Smooth operator: Modifying the Anhøj rules to improve runs analysis in statistical process control.

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.