On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

Many real-world phenomena generate count data with inflated number of zeroes. To model such datasets, the zero-inflated Poisson model has been used quite extensively and effectively. Examples of such datasets include the number of defects in manufacturing, the number of visits to a specific location and the number of times suffered a major health issue. Besides the engineering applications of the stress-strength reliability, its use as an index of stochastic comparison is well established. Stress-strength reliability studies for the power series distributions such as the binomial, the Poisson, the geometric and the negative binomial are recent additions in the literature. Realizing their shortcomings in modelling inflated count datasets, we consider two distinct independent marginal zero-inflated Poisson distributions, derive the structure of the corresponding stress-strength reliability parameter and study its nature. Then the stress-strength reliability is estimated in frequentist as well as in the Bayesian approach. Stan, a probabilistic programming language for Bayesian inference, is used for the computation of the Bayes’ estimate. Both the approaches of estimation have almost equivalent performance in terms of bias and mean squared error. Simulation experiments are performed to assess the performance of the estimators. We also present two important real-life applications for demonstrating the utility of the proposed estimators. The applications involve benchmark zero-inflated count datasets related to railway accidents and fishing by groups of people on a camping trip.