An extended optimal replacement model of systems subject to shocks |
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| Institution: | 1. Department of Statistics, National Taichung Institute of Technology, 129 Sec. 3, San-min Road, Taichung 404, Taiwan;2. Department of Industrial Management, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 107, Taiwan;3. Department of Decision Sciences, Western Washington University, Bellingham, WA 98225-9077, USA;4. Faculty of Business Administration, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;1. Rotterdam School of Management, Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands;2. Erasmus School of Economics, Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands;1. Industrial and Systems Engineering Department, Rutgers University, NJ, USA;2. Department of Computer Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand;3. Information Sciences and Technology, Penn State Berks, PA, USA;1. Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China, China;2. The Israel Electric Corporation, P.O. Box 10, Haifa 31000, Israel;3. University of Massachusetts, Dartmouth, MA 02747, USA;1. Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China, China;2. The Israel Electric Corporation, P. O. Box 10, Haifa 31000, Israel;3. University of Massachusetts, Dartmouth, MA 02747, USA;1. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA;2. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China;3. Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA |
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| Abstract: | A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur a system has two types of failures: type I failure (minor failure) is rectified by a minimal repair, whereas type II failure (catastrophic failure) is removed by replacement. The probability of a type II failure is permitted to depend on the number of shocks since the last replacement. This paper proposes a generalized replacement policy where a system is replaced at the nth type I failure or first type II failure or at age T, whichever occurs first. The cost of the minimal repair of the system at age t depends on the random part C(t) and deterministic paper c(t). The expected cost rate is obtained. The optimal n1 and optimal T1 which would minimize the cost rate are derived and discussed. Various special cases are considered and detailed. |
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