Monitoring the process mean and variance using a synthetic control chart with two-stage testing

Abstract

In this paper, we propose a synthetic control chart with two-stage testing (SyTS chart) to control the process mean and variance. As in the case of Shewhart control charts, samples are taken from the process at regular time intervals; however, testing is performed in two stages. During the first stage, one item of the sample is inspected; if its value is close to the target value of the process mean, then this terminates testing. Otherwise, the testing goes on to the second stage, where the remaining items are inspected and a non-central chi-square statistic is computed taking into account all items of the sample. When this statistic is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on the conforming run length (CRL). A comparative study shows that the SyTS chart and the joint and S charts with double sampling are very similar in performance. However, from a practical viewpoint, it is more convenient to monitor the process by looking at only one chart rather than looking at two charts separately. Comparisons with the joint and S charts and with several CUSUM schemes show that the SyTS chart has better overall performance.