New bivariate semiparametric control chart created

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  • Author: Markos V. Koutras and Elisavet M. Sofikitou
  • Date: 06 July 2016
  • Copyright: Image appears courtesy of Getty Images

In a new article published in Quality and Reliability Engineering International, a new bivariate semiparametric Shewhart-type control chart is presented by authors Markos V. Koutras and Elisavet M. Sofikitou.

The article is currently available via the link below in Early View and the authors expand on their topic below.

A Bivariate Semiparametric Control Chart Based on Order Statistics

DOI: 10.1002/qre.1999

thumbnail image: New bivariate semiparametric control chart created

The proposed chart is based on the bivariate statistic (X(r),Y(s)), where X(r) and Y(s) are the order statistics of the respective X and Y test samples. It consists a straightforward generalization of the well known univariate median control chart and can be easily applied since it calls for the computation of two single order statistics. The false alarm rate and the in-control run length are not affected by the marginal distributions of the monitored characteristics. However, its performance is typically affected by the dependence structure of the bivariate observations under study; therefore the suggested chart may be characterized as a semiparametric control chart.

An explicit expression for the operating characteristic function of the new control chart is obtained. Moreover, exact formulae are provided for the calculation of the alarm rate given that the characteristics under study follow specific bivariate distributions. In addition, tables and graphs are given for the implementation of the chart for some typical ARL values and false alarm rates. The performance of the suggested chart is compared to that of the traditional χ2 chart as well as to the nonparametric SN2 and SR2 charts which are based on the multivariate form of the sign test and the Wilcoxon signed-rank test, respectively. Finally, in order to demonstrate the applicability of our chart, a case study regarding a real-world problem related to winery production is presented.

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