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Reliability problem:industrial robots

One of the industrial robots designed by a leading producer of servomechanisms has four major components. Their reliabilities are .98, .95, .94, and .90. All of the components must function in order for the robot to operate effectively. The reliability of the robot is .7896.

Designers want to improve the reliability by adding a backup component. Due to space limitations, only 1 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? Answer is .90 just need to find out the steps/methods to attain it.

Also, if one backup with the reliability of .92 can be added to any one of the main components, which component should get it to obtain highest overall reliability?

Solution Summary

This posting contains solution to following problem on component reliability.