Abstract
In this study a Shewhart type control chart namely the V t chart, is proposed for improved monitoring of the process variability of a quality characteristic of interest Y. The proposed control chart is based on the ratio type estimator of the variance using a single auxiliary variable X. It is assumed that (Y, X) follows a bivariate normal distribution. The design structure of the V t chart is developed for Phase-I quality control and its comparison is made with those of the S 2 chart (a well-known Shewhart control chart) and the V r chart (a Shewhart type control chart proposed by Riaz (Comput Stat, 2008a) used for the same purpose. It is observed that the proposed V t chart outperforms the S 2 and V r charts, in terms of discriminatory power, for detecting moderate to large shifts in the process variability. It is observed that the performance of the V t chart keeps improving with an increase in |ρ yx | , where ρ yx is the correlation between Y and X.
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The authors are grateful to the editor and the referees for their recommendations and proposals which helped in improving substantially, the earlier version of this article.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Riaz, M., Does, R.J.M.M. A process variability control chart. Comput Stat 24, 345–368 (2009). https://doi.org/10.1007/s00180-008-0122-z
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DOI: https://doi.org/10.1007/s00180-008-0122-z