Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks

This study presents an extended replacement policy for a two-unit system which is subjected to shocks and exhibits failure rate from interaction. The external shocks that affect the system are of two types. A type I shock causes a minor failure of unit-A and the damage that is caused by such a failure affects unit-B, whereas a type II shock causes a total failure of the system (catastrophic failure). All unit-A failures can be recovered by making minimal repairs. The system also exhibits the interaction between the failure rates of units: a failure of any unit-A causes an internal shock that increases the failure rate of unit-B, whereas a failure of a unit-B causes instantaneous failure of unit-A. The goal of this study is to derive the long-run cost per unit time of replacement by introducing relative costs as a factor in determining optimality; then, the optimal replacement period, T*, and the optimal number of unit-A failures, n*, which minimise that cost can be determined. A numerical example illustrates the method.