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Bias-Corrected Estimation in Continuous Sampling Plans

机译：连续抽样计划中的偏差校正估计

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摘要

Continuous sampling plans (CSPs) are algorithms used for monitoring and maintaining the quality of a production line. Although considerable work has been done on the development of CSPs, to our knowledge, there has been no corresponding effort in developing estimators with good statistical properties for data arising from a CSP inspection process. For example, information about the failure rate of the process will affect the management of the process, both in terms of selecting appropriate CSP parameters to keep the failure rate after inspection at a suitable level, and in terms of policy, for example, whether the process should be completely inspected, or shut down. The motivation for this exercise was developing sampling protocols for Australia's Department of Agriculture and Water Resources for monitoring the biosecurity compliance of incoming goods at international borders. In this study, we show that maximum likelihood estimation of the failure rate under a sampling scheme can be biased depending on when estimation is performed, and we provide explicit expressions for the main contribution of the bias under various CSPs. We then construct bias-corrected estimators and confidence intervals, and evaluate their performance in a numerical study.
机译：连续抽样计划（CSP）是用于监视和维护生产线质量的算法。尽管在开发CSP方面已经做了大量工作，但据我们所知，还没有做出相应的努力来开发对CSP检查过程中产生的数据具有良好统计特性的估算器。例如，有关过程失败率的信息将影响过程的管理，包括选择适当的CSP参数以将检查后的失败率保持在适当的水平，以及政策（例如是否过程应进行彻底检查或关闭。这项工作的动机是为澳大利亚农业和水资源部制定抽样协议，以监测国际边界入境货物的生物安全合规性。在这项研究中，我们表明在抽样方案下，故障率的最大似然估计可能会根据执行估计的时间而产生偏差，并且我们为各种CSP下偏差的主要贡献提供了明确的表达式。然后，我们构造经过偏差校正的估计量和置信区间，并在数值研究中评估其性能。

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