Performance and properties of Q-Statistic monitoring schemes

Authors

  • Paul F. Zantek,

    Corresponding author
    1. Department of Operations and Management Science, Carlson School of Management, University of Minnesota, Minneapolis, Minnesota 55455
    • Department of Operations and Management Science, Carlson School of Management, University of Minnesota, Minneapolis, Minnesota 55455
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  • Scott T. Nestler

    1. Department of Mathematical Sciences, U.S. Military Academy, West Point, New York 10996
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Abstract

In this article, we study the Shewhart chart of Q statistics proposed for the detection of process mean shifts in start-up processes and short runs. Exact expressions for the run-length distribution of this chart are derived and evaluated using an efficient computational procedure. The procedure can be considerably faster than using direct simulation. We extend our work to analyze the practice of requiring multiple signals from the chart before responding, a practice sometimes followed with Shewhart charts. The results show that waiting to receive multiple signals severely reduces the probability of quickly detecting shifts in certain cases, and therefore may be considered a risky practice. Operational guidelines for practitioners implementing the chart are discussed. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

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