Bivariate control charts with double sampling

Abstract

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, n ₁ items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic is greater than CL₁, where CL₁>w, the control chart signals an out-of-control condition. If , the sampling goes on to the second stage, where the remaining n ₂ items of the sample are inspected and 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 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.

Keywords:

• the Hotelling statistic T ²
• bivariate processes
• double sampling

Acknowledgements

This work was supported by CAPES – High Level Staff Improvement Coordination –, CNPq – National Council for Scientific and Technological Development and FAPESP – The State of São Paulo Research Foundation. We would like to thank the new editor who handled the review process for this article.