A Computer Program to Calculate Two-Stage Short-Run Control Chart Factors for (X, v) and (X, v~(1/2)) Charts

摘要

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~(1/2)) 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~(1/2) churl 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.