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Behavior of EWMA type control charts for small smoothing parameters

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  • Lazariv, Taras
  • Okhrin, Yarema
  • Schmid, Wolfgang

Abstract

A general family of EWMA charts is considered for monitoring an arbitrary parameter of the target process. The distribution of the run length is analysed for the case when the smoothing parameter tends to zero. The key impact on the results from the use of the exact variance of the control statistics vs. the asymptotic one and the presence of a head start. For fixed head start, the run lengths for both the exact and asymptotic monitoring procedures degenerate to a binary quantity. To guarantee a feasible monitoring procedure, the head start has to be chosen proportional to the smoothing parameter and the control statistics have to be modified when used with the asymptotic variance. This result underlines the weakness of schemes with a fixed head start and of schemes based on the asymptotic variance if the smoothing parameter is small. The assumptions on the target process are very weak, and are usually satisfied for stationary processes. In addition, the asymptotic equivalence of the EWMA schemes and of repeated significance tests is shown.

Suggested Citation

  • Lazariv, Taras & Okhrin, Yarema & Schmid, Wolfgang, 2015. "Behavior of EWMA type control charts for small smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 115-125.
    • Handle: RePEc:eee:csdana:v:89:y:2015:i:c:p:115-125
    DOI: 10.1016/j.csda.2015.03.010
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    References listed on IDEAS

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    1. Seven Knoth, 2005. "Fast initial response features for EWMA control charts," Statistical Papers, Springer, vol. 46(1), pages 47-64, January.
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    Cited by:

    1. Robert Garthoff & Philipp Otto, 2017. "Control charts for multivariate spatial autoregressive models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 67-94, January.
    2. Golosnoy, Vasyl & Schmid, Wolfgang & Seifert, Miriam Isabel & Lazariv, Taras, 2020. "Statistical inferences for realized portfolio weights," Econometrics and Statistics, Elsevier, vol. 14(C), pages 49-62.

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