failure 1 ("Fresh) 3% 2 7% 3 12% 4 20% 34% 40% 6 or more Hatmobile (continued...) Another option is to replace the engine at the start of each day, regardless of whether it had failed the previous night. This is much cheaper than the emergency replacement, costing only $2,250, and allows Hatman to start that night with a fresh engine. Hatman has so many things to take care of and unlike the rich Batman who has Alfred and a lot of money, he does not have a butler to rely on and his budget is tight. You agree with Hatman and want to help him develop the best replacement strategy. Your strategy is to replace each engine after n days of use, or as soon as it fails, whichever comes first. What is the best choice of n out of the possibilities 1, 2, 3, 4, 5 and 6? Simulate each policy for an operating period of 100 days. Assume that you start the 100-day period with a scheduled replacement. For the best policy, what is the average number of scheduled and emergency replacements in the 100-day period? Hatmobile Simulation approach What is the decision variable? Range of values? >What are the input random variables? Distributions? >What is the output random variable? Metrics of interest?