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DYNAMIC ANALYSIS OF A MULTIVARIATE REWARD PROCESS DEFINED ON THE UMCP WITH APPLICATION TO OPTIMAL PREVENTIVE MAINTENANCE POLICY PROBLEMS IN MANUFACTURING

Published online by Cambridge University Press:  28 March 2013

Jia-Ping Huang  and
Ushio Sumita
Jia-Ping Huang
Affiliation:
Department of Econometrics and OR, FEWEB, VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands E-mail: j.huang@vu.nl
Ushio Sumita
Affiliation:
Division of Policy and Planning Sciences, Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8573, Japan E-mail: sumita@sk.tsukuba.ac.jp
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Abstract

The unified multivariate counting process (UMCP), previously studied by the same authors, enables one to describe most of the existing counting processes in terms of its components, thereby providing a comprehensive view for such processes often defined separately and differently. The purpose of this paper is to study a multivariate reward process defined on the UMCP. By examining the probabilistic flow in its state space, various transform results are obtained. The asymptotic behavior, as t→∞, of the expected univariate reward process in a form of a product of components of the multivariate reward process is studied. As an application, a manufacturing system is considered, where the cumulative profit given a preventive maintenance policy is described as a univariate reward process defined on the UMCP. The optimal preventive maintenance policy is derived numerically by maximizing the cumulative profit over the time interval [0, T].

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013 , pp. 187 - 208
Copyright
Copyright © Cambridge University Press 2013

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