RUN LENGTH COMPARISONS OF SHEWHART CHARTS AND MOST POWERFUL TEST CHARTS FOR THE DETECTION OF TRENDS AND SHIFTS

Abstract

This paper compares the performance of Shewhart charts with and without supplementary runs rules with Shewhart charts based on Most Powerful (MP) tests for the detection of shifts in the mean and/or the trend parameter of a linear trend model. MP tests for shifts in mean, trend, and a combined shift in both mean and trend are presented and their Average Run Lengths (ARL's) analyzed. ARL comparisons between an chart with no rules, MP-Shewhart Charts, and charts with runs rules are presented. Surprisingly, simple charts with no rules perform almost identically than Shewhart charts based on tests specifically designed to be most powerful for the shifts considered. This illustrates the robustness of Shewhart charts as a global detection mechanism against two different types of assignable causes. For small shifts in mean and/or trend, charts with runs rules perform better than both charts (no rules) and Shewhart charts based on MP tests. For large shift sizes, Shewhart charts (no rules) and MP test-based charts slightly outperform Shewhart charts with supplementary runs rules.