Question 2) (55 points) A production process has a machine that deteriorates rapidly in both quality and output under heavy usage during the week. Therefore, the machine is inspected at the end of each week. After each inspection, the condition of the machine is noted and classified into one of three possible states: State 1: Good as new, State 2: Operable and State 3: Inoperable. If the machine is "Good as new" when it is inspected, it will be "Good as new" at the next inspection epoch with probability (w.p) 0.2, and it will be "Operable" w.p. 0.4. If the machine is "Operable" when it is inspected, it will be "Good as new" at the next inspection epoch w.p.0.1, and will be "Operable" w.p. 0.1. Once it is found in the "Inoperable"condition at the end of a week, the machine is replaced with a new machine before the start of the new week, and it starts the week as "Good as new". a) (10 points) Given that the machine is good as new at the end of the current week, calculate the average number of weeks that it will stay in good condition before it deteriorates to either to "Operable" or to "Inoperable" condition. b) (10 points) Suppose that the machine is in "Operable" condition at the start of a week, what is the probability that it will be in "Operable" condition for the following two weeks before it goes back to "Good as new" condition or "Inoperable" condition. c) (15 points) What is the long-term fraction of weeks that the machine would be "Inoperable". d) (10 points) Suppose that we observe the machine for 50 weeks, which may be considered as long term. What would be the average number of weeks that the machine is "Good as new"? e) (10 points) Suppose that maintaining a good as new machine costs 80 KD per week, and maintaining a operable machine costs 120 KD per week. When a machine becomes inoperable the replacement cost is 350 KD per week. Calculate the average replacement cost per week on the long term. Question 2) (55 points) A production process has a machine that deteriorates rapidly in both quality and output under heavy usage during the week. Therefore, the machine is inspected at the end of each week. After each inspection, the condition of the machine is noted and classified into one of three possible states: State 1: Good as new, State 2: Operable and State 3: Inoperable. If the machine is "Good as new" when it is inspected, it will be "Good as new" at the next inspection epoch with probability (w.p) 0.2, and it will be "Operable" w.p. 0.4. If the machine is "Operable" when it is inspected, it will be "Good as new" at the next inspection epoch w.p.0.1, and will be "Operable" w.p. 0.1. Once it is found in the "Inoperable"condition at the end of a week, the machine is replaced with a new machine before the start of the new week, and it starts the week as "Good as new". a) (10 points) Given that the machine is good as new at the end of the current week, calculate the average number of weeks that it will stay in good condition before it deteriorates to either to "Operable" or to "Inoperable" condition. b) (10 points) Suppose that the machine is in "Operable" condition at the start of a week, what is the probability that it will be in "Operable" condition for the following two weeks before it goes back to "Good as new" condition or "Inoperable" condition. c) (15 points) What is the long-term fraction of weeks that the machine would be "Inoperable". d) (10 points) Suppose that we observe the machine for 50 weeks, which may be considered as long term. What would be the average number of weeks that the machine is "Good as new"? e) (10 points) Suppose that maintaining a good as new machine costs 80 KD per week, and maintaining a operable machine costs 120 KD per week. When a machine becomes inoperable the replacement cost is 350 KD per week. Calculate the average replacement cost per week on the long term