Extended optimal age-replacement policy with minimal repair of a system subject to shocks |
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| Institution: | 1. School of Management and Economics, Beijing Institute of Technology, Beijing, China;2. Beijing Institute of Astronautical System Engineering, Beijing, China;3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China;4. School of Petroleum Engineering, Yangtze University, Wuhan, China;5. AVIC China Aero-Polytechnology Establishment, Beijing, China;1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;2. Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819, China;3. China Northeast Architectural Design & Research Institute Co., LTD, Shenyang 110166, China;4. Department of Mechanical & Industrial Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA |
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| Abstract: | An operating system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur the system has two types of failure: type I failure (minor) or type II failure (catastrophic). A generalization of the age replacement policy for such a system is proposed and analyzed in this study. Under such a policy, if an operating system suffers a shock and fails at age y (⩽t), it is either replaced by a new system (type II failure) or it undergoes minimal repair (type I failure). Otherwise, the system is replaced when the first shock after t arrives, or the total operating time reaches age T (0 ⩽ t ⩽ T), whichever occurs first. The occurrence of those two possible actions occurring during the period 0, t] is based on some random mechanism which depends on the number of shocks suffered since the last replacement. The aim of this paper is to find the optimal pair (t1, T1) that minimizes the long-run expected cost per unit time of this policy. Various special cases are included, and a numerical example is given. |
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