Question: Exercise 1: A critical part used on a manufacturing machine has an exponential failure distribution with a mean of 1000 (operating) days. When the part

Exercise 1: A critical part used on a manufacturing machine has an exponential failure distribution with a mean of 1000 (operating) days. When the part fails, it is immediately replaced with a spare. All spares must be purchased now since the part's supplier will terminate production. The life of the machine is 3,650 (operating) days. 1. Explain why Poisson distribution can represent the number of part failures during the machine's life. Give the Poisson distribution mean. 2. If the manufacturer decides to buy four spares from the supplier, Find the probability of not running out of parts (causing the machine failure) during the machine life of 3,650 days. 3. How many spares should be purchased to guarantee a 99% reliability of no stock out resulting in machine failure? Why

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