On estimation of the quadratic hazard rate model parameters: Simulation and application

Abstract

This study applies both Bayesian and non-Bayesian methods to estimate the lifetime parameters of the quadratic hazard rate distribution using incomplete lifetime data under progressive Type-II censoring with binomial removal. The three-parameter quadratic hazard rate model generalizes traditional distributions, including linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, parameters, as well as reliability and hazard rate functions, are estimated using maximum likelihood estimation (MLE) and maximum product of spacing (MPS). Asymptotic confidence intervals are derived, with a focus on the delta method. Bayesian inference is then performed under both MLE and MPS approaches using independent informative priors (normal and gamma) and both symmetric (squared error) and asymmetric (linear exponential) loss functions to obtain point estimates and highest posterior density credible intervals. Given the complexity of closed-form Bayesian estimates, Markov chain Monte Carlo methods are employed to sample from the posterior distribution. The precision and consistency of point and interval estimates are assessed using four performance metrics: root mean squared error, mean relative absolute bias, average confidence interval length, and coverage probability. A simulation study explores these criteria across varying sample sizes and censoring schemes. The proposed methods are further validated on real-world data concerning the remaining service time of aircraft windshields. In addition, we analyzed the existence and uniqueness of the estimates before confirming them graphically. Finally, the results indicate that Bayesian approaches outperform non-Bayesian methods in terms of accuracy and robustness, offering valuable insights into reliability testing and decision-making in engineering applications.