A synthetic control chart for monitoring the pprocess mean and variance

Abstract

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control the process mean and variance. During the first stage, one item of the sample is inspected; if its value Xl is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the statistic T = Σ [X1 - μ0 + ξσ0]2 is computed taking into account all items of the sample. The design parameter ξ is function of X1. When the statistic T is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on Conforming Run Length (CRL). The CRL is the number of samples taken from the process since the previous nonconforming sample until the occurrence of the next nonconforming sample. If the CRL is sufficiently small, then a signal is generated. A comparative study shows that the SyTS chart and the joint X and S charts with double sampling are very similar in performance. However, from the practical viewpoint, the SyTS chart is more convenient to administer than the joint charts.