Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE

Abstract

In reliability analysis, lifetime data may be heavily censored and this censoring can have an adverse effect on parameter estimates. Using maximum-likelihood estimation (MLE) to estimate the parameters of reliability functions is common in practice especially with (right) censored observations. However, estimating parameters using MLE introduces an inherent bias which tends to increase as the number of observations decreases and/or the censoring proportion increases. Reliability demonstration tests (RDT) typically use a Type I or Type II censoring mechanism; however, in many real-life applications a generalized Type I censoring mechanism, where each observation has its own censoring times, is often more applicable. These examples occur in structural risk analyses, obsolescence predictions, and medical studies where items under study may have different introduction dates but have lifetimes from the same probability distribution. This research improves Weibull distribution parameter estimates by combining a modified MLE and an oversampling method. Empirical results are presented with recommendations for preferred oversampling sizes, dependent upon the sample size and censoring proportion, using the Kullback–Leibler divergence to measure the difference between the known distribution and estimated distributions. A case study is provided to highlight the method’s use in an obsolescence prediction application.