Independent or Dependent Competing Risks: Does It Make a Difference

摘要

This article investigates the consequences of departures from independence when the component lifetimes in a series system are exponentially distributed. Such departures are studied when the joint distribution is assumed to follow either one of the three Gumbel bivariate exponential models, the Downton bivariate exponential model, or the Oakes bivariate exponential model. Two distinct situations are considered. First, in theoretical modeling of series systems, when the distribution of the component lifetimes is assumed, one wishes to compute system reliability and mean system life. Second, errors in parametric and nonparametric estimation of component reliability and component mean life are studied based on life-test data collected on series systems when the assumption of independence is made erroneously. In both instances, one may be appreciably misled by falsely assuming independent component lifetimes. The amount of error incurred depends upon the correlation between lifetimes and the relative mean life of the two components. In the modeling problem, the level of reliability and the length of mean system life also affects the error. In the estimation problem sample size may be influential in determining the magnitude of the error.