Bivariate control charts with double sampling

In this article, we consider the T 2 chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n1 items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic T 2 1 for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic T 2 1 is greater than CL1, where CL1 > w, the control chart signals an out-of-control condition. Ifw < T2 1 ≤ CL1, the sampling goes on to the second stage, where the remaining n2 items of the sample are inspected and T 2 2 for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic T 2 2 is larger than CL2. A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T 2 chart and the adaptive bivariate T 2 charts with variable sample size and/or variable sampling interval.