A geometric process model for deteriorating operating system with periodic and random inspections

Abstract

In this paper, we consider a deteriorating operating system which executes a job with random working times. It is assumed that the working times form a geometric process. In Model 1, the system is checked at periodic times and also at every completion of working times to detect the failures. In Model 2, we extend Model 1 by further assuming that a preventive repair is taken when the failure is not found by periodic inspection. For both models, the explicit expressions of the total expected cost until the detection of the failure are obtained. The optimal periodic inspection policies are computed numerically.

Keywords:

• Geometric process
• periodic inspection
• random inspection
• preventive repair
• expected cost

Notes

No potential conflict of interest was reported by the authors.

School of Economics and Management, Yanshan University, Qinhuangdao, China.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 71071133] and in part by Natural Science Foundation of Hebei Province, China [grant number G2012203136], and is supported in part by Key Project of Natural Research of University of Hebei Province, China [grant number ZH2012021] and the National Natural Science Foundation of China [garnt number 11301458].