Second Stage Short Run (X,vc) and (X,sc) Control Charts

Matthew E. Elam, Kenneth E. Case, Jong-Min Kim

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In their 1970 paper titled "Mean and Variance Control Chart Limits Based on a Small Number of Subgroups" (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for ) v,X c( and )s ,X( c charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at

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