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首页> 外文期刊>International journal of quality, statistics, & reliability >Inference on Reliability of Stress-Strength Models for Poisson Data
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Inference on Reliability of Stress-Strength Models for Poisson Data

机译：泊松数据应力强度模型的可靠性推断

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摘要

Researchers in reliability engineering regularly encounter variables that are discrete in nature, such as the number of events (e.g., failures) occurring in a certain spatial or temporal interval. The methods for analyzing and interpreting such data are often based on asymptotic theory, so that when the sample size is not large, their accuracy is suspect. This paper discusses statistical inference for the reliability of stress-strength models when stress and strength are independent Poisson random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are here presented and empirically compared in terms of their mean square error; recalling the delta method, confidence intervals based on these point estimators are proposed, and their reliance is investigated through a simulation study, which assesses their performance in terms of coverage rate and average length under several scenarios and for various sample sizes. The study indicates that the two estimators possess similar properties, and the accuracy of these estimators is still satisfactory even when the sample size is small. An application to an engineering experiment is also provided to elucidate the use of the proposed methods.
机译：可靠性工程学的研究人员经常遇到本质上离散的变量，例如在特定的空间或时间间隔内发生的事件数（例如，故障）。分析和解释此类数据的方法通常基于渐近理论，因此当样本量不大时，可能会怀疑其准确性。本文讨论了当应力和强度是独立的泊松随机变量时，应力强度模型的可靠性的统计推断。本文介绍了最大似然估计器和一致最小方差无偏估计器，并根据它们的均方误差进行了经验比较；回想一下delta方法，提出了基于这些点估计量的置信区间，并通过模拟研究对它们的依赖性进行了研究，该模拟研究根据覆盖率和平均长度在几种情况下以及不同样本量下的性能进行了评估。研究表明，两个估计量具有相似的属性，即使样本量很小，这两个估计量的准确性仍然令人满意。还提供了工程实验应用程序，以阐明所提出方法的使用。

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