Bayesian hierarchical negative binomial-Lindley model for ammunition malfunction analysis: theory and empirical validation

The reliability of ammunition systems is of vital importance to the combat effectiveness and safety in modern warfare. Failure data often display notable features, including dataset with a preponderance of zero observations and overdispersion, which are not well captured by traditional models. This paper aims to establish a new count data model - the NB-L model, to more accurately capture the complex features of ammunition failure data. Under the framework of bayesian hierarchical models, parameter estimation is conducted using the Markov Chain Monte Carlo (MCMC) method, and Bayesian methods are adopted to integrate prior information and quantify uncertainty. After conducting an empirical analysis on a typical ammunition production quality control dataset with dataset with a preponderance of zero observations on and excessive dispersion, the comparative analysis is made between the Bayesian Poisson distribution and the negative binomial distribution models to verify the accuracy of the model. Based on the Deviance Information Criterion (DIC) and Deviance evaluation, the NB-L Generalized Linear Model (GLM) exhibits the optimal performance in fitting ammunition failure data with covariates. The results show that the NB-L distribution provides a powerful alternative tool for such complex count data and offers more precise statistical basis for related decisions expressions.