Monitoring a Bernoulli process subject to gradual changes in the success rates of a sequence of Bernoulli random variables

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2022-09-13 DOI:10.1080/07474946.2022.2092137

Marlo Brown

引用次数: 0

Abstract

Abstract We look at a sequence of Bernoulli random variables where the success rates change from θ 1 to θ 2. We will assume that both the success rates before and after the change are known. We also assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early.

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监测受一系列伯努利随机变量的成功率逐渐变化影响的伯努利过程

我们研究了一个伯努利随机变量序列，其成功率从θ 1到θ 2变化。我们将假设改变前后的成功率都是已知的。我们还假设这种变化不是突然发生的，而是在一段时间内逐渐发生的。我们计算变更已经开始和完成的概率。我们还研究了最优停车规则，假设存在假警报的成本和提前停车的单位时间成本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.