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The Robustness and Performance of CUSUM Control Charts Based on the Double-Exponential and Normal Distributions

  • Zachary G. Stoumbos
  • Marion R. ReynoldsJr.
Part of the Frontiers in Statistical Quality Control book series (FSQC, volume 7)

Abstract

We investigate the effects of non-normality on the statistical performance of cumulative sum (CUSUM) control charts for monitoring the process mean μ Our objective is to maintain tight control of the process so that detecting both small and large shifts in μ is important. We consider the standard CUSUM chart, which is based on the normal distribution, and a second CUSUM chart, which is based on the heavy-tailed doubleexponential distribution. We also investigate the issue of whether it is preferable from the perspective of statistical performance to base these control charts on samples of n > 1 observations or on individual observations (n = 1). We assume that the sampling rate in terms of the number of observations per unit time is fixed, so using n = 1 means that samples can be taken more frequently than when n > 1. We show that using n > 1 in either chart does not give a significant improvement in in-control robustness, compared to using n = 1. We also show that, unlike the double-exponential CUSUM chart, for n = 1, the standard CUSUM chart can be designed to be highly robust to non-normality and very effective at detecting shifts of all sizes, even for highly skewed and extremely heavy-tailed process distributions.

Keywords

Control Chart Exponentially Weighted Move Average CUSUM Chart Markov Chain Method Exponentially Weighted Move Average Chart 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Zachary G. Stoumbos
    • 1
  • Marion R. ReynoldsJr.
    • 2
  1. 1.RutgersUniversity of New JerseyNJUSA
  2. 2.Department of StatisticsVirginia Polytechnic Institute and State UniversityVAUSA

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