Full Text:   <2468>

Summary:  <1247>

Suppl. Mater.: 

CLC number: O213.1

On-line Access: 2019-05-14

Received: 2017-06-28

Revision Accepted: 2017-09-15

Crosschecked: 2019-04-11

Cited: 0

Clicked: 5964

Citations:  Bibtex RefMan EndNote GB/T7714


Shahid Hussain


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2019 Vol.20 No.4 P.554-570


A new auxiliary information based cumulative sum median control chart for location monitoring

Author(s):  Shahid Hussain, Li-xin Song, Shabbir Ahmad, Muhammad Riaz

Affiliation(s):  School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; more

Corresponding email(s):   shahid_libra82@hotmail.com

Key Words:  Average run length, Auxiliary information, CUSUM control charts, Location parameter, Median control charts

Shahid Hussain, Li-xin Song, Shabbir Ahmad, Muhammad Riaz. A new auxiliary information based cumulative sum median control chart for location monitoring[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 554-570.

@article{title="A new auxiliary information based cumulative sum median control chart for location monitoring",
author="Shahid Hussain, Li-xin Song, Shabbir Ahmad, Muhammad Riaz",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A new auxiliary information based cumulative sum median control chart for location monitoring
%A Shahid Hussain
%A Li-xin Song
%A Shabbir Ahmad
%A Muhammad Riaz
%J Frontiers of Information Technology & Electronic Engineering
%V 20
%N 4
%P 554-570
%@ 2095-9184
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1700428

T1 - A new auxiliary information based cumulative sum median control chart for location monitoring
A1 - Shahid Hussain
A1 - Li-xin Song
A1 - Shabbir Ahmad
A1 - Muhammad Riaz
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 20
IS - 4
SP - 554
EP - 570
%@ 2095-9184
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1700428

Control charts are commonly used tools in statistical process control for the detection of shifts in process parameters. Shewhart-type charts are efficient for large shift values, whereas cumulative sum (CUSUM) charts are effective in detecting medium and small shifts. Control chart use commonly assumes that data are free of outliers and parameters are known or correctly estimated based on an in-control process. In practice, these assumptions are not often true because some processes occasionally have outliers. Monitoring the location parameter is usually based on mean charts, which are seriously affected by violations of these assumptions. In this paper we propose several CUSUM median control charts based on auxiliary variables, and offer comparisons with their corresponding mean control charts. To monitor the location parameter, we examined the performance of mean and median control charts in the presence and absence of outliers. Both symmetric and non-symmetric processes were studied to examine the properties of the proposed control charts to monitor the location parameter using CUSUM control charts. We used different run length measures to study in-control and out-of-control performances of CUSUM charts. Results revealed that our proposed control charts perform much better than the traditional charts in the presence of outliers. A real application of our study was provided using data on concrete compressive strength as it relates to the quality of cement manufacturing.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Abbas N, Riaz M, Does RJMM, 2014. An EWMA-type control chart for monitoring the process mean using auxiliary information. Commun Stat Theory Methods, 43(16):3485- 3498.

[2]Abbasi SA, Riaz M, 2013. On enhanced control charting for process monitoring. Int J Phys Sci, 8(17):759-775.

[3]Abujiya MR, Lee MH, Riaz M, 2015a. Increasing the sensitivity of cumulative sum charts for location. Qual Reliab Eng Int, 31(6):1035-1051.

[4]Abujiya MR, Riaz M, Lee MH, 2015b. Enhanced cumulative sum charts for monitoring process dispersion. PLOS ONE, 10(4):e0124520.

[5]Adebola FB, Adegoke NA, Sanusi RA, 2015. A class of regression estimator with cum-dual ratio estimator as intercept. Int J Prob Stat, 4(2):42-50.

[6]Ahmad S, Lin ZY, Abbasi SA, et al., 2013. On efficient monitoring of process dispersion using interquartile range. Open J Appl Sci, 2(4B):39-43.

[7]Ahmad S, Riaz M, Abbasi SA, et al., 2014a. On efficient median control charting. J Chin Inst Eng, 37(3):358-375.

[8]Ahmad S, Riaz M, Abbasi SA, et al., 2014b. On median control charting under double sampling scheme. Eur J Ind Eng, 8(4):478-512.

[9]Brook D, Evans DA, 1972. An approach to probability distribution of CUSUM run length. Biometrika, 59(3):539-549.

[10]Castagliola P, 2001. An EWMA control chart for monitoring the process sample median. Int J Reliab Qual Saf Eng, 8(2):123-135.

[11]Castagliola P, Maravelakis PE, Figueiredo FO, 2015. The EWMA median chart with estimated parameters. IIE Trans, 48(1):66-74.

[12]Chen YK, Chiou KC, 2008. An evaluation of median Rankit control charts. IEEE Int Conf on Systems, Man and Cybernetics, p.3601-3605.

[13]Gupta S, Shabbir J, 2007. On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables. J Stat Plan Infer, 137(5):1606-1611.

[14]Haridy AMA, Elshabrawy AZ, 1996. The economic design of cumulative sum charts used to maintain current control of non-normal process means. Comput Ind Eng, 31(3-4): 783-790.

[15]Hawkins DM, 1981. A CUSUM for a scale parameter. J Qual Technol, 13(4):228-231.

[16]Hawkins DM, 1993. Regression adjustment for variables in multivariate quality control. J Qual Technol, 25(3):170- 182.

[17]Hawkins DM, Olwell DH, 2012. Cumulative Sum Charts and Charting for Quality Improvement. Springer Science & Business Media, Jensen.

[18]Hawkins DM, Wu QF, 2014. The CUSUM and the EWMA head-to-head. Qual Eng, 26(2):215-222.

[19]Huang WP, Shu LJ, Woodall WH, et al., 2016. CUSUM procedures with probability control limits for monitoring processes with variable sample sizes. IIE Trans, 48(8): 759-771.

[20]Kadilar C, Cingi H, 2003. Ratio estimators in stratified random sampling. Biometr J, 45(2):218-225.

[21]Kadilar C, Cingi H, 2005a. A new estimator using two auxiliary variables. Appl Math Comput, 162(2):901-908.

[22]Kadilar C, Cingi H, 2005b. A new ratio estimator in stratified random sampling. Commun Stat Theory Methods, 34(3): 597-602.

[23]Kanji GK, Arif OH, 2000. Median Rankit control chart by the quantile approach. J Appl Stat, 27(6):757-770.

[24]Kanji GK, Arif OH, 2001. Median Rankit control chart for Weibull distribution. Total Qual Manag, 12(5):629-642.

[25]Khoo MBC, 2005. A control chart based on sample median for the detection of a permanent shift in the process mean. Qual Eng, 17(2):243-257.

[26]Mehmood R, Riaz M, Does RJMM, 2013. Control charts for location based on different sampling schemes. J Appl Stat, 40(3):483-494.

[27]Montgomery DC, 2007. Introduction to Statistical Quality Control (6th Ed.). John Wiley & Sons, Hoboken, NJ.

[28]Mukherjee A, Graham MA, Chakraborti S, 2013. Distribution- free exceedance CUSUM control charts for location. Commun Stat Simul Comput, 42(5):1153-1187.

[29]Mundform DJ, Schaffer J, Kim MJ, et al., 2011. Number of replications required in Monte Carlo simulation studies: a synthesis of four studies. J Mod Appl Stat Methods, 10(1), Article 4.

[30]Nazir HZ, Riaz M, Does RJ, et al., 2013. Robust CUSUM control charting. Qual Eng, 25(3):211-224.

[31]Nazir HZ, Riaz M, Does RJ, 2015. Robust CUSUM control charting for process dispersion. Qual Reliab Eng Int, 31(3):369-379.

[32]Oakland JS, 2007. Statistical Process Control (6th Ed.). Routledge, London.

[33]Ou YJ, Wen D, Wu Z, et al., 2012a. A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance. Qual Reliab Eng Int, 28(1):3-17.

[34]Ou YJ, Wu Z, Tsung F, 2012b. A comparison study of effectiveness and robustness of control charts for monitoring process mean. Int J Prod Econ, 135(1):479-490.

[35]Page ES, 1954. Continuous inspection schemes. Biometrika, 41(1-2):100-115.

[36]Qiu PH, Hawkins D, 2011. A rank-based multivariate CUSUM procedure. Technometrics, 43(2):120-132.

[37]Rakitzis AC, Castagliola P, Maravelakis PE, 2018. Cumulative sum control charts for monitoring geometrically inflated Poisson processes: an application to infectious disease counts data. Stat Methods Med Res, 27(2):622-641.

[38]Rao GS, 2013. One-sided cumulative sum (CUSUM) control charts for the Erlang-truncated exponential distribution. Comput Methods Sci Technol, 19(4):229-234.

[39]Riaz M, 2008a. Monitoring process mean level using auxiliary information. Stat Neerl, 62(4):458-481.

[40]Riaz M, 2008b. Monitoring process variability using auxiliary information. Comput Stat, 23(2):253-276.

[41]Riaz M, 2015. Control charting and survey sampling techniques in process monitoring. J Chin Inst Eng, 38(3):342- 354.

[42]Riaz M, Does RJMM, 2009. A process variability control chart. Comput Stat, 24(2):345-368.

[43]Riaz M, Abbas N, Does RJMM, 2011. Improving the performance of CUSUM charts. Qual Reliab Eng Int, 27(4): 415-424.

[44]Riaz M, Mehmood R, Ahmad S, et al., 2013. On the performance of auxiliary-based control charting under normality and nonnormality with estimation effects. Qual Reliab Eng Int, 29(8):1165-1179.

[45]Roberts SW, 1959. Control chart tests based on geometric moving averages. Technometrics, 1(3):239-250.

[46]Ryu JH, Wan HG, Kim S, 2010. Optimal design of a CUSUM chart for a mean shift of unknown size. J Qual Technol, 42(3):311-326.

[47]Sanusi RA, Abujiya MR, Riaz M, 2017. Combined Shewhart CUSUM charts using auxiliary variable. Comput Ind Eng, 105:329-337.

[48]Sanusi RA, Abbas N, Riaz M, 2018. On efficient CUSUM- type location control charts using auxiliary information. Qual Technol Quant Manag, 15(1):87-105.

[49]Schaffer JR, Kim MJ, 2007. Number of replications required in control chart Monte Carlo simulation studies. Commun Stat Simul Comput, 36(5):1075-1087.

[50]Sepúlveda A, Nachlas JA, 1997. A simulation approach to multivariate quality control. Comput Ind Eng, 33(1-2): 113-116.

[51]Shafae MS, Dickinson RM, Woodall WH, et al., 2015. Cumulative sum control charts for monitoring Weibull- distributed time between events. Qual Reliab Eng Int, 31(5):839-849.

[52]Sheu SH, Yang L, 2006a. The generally weighted moving average control chart for monitoring the process median. Qual Eng, 18(3):333-344.

[53]Sheu SH, Yang L, 2006b. The generally weighted moving average median control chart. Qual Technol Quant Manag, 3(4):455-471.

[54]Sheu SH, Tai SH, Hsieh YT, et al., 2009. Monitoring process mean and variability with generally weighted moving average control charts. Comput Ind Eng, 57(1):401-407.

[55]Shewhart WA, 1924. Some applications of statistical methods to the analysis of physical and engineering data. Bell Syst Techn J, 3(1):43-87.

[56]Shu LJ, Tsung F, Tsui KL, 2005. Effects of estimation errors on cause-selecting charts. IIE Trans, 37(6):559-567.

[57]Singh HP, Solanki RS, 2012. An efficient class of estimators for the population mean using auxiliary information in systematic sampling. J Stat Theory Pract, 6(2):274-285.

[58]Singh HP, Upadhyaya LN, Chandra P, 2004. A general family of estimators for estimating population mean using two auxiliary variables in two-phase sampling. Stat Trans, 6(7):1055-1077.

[59]Singh HP, Tailor R, Singh S, et al., 2008. A modified estimator of population mean using power transformation. Stat Pap, 49(1):37-58.

[60]Singh R, Kumar M, 2011. A note on transformations on auxiliary variable in survey sampling. Model Assisted Stat Appl, 6(1):17-19.

[61]Singh R, Chauhan P, Sawan N, et al., 2007. Auxiliary information and a priori values in construction of improved estimators. https://arxiv.org/abs/0712.0096

[62]Singh R, Chauhan P, Sawan N, et al., 2009. Ratio estimators in simple random sampling using information on auxiliary attribute. https://arxiv.org/abs/0907.4182

[63]Solanki RS, Singh HP, Rathour A, 2012. An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys. ISRN Prob Stat, 2012:65682.

[64]Tailor R, Sharma B, 2009. A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis. Stat Trans, 10(1):15-24.

[65]Tailor R, Chouhan S, Tailor R, et al., 2012. A ratio-cum- product estimator of population mean in stratified random sampling using two auxiliary variables. Statistica, 72(3): 287-297.

[66]Team RC, 2015. R: a Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.

[67]Umble EJ, 2001. Cumulative sum charts and charting for quality improvement. Technometrics, 43(1):107.

[68]Woodall WH, Montgomery DC, 1999. Research issues and ideas in statistical process control. J Qual Technol, 31(4): 376-386.

[69]Wu Z, Jiao J, Yang M, et al., 2009. An enhanced adaptive CUSUM control chart. IIE Trans, 141(7):642-653.

[70]Yang L, Pai S, Wang YR, 2010. A novel CUSUM median control chart. Proc Int Multiconf of Engineers and Computer Scientists, p.1707-1710.

[71]Yeh IC, 1998. Modeling of strength of high-performance concrete using artificial neural networks. Cem Concr Res, 28(12):1797-1808.

[72]Yeh IC, 2003. Prediction of strength of fly ash and slag concrete by the use of artificial neural networks. J Chin Inst Civil Hydraul Eng, 15(4):659-663.

[73]Yeh IC, 2006. Analysis of strength of concrete using design of experiments and neural networks. J Mater Civ Eng, 18(4): 597-604.

[74]Zhang S, Wu Z, 2006. Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals. IIE Trans, 38(4):377- 387.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE