An Extension of the Freund's Bivariate Distribution to Model Load-Sharing Systems

摘要

Several authors have considered the analysis of load-sharing parallel systems. The main characteoristics of such a two-component system is that after the failure of one component, the surviving component has to shoulder extra load, and hence, it is more likely to fall earlier than would be expected under the original model. In other cases, the failure of one component may release extra resources to the other component, thus delaying the system failure. Freund introduced a bivariate extension of the exponential distribution, which is applicable to two-component load-sharing systems. It is based on the assumption that the lifetime distributions of the components are exponential random variables before and after the change. In this article, we introduce a new class of bivariate distribution using the proportional hazard model. It is observed that the bivariate model proposed by Freund is a particular case of our model. We study different properties of the proposed model. Different statistical inferences have also been developed. We have considered four different special cases: when the base distributions are exponential, Weibull, linear failure rate, and Pareto III distributions. One data analysis has been performed for illustrative purposes. Finally, we propose some generalizations.