A Novel Goodness-of-Fit Test for Lifetime Models Based on Type II Censored Data

In this paper, a novel test statistic is introduced to evaluate the goodness of fit of lifetime distributions when dealing with Type II censored data. The test statistic is derived from a local linear regression-based estimator of the Kullback-Leibler information. Extensive analysis is conducted to examine the properties of this test statistic, highlighting its nonnegative nature, as for KL information. The proposed test statistic is applied to various distributions, namely exponential, Weibull, log-normal, and Pareto. Critical values and Type I error rates for the tests are determined, demonstrating their exceptional accuracy and reliability. To further assess their performance, the proposed tests are subjected to Monte Carlo simulations, comparing their power values against alternative tests currently in use. Finally, the proposed method is applied to three real data sets from the engineering reliability aspect to prove their practical versatility.