Minimization of Misclassification of Component Failures in a Two-Component System

In this paper we assume we are repairing two-component series systems that have failed or are malfunctioning. It is further assumed that when a system is brought into the repair shop, it is not known with certainty which component has failed. If the repairman begins repairing the wrong component, a misclassification cost is incurred. It is also assumed that some resources are available for the purchase and operation of a failure detection mechanism that, depending on the amount allocated for detection, enhances the probability of correctly detecting the failed component. A study is then made that is designed to minimize the expected cost of failure detection. Examples are included.