A Robust Control Chart

Abstract

This article studies alternative standard deviation estimators that serve as a basis to determine the trueX¯ control chart limits used for real‐time process monitoring (phase II). Several existing (robust) estimation methods are considered. In addition, we propose a new estimation method based on a phase I analysis, that is, the use of a control chart to identify disturbances in a data set retrospectively. The method constructs a phase I control chart derived from the trimmed mean of the sample interquartile ranges, which is used to identify out‐of‐control data. An efficient estimator, namely the mean of the sample standard deviations, is used to obtain the final standard deviation estimate from the remaining data. The estimation methods are evaluated in terms of their mean squared errors and their effects on the performance of the trueX¯ phase II control chart. It is shown that the newly proposed estimation method is efficient under normality and performs substantially better than standard methods when disturbances are present in phase I. Copyright © 2012 John Wiley & Sons, Ltd.

Revisiting reweighted robust standard deviation estimators for univariate Shewhart S‐charts

“…First, dispersion estimates of the rational subgroups ( ) and an initial process standard deviation estimate ( ) are determined using the estimators in the second and the third columns of Table , respectively, and the first column shows the titles given to various combinations of the reweighted estimators. Except and ,() the estimation methods discussed below have not been used, to our knowledge, in a reweighting scheme in the literature.…”

“…Does and co‐workers improved the performance of S‐charts via reweighting robust estimators with respect to both subgroups and individual observations. ()…”

Robust Tukey–CUSUM Control Chart for Process Monitoring

“…In such cases we need robust structures that have the ability to perform better even for non‐normal situations. Nazir et al , 17‐19 Schoonhoven and Does, Schoonhoven et al , Tukey, and Weisberg may be seen in this regard.…”

Quality Quandaries: How to Set Up a Robust Shewhart Control Chart for Dispersion?

“…What remains is the determination of the factors U II and L II in order to obtain the desirable in-control performance. Schoonhoven et al (2011) presented a formula for U II and L II of the Phase II standard deviation control chart based on the pooled mean of the sample standard deviations,S S. They tested this formula for charts derived from a broad range of Phase I estimators and concluded that the formula is suitable when the variance of the estimator is close to the variance ofS S. Subsequently, Schoonhoven and Does (2013) showed that the variance of the estimator given in [5] is close toS S. Hence, the formula presented by Schoonhoven et al (2011) can also be applied in the procedure discussed here. This is a nice result because the formula is a plug-in so no simulations are required to obtain the constants.…”

“…For the sake of clarity, we shall add subscripts I and II to d UCL UCL, d LCL LCL, U, and L to indicate the phase to which we refer. Schoonhoven and Does (2013) analyzed the performance of the Phase I control charts. They showed that the type of estimator used to construct these charts is important.…”