Warranty analysis of a two-component system with failure interaction
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In recent decades, more and more attention has been paid to the warranty study of multicomponent systems. Compared to the reliability and cost analysis of single item systems, failure dependence between items is a major challenge which should been taken into account in the analysis of multi-component systems (Liu, Wu, & Xie 2015). In this paper we study the classical warranty policies ‘non-renewing free replacement policy’ (non-renewing FRW) and ‘renewing free replacement policy’ (RFRW) for a two-component system with failure interactions. Under the non-renewing FRW, the manufacturer covers the repair or replace cost up to warranty period W from the initial product purchase time. While under the RFRW, the failed product within the warranty period W is repaired/replaced by a new one with a full warranty period W. In reliability engineering, stochastic dependence was first introduced by Murthy & Nguyen (1985a) and Murthy & Nguyen (1985b) in which they defined different types of dependencies of 2-component-system and multicomponent system. In our study we consider the type III failure dependence between two components: unit 1 causes random damages to unit 2 when it fails. While the failure of unit 2 is catastrophic and it destroys unit 1 and so the whole system. Imperfect maintenance by using virtual age method (Kijima 1989) and perfect system replacement are carried out when failure occurs to component 1 and the whole system respectively. Under both the non-renewable FRW and RFRW, from the manufacturers’ point of view, the system expected total warranty costs per cycle are explored. Numerical results are presented to show the effects of failure interactions and the initial warranty length on warranty cost. It provides a reference for decision-makers to eliminate the warranty cost and to improve the product quality.