The variable sample size variable dimension T² control chart

Abstract

In this paper, we describe the development of the variable dimension and variable sample size T² control chart (VSSVDT²), which is an enhancement of the variable dimension T² chart (VDT²). In the VDT² control chart, the number of variables that are measured to compute the T² statistic is made variable. Some of the variables are easy or inexpensive to measure and are always monitored. The variables that are more difficult or expensive to measure are measured only when the T² value from the previous sample exceeds a specified threshold. The VDT² control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart’s performance in detecting such shifts, we propose the application of the variable sample size technique to the VDT² control chart, resulting in the VSSVDT² control chart. To promote the use of the VSSVDT² chart, a user-friendly software has been developed, which the final user can use to find the best parameters of the VSSVDT² chart for a particular process.

Keywords:

• control charts
• quality control

Acknowledgements

This work was supported by the CNPq (the Brazilian Council for Scientific and Technological Development), project number 307453/2011-1, and the SENESCYT-Ecuador (National Secretary of Higher Education, Science, Technology and Innovation of Ecuador). The authors are grateful to the referees for their comments, which led to significant improvement of the paper.