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

Abstract

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. Naïve 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.

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

“…Fourth, Bayesian methods can be considered as a competitor to the MLE methods of this paper. The choice of the marginal prior distributions could follow [2,16], while the bounded uniform prior could be recommended for the copula prior [56]. It is of interest to see if the difficulty of estimating the copula parameter is resolved by Bayesian methods.…”

“…Survival analysis deals with incomplete failure time data, such as censored and truncated data [1][2][3][4][5]. Left-truncation arises if early failures occur before the data collection period and their failures are simply ignored.…”

“…Naïve statistical analyses of truncated, censored, and competing risks data lead to biased inference for the population of interest. Left-truncation, right-censoring, and competing risks are a classical topic in survival analysis that is widely recognized in both biostatistics [3] and reliability engineering [1][2][3][4][5].…”

“…Comparison of the numerical methods for maximum likelihood estimator were considered by [12,15]. Bayesian approaches for the lognormal, Weibull, and gamma distributions were considered by [2,16]. The Lehmann family of distributions was considered by [17] and the log-location-scale family of distributions was considered by [18].…”

“…The spline model was proposed by [7]. In this research topic, the most up-to-date review paper is [2].…”