Run length comparisons of shewhart x̄ charts and most powerful test charts for the detection of trends and shifts

Rainer Göb, Enrique Del Castillo, Michael Ratz

Research output: Contribution to journalArticle

5 Scopus citations


This paper compares the performance of Shewhart X̄ 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 X̄ chart with no rules, MP-Shewhart Charts, and X̄ charts with runs rules are presented. Surprisingly, simple X̄ 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, X̄ charts with runs rules perform better than both X̄ 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. Key Words: Statistical process control; Linear trend models; Supplementary run rules.

Original languageEnglish (US)
Pages (from-to)355-376
Number of pages22
JournalCommunications in Statistics Part B: Simulation and Computation
Issue number2
StatePublished - Jan 1 2001


All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation

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