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Comparing the Performance of Cpk and X Control Charts With the Generalized Multiple Dependent State Sampling Supplementary Signaling Rule

The C_{pk} index was originally created to measure the ability of the processes to produce products meeting specifications but, more recently, Rao and team proposed the use of the C_{pk} index to control processes. In reality, they investigated the performance of the C_{pk} chart with the GMDS...

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Bibliographic Details
Published in:IEEE access 2022, Vol.10, p.2006-2012
Main Authors: Costa, Bruna S., Costa, Antonio F. B.
Format: Article
Language:English
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Online Access:Get full text
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Summary:The C_{pk} index was originally created to measure the ability of the processes to produce products meeting specifications but, more recently, Rao and team proposed the use of the C_{pk} index to control processes. In reality, they investigated the performance of the C_{pk} chart with the GMDS (Generalized Multiple Dependent State Sampling) supplementary signaling rule. With the GMDS supplementary run rule, the C_{pk} chart signals when a point falls in the action region or when a point falls in the warning region after a sequence of m points, with less than k , in the central region. The points on the C_{pk} chart are the estimated values of the C_{pk} index obtained with the mean and the variance of the samples. Rao and team obtained the ARLs of the GMDS C_{pk} chart by simulation; reminding the ARL is the average number of samples the chart requires to signal a change in the process. This present work uses the Markov chain approach to obtain the ARLs , once this approach leads to exact results. The main conclusion is that the GMDS \bar {X} chart is not only simpler to use than the GMDS C_{pk} chart, but it is also more sensitive to process changes.
ISSN:2169-3536
DOI:10.1109/ACCESS.2021.3139532