The effectiveness of Max-half-Mchart over Max-Mchart in simultaneously monitoring process mean and variability of individual observations |
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Authors: | Rumaisa Kruba Muhammad Mashuri Dedy Dwi Prastyo |
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Affiliation: | Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia |
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Abstract: | Control charts are widely used in industrial environments for the simultaneous or separate monitoring of the process mean and process variability. The Max-Mchart is a multivariate Shewhart-type simultaneous control chart that is used when monitoring subgroups. While this sampling design allows the computation of the generalized variance (GV) used to calculate the process variability, a GV chart cannot be plotted for individual observations. Hence, we cannot compute the single statistic in the Max-Mchart. This study aims to overcome the aforementioned issue. To this end, first, we develop a new Max-Mchart for individual observations by utilizing the statistic in the dispersion control chart. Second, instead of the standard normal distribution, we propose a new transformation using a half-normal distribution to calculate the statistic for the process mean and process variability. Thus, the proposed chart is called the Max-Half-Mchart, whose control limit is calculated using the bootstrap approach. An evaluation based on the average run length values shows the robustness of the Max-Half-Mchart for the simultaneous monitoring of the process mean and process variability. The single statistic in the Max-Half-Mchart is more consistent with the statistic in Hotelling's T2 and the dispersion chart than that of the Max-Mchart. |
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Keywords: | half-normal distribution individual observations multivariate control chart simultaneous control chart |
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