A Modified Stress-Strength Reliability Function for Discrete Family of Distributions

A modified definition of the stress-strength reliability function is proposed for discrete family of distributions. The newly introduced definition is utilized to derive expressions of the reliability function as well as its Uniformly Minimum Variance Unbiased Estimator (UMVUE) and unbiased estimator of the variance of the UMVUE for different members of the discrete Power Series family of Distributions (PSD). The performance of the UMVUE is compared with the corresponding Maximum Likelihood (ML) estimator in terms of relevant measures. The modified definition is further applied in the context of engineering data and real-world football data to demonstrate its usefulness.