The Updatable $\overline{X}$ & S Control Charts

Abstract

The tools for Statistical Process Control (SPC) should be continuously improved in order to continuously improve the product quality. This article proposes a scenario for continuously improving the $\overline {X}$ & S control charts during the use of the charts. It makes use of the information collected from the out-of-control cases in a manufacturing process to update the charting parameters (i.e. the sample size, sampling interval and control limits) step-by-step. Consequently, the resultant control charts (called the updatable charts) become more and more effective to detect the mean shift δ _μ and standard deviation shift δ _σ for the particular process. The updatable charts are able to considerably reduce the average value of the loss function due to the occurrences of the out-of-control cases. Noteworthily, unlike the designs of the economic control charts, the designs of the updatable charts only require limited number of specifications that can be easily decided.