Synthetic control charts with two-stage sampling for monitoring bivariate processes

Abstract

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control bivariate processes. During the first stage, one item of the sample is inspected and two correlated quality characteristics (x;y) are measured. If the Hotelling statistic T1² for these individual observations of (x;y) is lower than a specified value UCL1 the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the Hotelling statistic T2² for the sample means of (x;y) is computed. When the statistic T2² is larger than a specified value UCL2, the sample is classified as nonconforming. According to the synthetic control chart procedure, the signal is based on the number of conforming samples between two neighbor nonconforming samples. The proposed chart detects process disturbances faster than the bivariate charts with variable sample size and it is from the practical viewpoint more convenient to administer.