Title: Optimal replacement period with cumulative repair cost limit under a cumulative damage model

Authors: Min-Tsai Lai; Chung-Ho Chen

Addresses: Department of Business Administration, Southern Taiwan University of Science and Technology, No.1, Nan-Tai street, Yung-Kung District 710, Tainan City, Taiwan ' Department of Management and Information, Southern Taiwan University of Science and Technology, No.1, Nan-Tai street, Yung-Kung District 710, Tainan City, Taiwan

Abstract: In this paper, a periodic replacement policy for a system under a cumulative shock damage process is presented; this policy includes the concept of a cumulative repair cost limit. When an external shock occurs, this shock can be divided into two types. Each type-1 shock causes some damage to the system; these damages are additive, and the system goes into serious failure when the total damage has exceeded a failure level K. A type-2 shock causes the system to experience a minor failure that can be corrected by minimal repair. When a minor failure occurs, the repair cost will be evaluated, and the minimal repair is executed if the accumulated repair cost is less than a predetermined limit L. The system is replaced anticipatively at scheduled time T, or at the jth minor failure (j < n) at which the accumulated repair cost exceeds a predetermined limit L, or any serious failure. The long-term expected cost per unit time is formulated by introducing relative costs. By minimising that cost, the optimal period T* is also verified finite and unique under certain conditions.

Keywords: periodical replacement policy; cumulative damage model; cumulative repair cost limit; shock models; optimisation; modelling; system failure.

DOI: 10.1504/IJISE.2017.083185

International Journal of Industrial and Systems Engineering, 2017 Vol.26 No.1, pp.133 - 147

Received: 14 Mar 2015
Accepted: 22 May 2015

Published online: 22 Mar 2017 *

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