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Estimating the mixture of a proportional hazards model with three types of failure data

Cox’s Proportional Hazards Model (PHM) has been widely applied in the analysis of lifetime data. It can be characterized in terms of covariates that influence the system lifetime, where the covariates describe the operating environment (e.g., temperature, pressure, humidity). When the covariates are assumed to be random variables, the hazards model becomes the mixed PHM. In this article, a parametric method is proposed to estimate the unknown parameters in the mixed PHM. Three types of data are considered: uncategorized field observations, categorized field ones, and categorized experimental ones. The expectation-maximization algorithm is used to handle the incomplete data problem. Simulation results are presented to illustrate the precision and some properties of the estimation results. Accepted in 2005 for a special issue on Reliability co-edited by Hoang Pham, Rutgers University; Dong Ho Park, Hallym University, Korea; and Richard Cassady, University of Arkansas.