MODIFICATION OF CHARTS FOR ATTRIBUTES p, np, c and u TO IMPROVE THEIR APROXIMATION TO SIGNIFICANCE UNDER NORMALITY

Abstract

The users of the p and np charts (based on the Binomial distribution) and of the c and u charts (based on the Poisson distribution) have been applying eight standard tests to detect special causes of variation, since this is recommended in the classic literature of statistical process control. However, such tests were not designed especially for these charts; they were generated for the X chart, assuming that the variable to be controlled follows a Normal distribution. In this study it is demonstrated that the application of the standard tests to the charts for attributes (p, np, c and u) generates a greater number of false alarms (Type I error) than would be expected from the supposition of normality. Also, we propose a modification in these charts and evaluate it statistically, with the results that the significances of the eight standard tests approach to those that are expected under normality