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Computational Statistics

, Volume 24, Issue 2, pp 345–368 | Cite as

A process variability control chart

  • Muhammad RiazEmail author
  • Ronald J. M. M. Does
Open Access
Original Paper

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.

Keywords

Auxiliary information Normality Power curves Simulations S2 charts Vt chart Vr chart 

Notes

Acknowledgments

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.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Department of StatisticsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Institute for Business and Industrial StatisticsUniversity of AmsterdamAmsterdamThe Netherlands

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