Title: A bivariate replacement policy for system in an increasing failure rate model with double repair cost limits

Authors: Min-Tsai Lai

Addresses: Department of Business Administration, Southern Taiwan University of Science and Technology, No. 1, Nan-Tai street, Yungkang Dist., Tainan City 710, Taiwan

Abstract: This paper proposes a bivariate (T, L2) replacement policy with double repair-cost limits for a system subject to increasing failure rate model. External shocks are divided into two types: type-I shock and type-II shock. Each type-II shock makes the system suffer a minor failure, while each type-I shock increases the failure rate of the system by a certain amount and it will induce the system into critical failure. When a minor failure occurs, the repair cost is evaluated and minimal repair is executed if the repair cost is less than a single repair-cost limit L1 and the accumulated repair cost is less than a cumulative repair-cost limit L2, otherwise, the system is replaced by a new one. In addition, the system is replaced at scheduled time T or at critical failure. By formulating the optimisation problem, the optimal T* and L2* which minimise the long-run expected cost per unit time are found, respectively. We develop the corresponding computational algorithm to obtain the optimal replacement policy and present a numerical example to illustrate the effectiveness of the proposed model.

Keywords: bivariate replacement policy; repair-cost limit; cumulative repair-cost limit; shock model; minimal repair.

DOI: 10.1504/IJRS.2017.10010838

International Journal of Reliability and Safety, 2017 Vol.11 No.3/4, pp.220 - 237

Received: 27 May 2017
Accepted: 15 Nov 2017

Published online: 31 Jan 2018 *

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