Estimating Common-Cause Sigma in the Presence of Special Causes

Abstract

In statistical process monitoring we test process data for departures from some model of common-cause variation, usually independent, identically distributed (iid) normal. One task in the set-up phase is to estimate the common-cause standard deviation. Most comparisons of estimators have assumed normal or contaminated normal distributions. The usual “trends and oscillations” argument for the standard moving-range estimator has not been adequately investigated, nor have other special-cause scenarios where the data cannot be reduced to an iid subset. I compare five old estimators and one new one in this context. A new proposal for retrospective analysis is based on the results of these comparisons.

• Maximum Likelihood
• Median
• Moving Ranges
• Outliers
• Trends

Additional information

Notes on contributors

Russell A. Boyles

Dr. Boyles is a Research Fellow in Applied Mathematics. He is a Member of ASQ.