The New Exponentiated Half Logistic-Generalized-Topp-Leone Family: Theory, Estimation, and Applications in Reliability Engineering

Accurate modeling of failure times is critical for reliability engineering and risk assessment. This work presents the Exponentiated Half Logistic-Generalized-Topp-Leone-G (EHL-GEN-TL-G) family, a new statistical framework that provides exceptional flexibility in capturing diverse failure rate behaviors observed in engineering systems. We focus on the EHL-GEN-TL-Weibull (EHL-GEN-TL-W) distribution, a powerful model for lifetime data. After establishing robust parameter estimation via maximum likelihood and validating model consistency through simulations, we demonstrate its practical advantage. In comparative analyses of three engineering failure datasets including mechanical component and material lifetime data the EHL-GEN-TL-W model consistently provided a significantly better fit than competing equi-parameter models. The development of an associated regression model further extends its applicability for failure time prediction and reliability analysis.