Optimal Replacement Problem using Alpha Series Process

Raja Sekhara Reddy K

Abstract: This paper investigates a replacement policy N for the maintenance problem with two types of failures and one repairman. In proposed model it is assumed that the system experiences with two types of failures namely repairable failures and non-repairable failures. When repairable failure occurs, the repairs will be repaired once by the repairman. The repair is not as good as new. The successive working times after repair are stochastically decreasing and form a decreasing alpha series process, while the successive repair times form an increasing alpha series process. If un-repairable failures occur, the system will be replaced by a new one. When the number of repairable failures reaches N, then the system will not be repaired anymore and will be replaced immediately. With these assumptions, average cost rate (ACR) of an optimal replacement policy N* is determined analytically and numerical results were given to strengthen the theoretical results.

Keywords: Renewal Reward theorem, Renewal Process, Alpha series Process, Replacement policy N, Long-run Average cost Rate (ACR)

How to Cite?: Raja Sekhara Reddy K, "Optimal Replacement Problem using Alpha Series Process", Volume 14 Issue 11, November 2025, International Journal of Science and Research (IJSR), Pages: 1272-1275, https://www.ijsr.net/getabstract.php?paperid=SR251115200100, DOI: https://dx.doi.org/10.21275/SR251115200100