Phase I control chart for individual autocorrelated data: application to prescription opioid monitoring

IF 2.6 2区 工程技术 Q2 ENGINEERING, INDUSTRIAL Journal of Quality Technology Pub Date : 2023-01-23 DOI:10.1080/00224065.2022.2139783
Yuhui Yao, S. Chakraborti, X. Yang, J. Parton, Dwight Lewis, M. Hudnall
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引用次数: 2

Abstract

Abstract Phase I or retrospective process monitoring plays a key part in an overall statistical process monitoring (SPM) regime and is increasingly emphasized in the recent literature. At present, a lot of the data in a variety of settings (public and private sector organizations) are collected individually and sequentially and thus are serially correlated (or autocorrelated). Though a reasonable amount of work is available in the control charting literature for prospective (Phase II) autocorrelated data monitoring, very little work exists for the retrospective phase (Phase I). In this article, we present a Shewhart-type control chart for Phase I monitoring of individual autocorrelated data, assuming normality, with estimated parameters. The methodology, while developed and presented for the first-order autoregressive (AR(1)) model for simplicity, may be adapted to more general time series models. The correct charting constants, adjusted for autocorrelation and parameter estimation, are derived, and tabulated for a nominal in-control (IC) false alarm probability (FAP). Simulation results show that the proposed chart is favorably IC FAP robust and effective for reasonably small sample sizes, moderate autocorrelation, and some model miss-specifications, compared to other approaches. An illustration using some public health data involving prescription fentanyl transactions is provided to show the potential for broader areas of applications of the proposed methodology. Along with a summary and recommendations, some future research areas are indicated. An R package is developed and made available for implementing the proposed methodology on demand.
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个体自相关数据的第一阶段控制图:在处方阿片类药物监测中的应用
第一阶段或回顾性过程监测在整体统计过程监测(SPM)制度中起着关键作用,并且在最近的文献中越来越强调。目前,各种环境(公共和私营部门组织)中的许多数据都是单独和顺序收集的,因此是串行相关的(或自相关的)。尽管在前瞻性(第二阶段)自相关数据监测的控制图文献中有相当数量的工作可做,但对于回顾性阶段(第一阶段)的工作却很少。在本文中,我们提出了一个shewhart型控制图,用于第一阶段监测单个自相关数据,假设正态性,并估计参数。该方法虽然是为简化一阶自回归(AR(1))模型开发和提出的,但可以适用于更一般的时间序列模型。正确的图表常数,调整自相关和参数估计,推导,并制表为标称的控制(IC)虚警概率(FAP)。仿真结果表明,与其他方法相比,所提出的图表具有良好的IC FAP鲁棒性,并且对合理的小样本量,适度的自相关性和一些模型缺失规范有效。本文利用涉及处方芬太尼交易的一些公共卫生数据作了说明,以说明拟议方法在更广泛领域的应用潜力。在总结和建议的基础上,指出了今后的研究方向。开发了一个R包,并根据需要提供实施建议的方法。
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
Journal of Quality Technology
Journal of Quality Technology 管理科学-工程:工业
CiteScore
5.20
自引率
4.00%
发文量
23
审稿时长
>12 weeks
期刊介绍: The objective of Journal of Quality Technology is to contribute to the technical advancement of the field of quality technology by publishing papers that emphasize the practical applicability of new techniques, instructive examples of the operation of existing techniques and results of historical researches. Expository, review, and tutorial papers are also acceptable if they are written in a style suitable for practicing engineers. Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days
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