Parametric analysis of time-censored aggregate lifetime data

Many large organizations have developed ambitious programs to build reliability databases by collecting field failure data from a large variety of components. To make the database concise, only the number of component replacements in a component position during an operation time interval is reported in these databases. This leads to time-censoring in the aggregate failure data. Statistical inference for the time-censored aggregate data is challenging, because the likelihood function based on some common lifetime distributions can be intractable. In this study, we propose a general parametric estimation framework for the aggregate data. We first use the gamma distribution and the Inverse Gaussian (IG) distribution to model the aggregate data. Bayesian inference for the two models is discussed. Unlike the gamma/IG distribution, other lifetime distributions involve multiple integrals in the likelihood function, making the standard Bayesian inference difficult. To address the estimation problem, an approximate Bayesian computation algorithm that does not require evaluating the likelihood function is proposed, and its performance is assessed by simulation. As there are several candidate distributions, we further propose a model selection procedure to identify an appropriate distribution for the time-censored aggregate data. A real aggregate dataset extracted from a reliability database is used for illustration.