Random effects models for aggregate lifetime data

Field data provide important information about product quality and reliability. Many large organizations have developed ambitious reliability databases to trace field failure data of a variety of components on the systems they operate and maintain. Due to the exponential distribution assumption for the component lifetimes, the data in these databases are often aggregated. Specifically, individual lifetimes of the components are not available. Instead, each recorded data point is the cumulative operating time of one component position from system installation to the last component replacement, and the number of replacements in between. In the literature, the gamma distribution and the inverse Gaussian (IG) distribution have been used to fit the aggregate data, while the operating environment of different systems is often assumed the same. In order to capture possible heterogeneities among the systems, this study proposes the gamma random effects model and the IG random effects model. The expectation-maximization algorithm is used for point estimation of the parameters and an algorithm based on the generalized fiducial inference method is proposed for interval estimation. Simulation studies are conducted to assess the performance of the proposed inference methods. A real aggregate dataset is used for illustration.