Robust Estimation of the Process Standard Deviation for Control Charts

Abstract

Control charts are tools used to detect aberrant behavior in manufacturing processes. The x chart plots subsample averages as a function of time, and the R chart plots subsample ranges. Both of these charts rely on an estimate of the standard deviation of the process when it is operating correctly. The estimate has traditionally been based on the average range of 2040 subgroups, but this will produce an estimate that is biased high when outliers are present. One standard solution is to construct a range chart for the original subgroups and estimate the standard deviation only from those subgroups within the control limits, repeating the procedure as necessary. Proposals have also recently been made to use a trimmed mean of the subsample ranges with a fixed percentage of trimming, as well as the trimmed mean of the subsample interquartile ranges. This article presents a new approach to robust estimation of the process standard deviation. The procedure first centers each subsample on its own median and then applies a modified biweight A estimator to the pooled residuals. This method combines the strengths of the previous methods—the relatively high efficiency of the range-based methods when no disturbance is present, together with the strong resistance to disturbances of the trimmed interquartile iange method.

KEY WORDS:

• Biweight
• M estimator
• Range chart