Robustness of mean E(X) and R charts

Abstract

The effect of nonnormality on E(X) and R charts is reported. The effect of departure from normality can be examined by comparing the probabilities that E(X) and R lie outside their three-standard-deviation and two-standard-deviation control limits. Tukey's lambda -family of symmetric distributions is used because it contains a wide spectrum of distributions with a variety of tail areas. The constants required to construct E(X) and R charts for the lambda -family are computed. Control charts based on the assumption of normality give inaccurate results when the tails of the underlying distribution are thin or thick. The validity of the normality assumption is examined by using a numerical example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>