An ideal way of obtaining an optimal inspection permutation for a system with components connected in series

Abstract

The problem of an inspection permutation or inspection strategy (first discussed in a research paper in 1989 and reviewed in another research paper in 1991) is revisited. The problem deals with an N‐component system whose times to failure are independent but not identically distributed random variables. Each of the failure times follows an exponential distribution. The components in the system are connected in series such that the failure of at least one component entails the failure of the system. Upon system failure, the components are inspected one after another in a hierarchical way (called an inspection permutation) until the component causing the system to fail is identified. The inspection of each component is a process that takes a non‐negligible amount of time and is performed at a cost. Once the faulty component is identified, it is repaired at a cost, and the repair process takes some time. After the repair, the system is good as new and is put back in operation. The inspection permutation that results in the maximum long run average net income per unit of time (for the undiscounted case) or maximum total discounted net income per unit of time (for the discounted case) is called the optimal inspection permutation/strategy. A way of determining an optimal inspection permutation in an easier fashion, taking advantage of the improvements in computer software, is proffered. Mathematica is used to showcase how the method works with the aid of a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.