Bayesian and Classical Insights into a Novel Probability Model for Aircraft Windshield Failures

ABSTRACT The development of new statistical distributions is essential for modeling complex real‐world phenomena, especially when existing models fail to capture skewness, heavy tails, or censoring. This paper introduces the QR distribution, a flexible extension of the one‐parameter Ailamujia distribution (AD), designed to model positive data with diverse asymmetry and failure rate behaviors. The study explores the properties of the QR distribution under Type‐II censoring (T‐II C), a common scenario in resource‐constrained experiments. Parameter estimation is conducted using both classical and Bayesian approaches. In Bayesian analysis the Tierney–Kadane (T‐K) approximation and Markov Chain Monte Carlo (MCMC) techniques are employed to derive Bayes estimators (BEs). For interval estimation, the study incorporates the percentile Bootstrap method (BootP) and the Bootstrap‐T method (BootT) and Bayesian highest posterior density (HPD) intervals, allowing a comprehensive assessment of parameter uncertainty under censored settings. A key application of the proposed QR distribution is demonstrated using real‐world aircraft windshield failure data, where the model effectively captures the censored nature and variability of the observed lifetimes. The QR distribution demonstrates superior performance in modeling aircraft windshield failure times compared to existing distributions. Bayesian methods, particularly the T‐K approximation under the LINEX‐based loss function (LBLF), consistently provide more accurate parameter estimates. Real‐data applications confirm the QR distribution's effectiveness in analyzing censored data and reliability problems, establishing it as a robust tool for statistical modeling in diverse fields.