Analysis of Ammunition Malfunctions Based on the Negative Binomial-Lindley Distribution

The reliability of ammunition systems is of vital importance to the combat effectiveness and safety in modern warfare.However, the failure data often exhibit significant characteristics of excessive zeros and excessive dispersion, which cannot be effectively fitted by traditional data.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 zero inflation and excessive dispersion, a 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 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 decisionsexpressions