2. Explain why a product or system might have an overall reliability that is low even though it is comprised of components that have fairly high reliabilities.
4. A product engineer has developed the following equation for the cost of a system component: C _ (10 P ) 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?
6. One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilities are .98, .95, .94, and .90. All of the components must function in order for the robot to operate effectively.
a. Compute the reliability of the robot.
b. Designers want to improve the reliability by adding a backup component. Due to space limitations, only one backup can be added. The backup for any component will have the same reliability as the unit for which it is the backup. Which component should get the backup in order to achieve the highest reliability?
c. If one backup with a reliability of .92 can be added to any one of the main components, which component should get it to obtain the highest overall reliability?
17. A major television manufacturer has determined that its 19-inch color TV picture tubes have a mean service life that can be modeled by a normal distribution with a mean of six years and a standard deviation of one-half year.
a. What probability can you assign to service lives of at least (1) Five years? (2) Six years? (3) Seven and one-half years?
b. If the manufacturer offers service contracts of four years on these picture tubes, what percentage can be expected to fail from wear-out during the service period?
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