Reliability analysis of ammunition system based on zero-inflated negative binomial distribution

Traditional counting models often fail to accurately fit ammunition failure data with excessive zero values. This study aims to construct a zero-inflated negative binomial (ZINB) distribution model to more accurately characterize the complex statistical features of ammunition failure data with excessive zero values. Within the framework of a Bayesian hierarchical model, parameter estimation is conducted using the Markov Chain Monte Carlo (MCMC) method, and the Bayesian method is employed to integrate prior information and quantify uncertainty. Through an empirical analysis of typical zero-inflated ammunition production quality control data, the Bayesian Poisson and negative binomial distribution models are compared to verify model accuracy. Based on Deviance Information Criterion (DIC) and deviance evaluation results, the ZINB model demonstrates the best goodness-of-fit and prediction performance for fitting ammunition failure data with covariates. The results show that the ZINB model serves as an effective statistical tool for analyzing complex count data with excessive zeros, providing a more precise theoretical basis for ammunition reliability assessment and related decision-making.