Linear combination of chi-squares for multinomial process monitoring

Q3 Engineering

Gestao e Producao Pub Date : 2021-07-02 DOI:10.1590/1806-9649-2021v28e41

Ramzi Talmoudi, Ali Achouri, H. Taleb

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Abstract

Abstract: Marcucci (1985) proposed a chi square goodness of fit statistic based generalized p-chart for multinomial process monitoring. A chi square distribution quantile was considered as a control chart limit. A weighted chi square goodness of fit statistic-based control chart is proposed for multinomial process monitoring in this paper, where more important weights are advocated to poor quality categories. The statistic distribution is approximated by a well-known linear combination of chi squares distribution. The approximation is assessed through a simulation, an extreme percentile of the approximated distribution is used as an upper control chart limit and a comparison is carried out with a chi square goodness of fit statistic-based control chart. The average run length is used as a benchmark and the comparison is performed using simulations considering two process shifts scenarios. Under some restrictions, the weighted statistic-based control chart allows an earlier detection of process shift in case of deterioration and postpones out of control signals in case of improvement. This benefit is clearer when the process is improved by a decrease in the poor quality probability category and an increase in the best quality category probability.

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多项式过程监控的卡方线性组合

摘要:Marcucci(1985)提出了一种基于卡方拟合优度统计的广义p图用于多项过程监控。卡方分布分位数被认为是控制图极限。本文提出了一种基于加权卡方拟合优度统计的多项过程监控控制图，其中对质量较差的类别赋予更重要的权重。统计分布近似于著名的卡方分布的线性组合。通过模拟评估近似，使用近似分布的极端百分位数作为控制图上限，并与基于卡方拟合优度统计的控制图进行比较。使用平均运行长度作为基准，并使用考虑两种流程转移场景的模拟进行比较。在一定的限制条件下，基于加权统计的控制图允许在恶化情况下更早地发现过程移位，并在改进情况下延迟失控信号。当过程通过减少低质量概率类别和增加最佳质量类别概率来改进时，这种好处就更明显了。

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

Gestao e Producao Engineering-Industrial and Manufacturing Engineering

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

44 weeks

期刊介绍： Gestão & Produção is a journal published four times a year year (March, June, September and December) by the Departamento de Engenharia de Produção (DEP) of Universidade Federal de São Carlos (UFSCar). The first issue of Gestão & Produção was published in April, 1994. Actually, G&P was result of experience of professors of DEP/UFSCar in editing, in the beginning, "Cadernos DEP" in the 1980s, followed by "Cadernos de Engenharia de Produção". The last three issues of "Cadernos de Engenharia de Produção" were a test previous to the launch of Gestão & Produção because most of the journal characteristics were already established, like regularity.