A Computer Program To Calculate Two-stage Short-run Control Chart Factors For (X¯,v) And (X¯,√v) Charts

Abstract

This paper describes the development and execution of a computer program that will accurately calculate first- and second-stage short-run control chart factors for (X¯,v) and (X¯,√v) charts. The software used is Mathcad 8.03 Professional with the Numerical Recipes Extension Pack. Exact equations for the distributions of the variance and the studentized variance, degrees of freedom calculations, short-run calculations, and conventional control chart calculations are used. Numerical routines provided by the software are also used. The program accepts values for subgroup size, number of subgroups, alpha for the X¯ chart, and alpha for the v or √v chart both above the upper control limit and below the lower control limit. Tables are generated for specific values of these inputs. Comparison of the tabulated results to legitimate results in the literature validates the program. The tables correct and extend previous results in the literature. Download instructions for the program are available at http://program.20m.com.

^#Editor's Note: This article is the second in a set of two articles, the first of which appeared in Volume 15, Number 3. The first article was titled “Two-Stage Short-Run (X¯,v) and ( X¯, √v) Control Charts” and this one uses the theory developed in that first article to develop a computer program based on that theory.

Keywords:

• Control chart
• Short-run statistical process control
• Two-stage control charting
• Distribution of the variance
• Distribution of the studentized variance

Acknowledgments

Notes

^#Editor's Note: This article is the second in a set of two articles, the first of which appeared in Volume 15, Number 3. The first article was titled “Two-Stage Short-Run (X¯,v) and ( X¯, √v) Control Charts” and this one uses the theory developed in that first article to develop a computer program based on that theory.