Browse > Article

Effects of Non-normality on the Performance of Univariate and Multivariate CUSUM Control Charts  

Chang, Young-Soon (Department of Business Administration, Myongji University)
Publication Information
Journal of Korean Society for Quality Management / v.34, no.4, 2006 , pp. 102-109 More about this Journal
Abstract
This paper investigates the effects of non-normality on the performance of univariate and multivariate cumulative sum(CUSUM) control charts for monitoring the process mean. In-control and out-of-control average run lengths of the charts are examined for the univariate/multivariate lognormal and t distributions. The effects of the reference value and the correlation coefficient under the non-normal distributions are also studied. Simulation results show that the CUSUM charts with small reference values are robust to non-normality but those with moderate or large reference values are sensitive to non-normal data especially to process data from skewed distributions. The performance of the chart to detect mean shift of a process is not invariant to the direction of the shift for skewed distributions.
Keywords
CUSUM Control Chart; Non-normality; Average Run Length;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Stoumbos, Z. G. and Reynolds, M. R. Jr. (2000), 'Robustness to Non-normality and Autocorrelation of Individuals Control Charts', Journal of Statistical Computation and Simulation, Vol. 66, pp. 145-187   DOI   ScienceOn
2 Borror, C. M., Montgomery, D. C., and Runger, G. C.(1999), 'Robustness of the EWMA Control Chart to Non-normality', Journal of Quality Technology, Vol. 31, pp. 309-316   DOI
3 Healy, J. D.(1987), 'A Note on Multivariate CUSUM Procedures', Technometrics, Vol. 29, pp. 409-412   DOI
4 IMSL Library(1990), Reference Manual, Visual Numerics, Inc., Houston, TX
5 Lowry, C. A. and Montgomery, D. C.(1995), 'A Review of Multivariate Control Charts', lIE Transactions, Vol. 27, pp. 800-810
6 Crosier, R. B.(1988), 'Multivariate Generalizations of Cumulative Sum Quality-Control Schemes', Technometrics, Vol. 30, pp. 291-303   DOI
7 Chang, Y. S. and Bai, D. S.(2001), 'Control Charts for Positively-Skewed Populations with Weighted Standard Deviations', Quality and Reliability Engineering International, Vol. 17, pp. 397-406   DOI   ScienceOn
8 Stoumbos, Z. G. and Sullivan, J. H.(2002), 'Robustness to Non-normality of the Multivariate EWMA Control Chart', Journal of Quality Technology, Vol. 34, pp. 260-276   DOI
9 Maravelakis, P. E., Panaretos, J., and Psarakis, S.(2005), 'An Examination of the Robustness to Non Normality of the EWMA Control Charts for the Dispersion', Communications in Statistics-Simulation and Computation, Vol. 34, pp. 1069-1079   DOI   ScienceOn
10 Cheng, A. Y., Liu, R. Y., and Luxhoj, J. T. (2000), 'Monitoring Multivariate Aviation Safety Data by Data Depth: Control Charts and Threshold Systems', IIE Transactions, Vol. 32, pp. 861-872
11 Hawkins, D. M.(1991), 'Multivariate Quality Control Based on Regression-adjusted Variables', Technometrics, Vol. 33, pp. 61-75   DOI
12 Testik, M. C., Runger, G. C., and Borror, C. M.(2003), 'Robustness Properties of Multivariate EWMA Control Charts', Quality and ReliabIlity Engineering International, Vol. 19, pp. 31-38   DOI   ScienceOn
13 Mason, R. L., Champ, C. W., Tracy, N. D., Wierda, S. J., and Young, J. C.(1997), 'Assessment of Multivariate Process Control Techniques', Journal of Quality Technology, Vol. 29, pp. 140-143   DOI
14 Balakrishnan, N. and Kocherlakota, S.(1986), 'Effects of Non-normality on X Charts: Single Assignable Cause Model', Sankya Series B, Vol. 48, pp. 439-444
15 Montgomery, D. C.(2001), Intorduction to Statistical Quality Control 4th ed., Wiley, New York, NY
16 Pignatiello, J. J. and Runger, G. C.(1990), 'Comparisons of Multivariate CUSUM Charts', Journal of Quality Technology, Vol. 22, pp. 173-186   DOI
17 Qiu, P. and Hawkins, D.(2001), 'A Rank-based Multivariate CUSUM Procedure', Technometrics, Vol. 43, pp. 120-132   DOI   ScienceOn
18 Page, E. S.(1954), 'Continuous Inspection Schemes', Biometrika, Vol. 41, pp. 100-115   DOI
19 Coleman, D. E.(1997), 'Individual Contributions in a Discussion on Statistically-based Process Monitoring and Control eds. Montgomery, D. C. and Woodall, W. H.', Journal of Quality Technology, Vol. 29, pp. 148149
20 Woodall, W. H. and Ncube, M. M.(1985), 'A Multivariate CUSUM Quality-control Procedures', Technometrics, Vol. 27, pp. 285-292   DOI