Switching properties of bivariate Shewhart control charts for monitoring the covariance matrix

- Journal title : Journal of the Korean Data and Information Science Society
- Volume 26, Issue 6, 2015, pp.1593-1600
- Publisher : Korean Data and Information Science Society
- DOI : 10.7465/jkdi.2015.26.6.1593

Title & Authors

Switching properties of bivariate Shewhart control charts for monitoring the covariance matrix

Gwon, Hyeon Jin; Cho, Gyo-Young;

Gwon, Hyeon Jin; Cho, Gyo-Young;

Abstract

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. We construct bivariate Shewhart control charts based on the trace of the product of the estimated variance-covariance matrix and the inverse of the in-control matrix and investigate the properties of bivariate Shewart control charts with VSI procedure for monitoring covariance matrix in term of ATS (Average time to signal) and ANSW (Average number of switch) and probability of switch, ASI (Average sampling interval). Numerical results show that ATS is smaller than ARL. From examining the properties of switching in changing covariances and variances in , ANSW values show that it does not switch frequently and does not matter to use VSI procedure.

Keywords

Average run length;average number of switches;average sampling interval;average time to signal;switching property;

Language

English

References

1.

Amin, R. W. and Lestinger, W. C. (1991) Improved switching rules in control procedures using variable sampling interval. Communications in Statistics-Simulation and Computation, 20, 205-203.

2.

Amin, R. W. and Hemasinha, R. (1993). the switching behavior of X charts with variable sampling intervals. Theory and Methods, 22, 2081-2102.

3.

Arnold, J. C. (1970). A Markovian sampling policy applied to quality monitoring of streams. Biometrics, 26, 739-747.

4.

Chang, D. J. and Heo S. Y. (2012). Switching properties of CUSUM charts for controlling mean vector. Journal of the korean Data & Information Science Society, 23, 859-866.

5.

Chang, D. J. and Cho G. Y. (2005). CUSUM charts for monitoring mean vector with variable sampling intervals. Journal of the korean Data Analysis Society, 7, 1133-1143.

6.

Hotelling, H. (1947). Multivariate quality control, techniques of statistical analysis, McGraw-Hill, New York, 111-184.

7.

Jeong, J. I. and Cho G. Y. (2012). Multivariate Shewhart control charts for monitoring the vatiancecovariance matrix. Journal of the Korean Data & Information Science Society, 23, 617-626.

8.

Reynolds, Jr, M. R. (1989). Optimal two-sided variable sampling interval control charts for the exponential family. Sequential Analysis, 8, 361-379.

9.

Reynolds, Jr, M. R. (1995). Evaluating properties of variable sampling interval control charts. Sequential Analysis, 14, 59-97.

10.

Reynolds, Jr, M. R. and Arnold, J. C. (1989). Optimal one-sided Shewhart control charts with variable sampling intervals between samples. Sequential Analysis, 8, 51-77.

11.

Reynolds, Jr, M. R. and Cho, G. Y. (2006). Multivariate control charts for monitoring the mean vector and covariance Matrix. Journal of Quality Technology, 38, 230-253.

12.

Reynolds, Jr, M. R. and Cho. G. Y. (2011). Multivariate control charts for Monitoring the mean vector and covariance matrix with variable sampling intervals. Sequential Analysis, 30, 1-40.

13.

Reynolds, Jr, M. R. and Stoumbos, Z. G. (2001). Monitoring the process mean and variance using individual observations and variable sampling intervals. Journal of Quality Technology, 33, 181-205.

14.

Reynolds, Jr, M. R. and Stoumbos, Z. G. (2004a). Control charts and the optimal allocation of sampling resources. Technometrics, 46, 200-214.

15.

Reynolds, Jr, M. R. and Stoumbos, Z. G. (2004b). Should observations be grouped for effective process monitoring?. Journal of Quality Technology, 36, 343-366.