Goodness-of-Fit Tests for Imperfect Maintenance Models Based on Entropy and Extropy

This study investigates the performance of goodness-of-fit tests for the ARA ∞ –PLP imperfect maintenance model, with a particular emphasis on entropy- and extropy-based test statistics. Test statistics are constructed using three different approaches: martingale residuals, probability integral transform, and information-based measures. Extensive simulation studies are conducted under several alternative hypotheses, including ARA 1 , ARA ∞ –LLP, QR, EGP, and Brown–Proschan models, to evaluate the empirical power of the proposed tests. In addition to numerical power comparisons, graphical analyses are employed to illustrate the behavior of the test statistics and to provide further insight into their sensitivity under different repair scenarios. The simulation results demonstrate that entropy- and extropy-based statistics generally outperform classical goodness-of-fit tests, particularly in detecting deviations from the null model under moderate and severe imperfect repair effects. The consistency observed between graphical patterns and numerical findings further confirms the robustness and interpretability of the proposed procedures. An application to a real dataset related to automobile failure times illustrates the practical effectiveness of the methodology and supports the suitability of the ARA ∞ –PLP model for real-world repairable systems.