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

Abstract

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.

Keywords:

• two-unit system
• periodic replacement policy
• discrete replacement policy
• minimal repair
• failure rate interaction
• external shocks

Acknowledgements

The authors express their appreciation to an anonymous referee and to the associate editor for their valuable comments and suggestions, which greatly enhanced the clarity of the article. All the suggestions were incorporated directly in the text.