A mixed-Weibull regression model for the analysis of automotive warranty data

This paper presents a case study regarding the reliability analysis of some automotive components based on field failure warranty data. The components exhibit two different failure modes, namely early and wearout failures, and are mounted on different vehicles, which differ among themselves for car model and engine type, thus involving different operating conditions. Hence, the failure time of each component is a random variable with a bimodal pdf which also depends upon a vector of covariates that indexes the specific operating condition. Then, a mixed-Weibull distribution, where the pdf of each subpopulation (namely the ‘weak’ and ‘strong’ subpopulation) depends on the covariates through the scale parameter, is used to analyze the component lifetime. A Fortran algorithm for the maximum likelihood estimation of model parameters has been implemented and a stepwise procedure, in its backwards version, has been used to test the significance of covariates and to construct the regression model. The presence of a weak subpopulation has been verified and the fraction of weak units in the population has also been estimated. Finally, the adequacy of the proposed model to fit the observed data has been assessed.