On ARL-Unbiased Control Charts

  • Sven Knoth
  • Manuel Cabral Morais
Part of the Frontiers in Statistical Quality Control book series (FSQC)


Manufacturing processes are usually monitored by making use of control charts for variables or attributes. Controlling both increases and decreases in a parameter, by using a control statistic with an asymmetrical distribution, frequently leads to an ARL-biased chart, in the sense that some out-of-control average run length (ARL) values are larger than the in-control ARL, i.e., it takes longer to detect some shifts in the parameter than to trigger a false alarm. In this paper, we are going to:
  • explore what Pignatiello et al. (4th Industrial Engineering Research Conference, 1995) and Acosta-Mejía et al. (J Qual Technol 32:89–102, 2000) aptly called an ARL-unbiased chart;

  • provide instructive illustrations of ARL-(un)biased charts of the Shewhart-, exponentially weighted moving average (EWMA)-, and cumulative sum (CUSUM)-type;

  • relate ARL-unbiased Shewhart charts with the notions of unbiased and uniformly most powerful unbiased (UMPU) tests;

  • briefly discuss the design of EWMA charts not based on ARL(-unbiasedness).


Power function Run length Statistical process control 



The second author gratefully acknowledges the financial support received from CEMAT (Centro de Matemática e Aplicações) to attend the XIth International Workshop on Intelligent Statistical Quality Control, Sydney, Australia, August 20–23, 2013.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and Statistics, Department of Economics and Social SciencesHelmut Schmidt University HamburgHamburgGermany
  2. 2.CEMAT & Department of MathematicsInstituto Superior TécnicoLisbonPortugal

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