Cost evaluation for an imperfect-repair model with random repair time

Abstract

A repair can bring the state of a failed system to a level which is somewhere between new and prior to repair. In most repair models proposed in the literature so far, the repair time is assumed to be negligible, and so the length of repair time has not been a factor in developing the maintenance models. However, it is more realistic to assume that it takes a certain amount of repair time. In this paper, we discuss an imperfect repair model with random repair times. We first derive a formula that can be used to evaluate the expected numbers of perfect and minimal repairs. The expected costs during (0, t], t>0 fixed, are also evaluated based on the convolution of the failure and repair distributions of the system.

Keywords:

• Cost evaluation
• Imperfect-repair model
• Repair time

Acknowledgements

The authors thank the anonymous referees for helpful comments and valuable suggestions, which have improved the presentation of this paper considerably. This work was supported by Korea Research Foundation Grant (KRF-99-042-d00022-d1201).

Jae-Hak Lim is an associate professor at Hanbat National University, Korea. He received his BS(1983) and MS(1986) in Computer Science and Statistics from Chungnam National University, and PhD(1994) in Statistics from University of Nebraska-Lincoln, USA. His research areas include life testing and reliability, maintenance policy, and industrial statistics.

Dae-Kyung Kim is an associate professor at Chonbuk National University, Korea. He received his MS(1985) and PhD(1994) in Statistics from Dongguk University, Korea. His research interests include computational methods, reliability theory and applications, and maintenance policy.

Dong Ho Park is a full professor at Hallym University since 1993. He received his BS(1968) in Applied Mathematics from Seoul National University, and MS(1980) and PhD(1982) in Statistics from Florida State University. He was formerly an associate professor at University of Nebraska-Lincoln, USA, until 1995 and was president of the Korean Reliability Society. He has published on reliability theory, accelerated life testing, software reliability and system maintenance policy in a wide variety of international journals. He is a member of ASA, IMS, ASQ, ISI, IEICE, and IEEE.