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Generalized run tests for statistical process control

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  • Young H. Chun

Abstract

In a sequence of elements, a run is defined as a maximal subsequence of like elements. The number of runs or the length of the longest run has been widely used to test the randomness of an ordered sequence. Based on two different sampling methods and two types of test statistics used, run tests can be classified into one of four cases. Numerous researchers have derived the probability distributions in many different ways, treating each case separately. In the paper, we propose a unified approach which is based on recurrence arguments of two mutually exclusive sub-sequences. We also consider the sequence of nominal data that has more than two classes. Thus, the traditional run tests for a binary sequence are special cases of our generalized run tests. We finally show that the generalized run tests can be applied to many quality management areas, such as testing changes in process variation, developing non-parametric multivariate control charts, and comparing the shapes and locations of more than two process distributions.

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  • Young H. Chun, 2019. "Generalized run tests for statistical process control," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(12), pages 2164-2179, September.
    • Handle: RePEc:taf:japsta:v:46:y:2019:i:12:p:2164-2179
    DOI: 10.1080/02664763.2019.1581147
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    Cited by:

    1. Ata Amini, 2020. "The role of climate parameters variation in the intensification of dust phenomenon," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 102(1), pages 445-468, May.

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