Left-truncated and right-censored field failure data: Review of parametric analysis for reliability

In field reliability analyses, a data collection period is given to monitor the failure events from the field. Left-truncation arises due to early failures occurring before the data collection period, and right-censoring arises for late failures occurring beyond the monitoring period. Naive analyses of left-truncated and right-censored data lead to biased estimation of the population lifetime of interest. A variety of models and methods have been developed to analyze the left-truncated and right-censored data for field reliability analyses. The goal of the paper is to review the existing models and methods for fitting left-truncated and right-censored data. Our review includes the existing statistical models, such as the exponential, Weibull, lognormal, gamma, Gompertz, Lomax, and spline models. We comprehensively review the statistical issues of maximum likelihood estimation, model selection, residual lifetime prediction, and Bayesian methods. Some of these methods are illustrated through the field reliability analysis of the electric power transformer dataset.