(X)OVER-BAR CHARTS WITH VARIABLE SAMPLE-SIZE

Abstract

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours This article considers the properties of the XBAR chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) XBAR chart are obtained using Markov chains. The VSS XBAR chart is substantially quicker than the traditional XBAR chart in detecting moderate shifts in the process.