An Optimum Component Testing Procedure for a Series System With Redundant Subsystems

Abstract

We consider the problem of optimizing component testing for a series system with redundant subsystems so as to minimize the total cost of testing given the requirements: the probability of accepting the system must be less than α if the system reliability is less than R ₀, and the probability of rejecting the system must be less than β if the system reliability is greater than R ₁. This problem was solved previously for a series system under the acceptance criterion that the total number of test failures is less than a prescribed number k. That result is extended in this paper to cover the more general case of a series system that has built-in redundancy in that it consists of subsystems each of which contains several identical components in parallel. The optimum value of k and the associated component testing times which will satisfy the above probability requirements are obtained. These requirements can be guaranteed only if R ₁ is larger than a value that depends on R ₀. The optimum testing time is shown to be independent of the individual component testing costs.

KEY WORDS:

• Component testing
• Optimization
• Series system
• Reliability
• Redundancy