A generalised maintenance policy with age-dependent minimal repair cost for a system subject to shocks under periodic overhaul

Abstract

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur, the system has two types of failures: type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by overhaul or replacement. The cost of minimal repair depends on age. A system is overhauled when the occurrence of a type 2 failure or at age T, whichever occurs first. At the N-th overhaul, the system is replaced rather than overhauled. A maintenance policy for determining optimal number of overhauls and optimal interval between overhauls which incorporate minimal repairs, overhauls and replacement is proposed. Under such a policy, an approach which using the concept of virtual age is adopted. It is shown that there exists a unique optimal policy which minimises the expected cost rate under certain conditions. Various cases are considered.

Keywords:

• preventive maintenance
• minimal repair
• periodic overhaul
• replacement policy

Acknowledgements

The authors wish to express our 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 of their suggestions were incorporated directly in the text. This research was supported by the National Science Council of Taiwan, under Grant No. NSC96-2221-E-011-003.