Epanechnikov Pearson Type V distribution for reliability and predictive maintenance modeling

Modeling positive-support and heavy-tailed data is a fundamental problem in reliability engineering and predictive maintenance. In this study, we introduced the Epanechnikov–Pearson Type V (EPV) distribution as a kernel-based extension of the classical Pearson V model to enhance flexibility in capturing asymmetric and heavy-tailed behavior. The EPV distribution was constructed by integrating the Epanechnikov kernel with the Pearson V baseline through a transformation approach. Closed-form expressions for the probability density function, cumulative distribution function, reliability function, and hazard rate were derived, and parameter estimation was carried out using maximum likelihood methods. A comprehensive Monte Carlo simulation with 500 replications was conducted to evaluate the finite-sample performance of the estimators. The results showed a systematic decrease in bias, mean squared error, and mean relative error as the sample size increased. In addition, the empirical coverage probabilities of the approximate \(95\%\) confidence intervals remained generally close to the nominal level, while the average confidence-interval lengths decreased with increasing sample size. The empirical performance of the model was further evaluated using real datasets, including industrial fatigue-life data from two companies and the AI4I 2020 Predictive Maintenance Dataset . Across all cases, the EPV model provided improved goodness-of-fit compared to the classical Pearson V distribution, achieving lower AIC and BIC values and reduced Kolmogorov–Smirnov statistics. Overall, the EPV distribution was shown to provide a flexible, analytically tractable, and computationally efficient framework for modeling complex reliability and degradation data, with potential applications in engineering and predictive maintenance.