Two-Stage Short-Run ([Xbar], s) Control Charts

Abstract

This article develops the theory that is needed to apply the two-stage short-run theory of control charting to ([Xbar], s) charts. It then uses this theory to derive the equations for calculating the factors required to determine two-stage short-run control limits for ([Xbar], s) charts. Also, equations to calculate conventional control chart constants for ([Xbar], s) charts are derived. Additionally, this article gives advantages of two-stage short-run ([Xbar], s) control charts.

Keywords:

• control chart
• short-run statistical process control
• two-stage control charting
• distribution of the standard deviation
• distribution of the studentized standard deviation
• distribution of the mean standard deviation