Extended optimal replacement policy for a system subject to non-homogeneous pure birth shocks |
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Authors: | Shey-Huei Sheu Yen-Luan Chen Chin-Chih Chang Zhe George Zhang |
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Affiliation: | 1. Department of Statistics and Informatics Science, Providence University, Taichung 433, Taiwan;2. Department of Industrial Management, National Taiwan University of Science and Technology, Taipei 106, Taiwan;3. Department of Marketing Management, Takming University of Science and Technology, Taipei 114, Taiwan;4. Department of Decision Sciences, Western Washington University, Bellingham, WA 98225-9077, USA;5. Beedie School of Business, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 |
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Abstract: | This article studies the optimal replacement policy with general repairs for an operating system subject to shocks occurring to a non-homogeneous pure birth process (NHPBP). A shock causes that the system experiences one of two types of failures: type-I failure (minor failure) is rectified by a general repair, or type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a bivariate replacement policy (n, T) under which the system is replaced at planned life age T, or at the nth type-I failure, or at any type-II failure, whichever occurs first. The optimal replacement schedule which minimizes the expected cost rate model is derived analytically and discussed numerically. |
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