Effect of use‐rate on system life and failure models for 2D warranty

Purpose – The purpose of this paper is to characterise the failure model of a system that is covered by a two‐dimensional warranty, one dimension depicting time and the other usage. Specifically, the authors study the effect of use‐rate on system life when each constituent component life is described by an accelerated‐failure‐time (AFT) type model. Design/methodology/approach – The paper evaluates the effect of use‐rate on the expected failure time of a system having different internal configurations involving components. Firstly, the coherent structure as well as modules with redundant structures (standby and load‐sharing) are analysed, whereby component failures are assumed to be conditionally independent. Study systems of some basic configurations with a general dependence structure among component failure instances are also studied. Findings – The results strongly indicate that, irrespective of the internal component‐configuration of the system, the models should posses the property that the expected failure time given the use‐rate is a non‐increasing function of use‐rate. The study also reveals that dependence among components arises quite naturally due to variability in use‐rate, even when all other factors of the usage environment are held constant. Research limitations/implications – The findings of this paper are the outcome of a theoretical investigation. Although they are supported by some real‐life cases as cited from the literature, it is important that they are validated through more examples. Practical implications – The results would find a direct application in the analysis of two‐dimensional warranty policies as well as the reliability assessment of consumer durables. Originality/value – The proposed approach to the characterisation of a bivariate failure model (indexed by time and usage) is quite realistic. This investigation may lead to the development of a more suitable model.