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Design and Optimization Strategies of a High-Performance Vented Box
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Smooth operator: Modifying the Anhøj rules to improve runs analysis in statistical process control.

Jacob Anhøj1, Tore Wentzel-Larsen2

  • 1Centre of Diagnostic Investigation, Rigshospitalet, University of Copenhagen, Copenhagen, Denmark.

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Summary

This study enhances run chart analysis by calculating exact joint probabilities for longest run (L) and number of crossings (C). Adjusting critical values improves the diagnostic value of Anhøj rules for detecting data shifts.

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Area of Science:

  • Statistical Process Control
  • Data Analysis and Interpretation

Background:

  • Run charts are statistical process control tools for detecting data shifts over time.
  • Anhøj rules assess shifts using longest run (L) and number of crossings (C) of the process centre.
  • Previous studies isolated C and L, lacking analysis of their joint distribution.

Purpose of the Study:

  • To calculate exact joint probabilities for C and L using the crossrun R package.
  • To evaluate the diagnostic properties of Anhøj rules based on exact joint distributions.
  • To propose adjustments to critical values for improved diagnostic accuracy.

Main Methods:

  • Calculated exact joint distributions of C and L for N=10-100 using the crossrun R package.
  • Developed bestbox() and cutbox() functions to adjust critical values for C and L.
  • Assessed diagnostic value by balancing sensitivity and specificity.

Main Results:

  • Presented measures of diagnostic value for Anhøj rules based on exact joint distributions.
  • Demonstrated that best box and cut box procedures enhance diagnostic value.
  • Achieved specificity and sensitivity close to target values with adjusted critical values.

Conclusions:

  • Exact joint distribution calculations enable improved diagnostic properties for run charts.
  • Minor adjustments to critical values for C and L enhance run chart diagnostic value.
  • The study provides a method for optimizing run chart analysis for shift detection.