EWMA charts: ARL considerations in case of changes in location and scale

• Published in: Advances in statistical analysis : AStA : a journal of the German Statistical Society Vol. 98; no. 4; pp. 371 - 387
• Main Author: Steinmetz, Sebastian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
• Subjects: Econometrics; Economics; Finance; Insurance; Management; Mathematics and Statistics; Original Paper; Probability Theory and Stochastic Processes; Statistics; Statistics for Business; ARL isolines; chart; EWMA; Percent defective; SPC
• ISSN: 1863-8171; 1863-818X
• DOI: 10.1007/s10182-013-0221-1

Widely spread tools within the area of Statistical Process Control are control charts of various designs. Control chart applications are used to keep process parameters (e.g., mean μ , standard deviation σ or percent defective p ) under surveillance so that a certain level of process quality can be assured. Well-established schemes such as exponentially weighted moving average charts (EWMA), cumulative sum charts or the classical Shewhart charts are frequently treated in theory and practice. Since Shewhart introduced a p chart (for attribute data), the question of controlling the percent defective was rarely a subject of an analysis, while several extensions were made using more advanced schemes (e.g., EWMA) to monitor effects on parameter deteriorations. Here, performance comparisons between a newly designed EWMA p control chart for application to continuous types of data, p = f ( μ , σ ) , and popular EWMA designs ( X ¯ , X ¯ - S 2 ) are presented. Thus, isolines of the average run length are introduced for each scheme taking both changes in mean and standard deviation into account. Adequate extensions of the classical EWMA designs are used to make these specific comparisons feasible. The results presented are computed by using numerical methods.