A note on replacement policy for a system subject to non-homogeneous pure birth shocks

• Published in: European journal of operational research Vol. 216; no. 2; pp. 503 - 508
• Main Authors: Sheu, Shey-Huei, Chang, Chin-Chih, Zhang, Zhe George, Chien, Yu-Hung
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.01.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Age; Age replacement; Algorithms; Applied sciences; Birth; Birth process; Exact sciences and technology; Failure; Maintenance; Mathematical functions; Mathematical models; Operating systems; Operational research; Operational research and scientific management; Operational research. Management science; Operations research; Optimization; Policies; Reliability; Reliability theory. Replacement problems; Repair; Studies; Maintenance; Reliability; Repair; Birth process; Age replacement; Optimization; Replacement problem; Optimal policy; Replacement; Homogeneous process; Failures; Modeling; Function decomposition; Cost function; Age; Operating system
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.07.056

► A system is subject to non-homogeneous pure birth process shocks. ► Two types of failures are removed by a general repair or replacement. ► The expected cost functions are derived. ► Optimal policy structure is characterized. ► Previous models are special cases of our general model. A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.