Estimation in aMixed Proportional Hazards Model

Cox’s proportional hazards model (PHM) has been widely applied in the analysis of lifetime data, and can be characterized by covariates influencing lifetime of asystem, where the covariates describe operating environments (e.g. temperature, pressure, humidity). When environments are uncertain, the covariates may be often modeled as random variables. We assume that acovariate is adiscrete random variable, and propose anew mixture type of PHM, called the mixed PHM. We develop the Expectation-Maximization(EM) algorithm to estimate the model parameters. Two types of observations are considered; one type of observations is obtained ffom experimental units, which are tested in laboratories and the other type of observations is obtained ffom field units which are operated by customers. An illustrative example is given.

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