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International Journal of Statistika and Mathematika, ISSN: 2277- 2790 E-ISSN: 2249-8605

Volume 6, Issue 2, June 2013 pp 91-95

Research Article

A Bivariate Optimal Replacement Policy for a Repairable System Using Two Monotone Processes

A. Mallikarjuna Reddy¹, B. Venkata Ramudu², M. Bhagya Lakshmi³

^{1Professor, ³Research Scholar} Department of Mathematics, S. K. University, Anantapur-515 003, Andhra Pradesh, INDIA.

Academic Editor:  Dr. Dase R.K.

This paper studies a bivariate repairable system with one repairman is studied. Assume that the system after repair is not ‘as good as new’ and also the successive working times form a decreasing -series process, the successive repair time’s form an increasing geometric process and both the processes are exposing to Weibull failure law. Under these assumptions, we study an optimal replacement policy N in which we replace the system when the number of failures of the system reaches N. We derive an explicit expression for the long-run average cost per unit of time for the bivariate replacement policy (T,N) under which we replace the system when the number of failures  reaches N or the age of the system  reaches T or whichever occurs first. Under some mild conditions, we determine an optimal repair replacement policy N* such that the long run average cost per unit time is minimized. Numerical results are provided to support the theoretical results.