IE 305 - Assignment 6 (Reliability and Maintainability) Problem 1: Repairs arrive at a small-engine repair shop in a totally random fashion at the rate of 10 per day. 1. What is the average number of jobs that are received daily at the repair shop. 2. What is the probability that no jobs will arrive during any 1 hour, assuming that the ship is open 8 hours a day? Problem 2: Cars arrive at a gas station randomly every 2 minutes, on the average. 1. Determine the probability that the interarrival time of cars does not exceed 1 minute. 2. Determine the probability that the interarrival time of cars is 5 minutes at most. Problem 3: A device has a constant failure rate of = 0:02 failures per hour. 1. What is the probability that it will fail during the first 10 hours of operations? 2. Suppose that the device has been successfully operated for 100 hours. What is the probability that it will fail during the next 10 hours of operations? Problem 4: The lifetimes of two independent components have hazard functions r(t) = 1 and (t) = 2;t 20. Find the survivor and the hazard functions for the system lifetime, and the mean time to system failure in the following two cases: 1. the two components are arranged in series. 2. the two components are arranged in parallel