Arithmetic Mean and Reliability
PROBLEMS FOR RELAIBILITY 1. Consider the following system: Determine the probability that the system will operate under each of these conditions: a. The system as shown. b. Each system component has a backup with a probability of .90 and a switch that is 100 percent reliable. c. Backups with .90 probability and a switch that is 99 percent reliable.Solutions 1. a. P(operate) = .92 = .81 .9
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b. [.90 + .10(.90)] [.90 + .10(.90)] = .9801 c. [.90 + .99(.10)(.90)]2 = .9783 2. A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and two have a probability of .99. What is the overall probability that the product will function properly? Solution: .96 x .96 x .99 x .99 = .9033 3. A system consists of three identical components. In order for the system to perform as intended, all of the components must perform. Each has the same probability of performance. If the system is to have a .92 probability of performing, what is the minimum probability of performing needed by each of the individual components?3. X3 = .92x = .9726 4. A product engineer has developed the following equation for the cost of a system component: C = (10P)2 where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate for the system to operate. The engineer can spend $173 for the two components. To the nearest two decimal places, what is the largest component probability that can be achieved?4. C = (10P) 2 per component 2 (10P) 2 = 173 100P2 = 86.5 P2 = .865 P = .93 5. The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .97, and the
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b. [.90 + .10(.90)] [.90 + .10(.90)] = .9801 c. [.90 + .99(.10)(.90)]2 = .9783 2. A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and two have a probability of .99. What is the overall probability that the product will function properly? Solution: .96 x .96 x .99 x .99 = .9033 3. A system consists of three identical components. In order for the system to perform as intended, all of the components must perform. Each has the same probability of performance. If the system is to have a .92 probability of performing, what is the minimum probability of performing needed by each of the individual components?3. X3 = .92x = .9726 4. A product engineer has developed the following equation for the cost of a system component: C = (10P)2 where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate for the system to operate. The engineer can spend $173 for the two components. To the nearest two decimal places, what is the largest component probability that can be achieved?4. C = (10P) 2 per component 2 (10P) 2 = 173 100P2 = 86.5 P2 = .865 P = .93 5. The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .97, and the