A QUASI ARL-UNBIASED U CONTROL CHART

Abstract

The u-Chart serves to monitor processes by means of the number of defects per inspection unit. The Standard u-Chart, whose principles are based on the normal approximation to the Poisson distribution, was the first of its type and has remained widely popular to this day. In this paper it is shown that this chart is inherently ARL-biased and that this condition greatly affects its capability to detect process improvements. It was found that several superior alternatives to the Standard u-Chart had been proposed over the years, in order to compare them, an analysis of their capability to produce optimal control charts was carried out on the basis of their ARLBSL (ARL-bias severity level) and ARL0 (In-Control ARL). The analysis results showed that they produce optimal control charts far less often than expected. A new u-Chart called "Kmod" is proposed, its capability to produce optimal control charts exceeds that of any other alternative chart, and apart from that, it also includes an easy-to-use method for verifying if its ARLBSL is, or is not, adequate.

Keywords

• Control Chart
• Attribute Chart
• ARL-biased
• ARL-unbiased
• Process control