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

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  • Sebastian Steinmetz

Abstract

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 $$\mu $$ μ , standard deviation $$\sigma $$ σ or percent defective $$p$$ 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 $$p$$ 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 $$p$$ p control chart for application to continuous types of data, $$p=f(\mu ,\sigma )$$ p = f ( μ , σ ) , and popular EWMA designs ( $$\bar{X}$$ X ¯ , $$\bar{X}$$ X ¯ - $$S^2$$ 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. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Sebastian Steinmetz, 2014. "EWMA charts: ARL considerations in case of changes in location and scale," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 371-387, October.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:4:p:371-387
    DOI: 10.1007/s10182-013-0221-1
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    References listed on IDEAS

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    1. S. Knoth & W. Schmid, 2002. "Monitoring the mean and the variance of a stationary process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 77-100, February.
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