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Unconditional performance of the X¯ chart: Comparison among five standard deviation estimators
Quality and Reliability Engineering International ( IF 2.3 ) Pub Date : 2020-05-10 , DOI: 10.1002/qre.2661
Cassio Eduardo Faria Sobue 1 , Felipe Schoemer Jardim 2 , Victor Claudio Bento Camargo 1 , Fabiane Leticia Lizarelli 1 , Pedro Carlos Oprime 1
Affiliation  

To design the X ¯ control chart, the in‐control process mean and standard deviation must be estimated from historical samples, negatively affecting the chart's performance. The grand mean of a sample is the well‐established estimator for the process mean. However, regarding the standard deviation, the chart's user has at least five different estimators available in the literature to choose from. In this paper, using intensive simulations, we study and compare the performance of the X ¯ chart (under normality assumption and three‐sigma limits) among the most five used standard deviation estimators. The unconditional in‐control run length (RL0) is the most commonly used performance measure of a control chart, and many authors base their comparisons on the expectation of the RL0 or on the mean square error of the estimators. In contrast, we based our comparison on the proportions of the RL0 concentrated at some intervals that are usually considered undesired by the practitioner due to the high incidence of false alarms during the process monitoring (e.g., RL0 between 1 and 200), occurring earlier than expected when compared with known parameter situations. From our results, all the studied standard deviation estimators generate similar performances. However, even with this similarity, we showed that one of the most recommended standard deviation estimators in the literature in control charts with estimated parameters may be the most inappropriate choice based on the undesired RL0 proportions.

中文翻译:

X图表的无条件性能:五个标准偏差估计量之间的比较

设计 X ¯ 对于控制图,必须从历史样本中估计控制中过程的平均值和标准偏差,这会对控制图的性能产生负面影响。样本的总体均值是过程均值的公认估计量。但是,关于标准偏差,图表的用户在文献中至少可以选择五个不同的估计量。在本文中,我们通过深入的模拟研究和比较了 X ¯ 最多使用的五个标准差估计量中的图表(在正态假设和三个sigma限制下)。无条件控制内游程长度(R L 0)是控制图最常用的性能指标,许多作者的比较都基于R L 0的期望值或估计量的均方误差。与此相反,我们基于我们对的比例比较ř大号0浓缩在该通常被认为是由医生不希望的一些间隔由于假警报的过程监测期间的高发病率(例如,[R大号0(介于1到200之间),与已知参数情况相比,发生的时间早于预期。从我们的结果来看,所有研究的标准偏差估计量都产生相似的性能。但是,即使有这种相似性,我们也表明,基于不希望的R L 0比例,在控制图中带有估计参数的文献中,最推荐的标准偏差估计器之一可能是最不合适的选择。
更新日期:2020-05-10
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