A New Generalized Burr‐III Model for Load‐Sharing Reliability: Bayesian and Frequentist Inference With a Sports Application

ABSTRACT We propose the alpha power modified Burr‐III (APMB‐III) distribution, an extension of the modified Burr‐III (MB‐III) model formulated to broaden the variety of shapes available within lifetime distribution theory. By varying its parameters, the APMB‐III model reproduces decreasing, bathtub‐shaped (decreasing‐then‐increasing), and unimodal hazard patterns, a property that suits it to non‐negative measurements encountered in applied work. Closed‐form results are obtained for the model principal descriptors, namely its moments, quantiles, variance, skewness, and kurtosis. The unknown parameters are fitted by maximum likelihood, and two bootstrap‐based interval procedures are added to gauge estimation uncertainty. An empirical illustration confirms that the APMB‐III model tracks the data more closely than the MB‐III, Burr‐III, inverse Weibull, and log‐logistic alternatives. We then study the reliability of a 1‐out‐of‐k load‐sharing parallel system model (LSPSM) whose component lifetimes follow the APMB‐III model. Estimates of system reliability and of the system hazard rate are derived under both classical and Bayesian inference. A worked application of the LSPSM then shows how readily the model adapts to practical settings.