Reweighted robust dispersion estimation methods for univariate s-charts

Abstract

Maintaining the quality of manufactured products at a desired level depends on the stability of process dispersion and location parameters and detection of perturbations in these parameters as promptly as possible. In the application of S-Charts, which are one of the most widely used techniques to monitor process variability in statistical process monitoring, sample standard deviation and sample mean are known to be the most e cient traditional estimators in determining process parameters, based on the assumption of independent and normally distributed datasets. In the cases of estimated process parameters from Phase I data clouded with outliers, e ciency of traditional estimators is signi cantly reduced, and performance of S-Charts are undesirably low. The aim of this thesis is to propose various robust estimators and reweighting procedures to increase the performance of S-Charts in Phase II monitoring. Three dispersion estimators: sample standard deviation, median absolute deviation and scale M-estimator, and three location estimators: sample mean, Harrell-Davis qth quantile estimator and location M-estimator, are employed to directly construct the Phase II control limits of S-Charts, and also reweighted via di erent methods. Phase I e ciency of the proposed estimators and Phase II performance of S-Charts constructed from these estimators are assessed both under normality and against di use-localized and symmetric-asymmetric contaminations at di erent contamination density and magnitudes using 50,000-100,000 Monte Carlo simulations. As a result, scale M-estimator combined with Harrell-Davis 0:5th quantile estimators yield parameter estimates with the highest e ciency, and reweighting at skipping level 2-4% using a common location estimate in individuals charts to screen outlier subgroups, and individual observations are found to improve the Phase II performance of the S-Charts.