Researchers in reliability engineering regularly encounter variables that are discrete in nature, such as the number of events (e.g.,\r\nfailures) occurring in a certain spatial or temporal interval. ?e methods for analyzing and interpreting such data are o?en based\r\non asymptotic theory, so that when the sample size is not large, their accuracy is suspect. ?is paper discusses statistical inference\r\nfor the reliability of stress-strength models when stress and strength are independent Poisson random variables. ?e maximum\r\nlikelihood estimator and the uniformly minimum variance unbiased estimator are here presented and empirically compared in\r\nterms of their mean square error; recalling the delta method, con??dence intervals based on these point estimators are proposed,\r\nand their reliance is investigated through a simulation study, which assesses their performance in terms of coverage rate and average\r\nlength under several scenarios and for various sample sizes. ?e study indicates that the two estimators possess similar properties,\r\nand the accuracy of these estimators is still satisfactory even when the sample size is small. An application to an engineering\r\nexperiment is also provided to elucidate the use of the proposed methods.
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