A New Lifetime Model: Properties, Estimation, and Applications in Quality Control

This paper introduces a new lifetime distribution derived by applying a transformation to the inverted Dagum distribution. We examine its statistical properties, including moments, hazard rate, quantile functions, and order statistics. The three unknown parameters are estimated using twelve methods, and a comprehensive Monte Carlo simulation reveals that the Kolmogorov-based estimator outperforms alternatives like maximum likelihood and least squares for some criteria. The proposed distribution demonstrates superior flexibility in modeling real data, outperforming established competitors such as the Dagum, inverted Dagum, extended Dagum, Gamma, and Weibull distributions in goodness-of-fit tests for two datasets: bladder cancer remission times and Thorium sediment measurements. Furthermore, we adapt the process capability index Cpk∗ to the new model and validate its utility in quality control through three engineering applications: electronic component failure times, carbon fiber tensile strength, and ball size measurements. The results highlight the new distribution’s practical relevance in real data analysis and quality control.