Longitudinal models for non-stationary exponential data

In many manufacturing studies, longitudinal failure time data comprise repeated exponential responses, and a set of multi-dimensional covariates for a large number of independent components or objects. When the covariates collected along with exponential failure times are time dependent, the responses of an object exhibit non-stationary correlations. We examine the effects of the covariates by taking this non-stationary correlation structure into account. First, we develop Gaussian type non-stationary AR(1), MA(1), and exchangeable correlation structures for the repeated exponential failure times; and then exploit the suitable auto-correlation structure to obtain consistent, efficient estimates for the effects of the covariates by using a generalized quasi-likelihood (GQL) estimating equation approach. The finite sample estimation performance of the GQL approach is examined through a simulation study.