Research Article

Self-starting single control charts for multivariate processes: a comparison of methods

Eralp Dogu; Min Jung Kim

Downloads: 0
Views: 24


Abstract: Paper aims: Based on challenges faced in real SPC application, this paper considers implementation and performance of self-starting methodology in multivariate process monitoring.

Originality: Traditional omnibus charts depend on in-control process parameters while parameters are generally known. However, in real settings, this information may not exist. This paper proposes and compares novel methods to overcome this difficulty.

Research method: This paper introduces, evaluates the performance and implements multivariate self-starting charts (SSMEC, SSMELR, and SSMME) for multivariate process monitoring.

Main findings: Proposed SSMME chart is the best choice in real application because it proves better performance in response to various simulation scenarios and gives diagnostic tools for further analysis.

Implications for theory and practice: The main contributions are the comparison of different self-starting approaches and introducing a novel multivariate self-starting chart that are suitable in real process monitoring and illustrate the benefit of the selected SPC chart with hypertension monitoring.


Multivariate quality control. Self-starting method. Single control chart. Hypertension monitoring.


Albloushi, T., Suwaidi, A., Zarouni, N., Abdelrahman, A., & Shamsuzzaman, M. (2015). Design of X̅&R control charts for monitoring quality of care for hypertension. In 2015 International Conference on Industrial Engineering and Operations Management (IEOM) (pp. 1-5). Piscataway: IEEE.

Alt, F. B. (1985). Multivariate quality control. In S. Kotz & N. L. Johnson (Ed.), The encyclopedia of statistical sciences (pp. 110-122). Hoboken: Wiley.

Alt, F. B., & Smith, N. D. (1988). 17 multivariate process control. In P. R. Krishnaiah & C. R. Rao Larsen (Eds.), Handbook of statistics (Vol. 7, pp. 333-351). Amsterdam: Elsevier.

Chen, G., Cheng, S. W., & Xie, H. (2005). A new multivariate control chart for monitoring both location and dispersion. Communications in Statistics: Simulation and Computation, 34(1), 203-217.

Cheng, S. W., & Thaga, K. (2005). Multivariate Max-CUSUM Chart. Quality Technology & Quantitative Management, 2(2), 221-235.

Cheng, S. W., & Thaga, K. (2006). Single variables control charts: an overview. Quality and Reliability Engineering International, 22(7), 811-820.

Cornélissen, G., Halberg, F., Hawkins, D., Otsuka, K., & Henke, W. (1997). Individual assessment of antihypertensive response by self-starting cumulative sums. Journal of Medical Engineering & Technology, 21(3–4), 111-120. PMid:9222952.

Diko, M. D., Goedhart, R., & Does, R. J. (2019). A head-to-head comparison of the out-of-control performance of control charts adjusted for parameter estimation. Quality Engineering. In press.

Doǧu, E. (2012). Monitoring time between medical errors to improve health-care quality. International Journal of Qualitative Research, 6(2), 151-157.

Doǧu, E. (2015). Identifying the time of a step change with multivariate single control charts. Journal of Statistical Computation and Simulation, 85(8), 1529-1543.

Doǧu, E., & Kocakoc, I. D. (2011). Estimation of change point in generalized variance control chart. Communications in Statistics. Simulation and Computation, 40(3), 345-363.

Doǧu, E., & Kocakoc, I. D. (2013). A multivariate change point detection procedure for monitoring mean and covariance simultaneously. Communications in Statistics. Simulation and Computation, 42(6), 1235-1255.

Eren-Dogu, Z. F., & Dogu, E. (2013). Monitoring the efficiency of use of operating room time with CUSUM charts. Quality Issues and Insights in the 21st Century, 2(2), 1-6.

Faraz, A., Woodall, W. H., & Heuchenne, C. (2015). Guaranteed conditional performance of the S 2 control chart with estimated parameters. International Journal of Production Research, 53(14), 4405-4413.

Hawkins, D. M. (1987). Self-starting CUSUM charts for location and scale. The Statistician, 36(4), 299-316.

Hawkins, D. M., & Maboudou-Tchao, E. M. (2007). Self-starting multivariate exponentially weighted moving average control charting. Technometrics, 49(2), 199-209.

Hawkins, D. M., & Maboudou-Tchao, E. M. (2008). Multivariate exponentially weighted moving covariance matrix. Technometrics, 50(2), 155-166.

Hawkins, D. M., & Olwell, D. H. (2012). Cumulative sum charts and charting for quality improvement. New York: Springer Science & Business Media.

Hawkins, D. M., & Zamba, K. D. (2005). Statistical process control for shifts in mean or variance using a changepoint formulation. Technometrics, 47(2), 164-173.

Holmes, D. S., & Mergen, A. E. (1993). Improving the performance of the T^2 control chart. Quality Engineering, 5(4), 619-625.

Hu, X., Castagliola, P., Zhou, X., & Tang, A. (2019). Conditional design of the EWMA median chart with estimated parameters. Communications in Statistics. Theory and Methods, 48(8), 1871-1889.

Jardim, F. S., Chakraborti, S., & Epprecht, E. K. (2019). Chart with estimated parameters: the conditional ARL distribution and new insights. Production and Operations Management, 28(6), 1545-1557.

Jardim, F. S., Chakraborti, S., & Epprecht, E. K. (2020). Two perspectives for designing a phase II control chart with estimated parameters: the case of the Shewhart Xbar chart. Journal of Quality Technology, 52(2), 198-217.

Jensen, W. A., Jones-Farmer, L. A., Champ, C. W., & Woodall, W. H. (2006). Effects of parameters estimation on Control Charts properties: a literature review. Journal of Quality Technology, 38(4), 349-364.

Jones, L. A., Champ, C. W., & Rigdon, S. E. (2001). The performance of exponentially weighted moving average charts with estimated parameters. Technometrics, 43(2), 156-167.

Jones, L. A., Champ, C. W., & Rigdon, S. E. (2004). The run length distribution of the CUSUM with estimated parameters. Journal of Quality Technology, 36(1), 95-108.

Keefe, M. J., Woodall, W. H., & Jones-Farmer, L. A. (2015). The conditional in-control performance of self-starting control charts. Quality Engineering, 27(4), 488-499.

Khosravi, P., & Amiri, A. (2019). Self-Starting control charts for monitoring logistic regression profiles. Communications in Statistics: Simulation and Computation, 48(6), 1860-1871.

Kim, M.-J. (2012). Statistical quality methods to monitor and transform healthcare data. University Park: The Pennsylvania State University.

Li, Z., Zhang, J., & Wang, Z. (2010). Self-starting control chart for simultaneously monitoring process mean and variance. International Journal of Production Research, 48(15), 4537-4553.

Maboudou-Tchao, E. M., & Hawkins, D. M. (2011). Self-starting multivariate control charts for location and scale. Journal of Quality Technology, 43(2), 113-126.

Quesenberry, C. P. (1991). SPC Q charts for start-up processes and short or long runs. Journal of Quality Technology, 23(3), 213-224.

Quesenberry, C. P. (1993). The effect of sample size on estimated limits for X and S control charts. Journal of Quality Technology, 25(4), 237-247.

Quesenberry, C. P. (1995). On properties of Q charts for variables. Journal of Quality Technology, 27(3), 184-203.

Quesenberry, C. P. (1997). SPC methods for quality improvement. New York: John Wiley & Sons.

Shen, X., Tsui, K.-L., Zou, C., & Woodall, W. H. (2016). Self-starting monitoring scheme for poisson count data with varying population sizes. Technometrics, 58(4), 460-471.

Thaga, K., & Gabaitiri, L. (2006). Multivariate Max-Chart. Economic Quality Control, 21(1), 113-125.

Zamba, K. D., & Hawkins, D. M. (2009). A multivariate change point model for change in mean vector and/or covariance structure. Journal of Quality Technology, 41(3), 285-303.

Zhang, J., Li, Z., & Wang, Z. (2010). A multivariate control chart for simultaneously monitoring process mean and variability. Computational Statistics & Data Analysis, 54(10), 2244-2252.

Zwetsloot, I. M., & Ajadi, J. O. (2019). A comparison of EWMA control charts for dispersion based on estimated parameters. Computers & Industrial Engineering, 127, 436-450.

Zwetsloot, I. M., & Woodall, W. H. (2017). A head-to-head comparative study of the conditional performance of control charts based on estimated parameters. Quality Engineering, 29(2), 244-253.

5f0f049c0e8825c106e52f60 production Articles
Links & Downloads


Share this page
Page Sections