Modified EWMA Control Chart for Skewed Distributions and Contaminated Processes

Authors

  • Thanyaporn Noiplab Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand
  • Tidadeaw Mayureesawan Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand

Keywords:

EWMA control chart, modified EWMA control chart, skewed distribution, contaminated data, average run length

Abstract

In this paper, we proposed the variable control chart for monitoring process mean by modified the traditional Exponentially Weighted Moving Average (EWMA) control chart for skewed and contaminated processes. The proposed EWMA control charts are modified both of mean and standard deviation in the control limits of the traditional EWMA control chart based on three different heuristic methods, namely, the Modified Exponentially Weighted Moving Average (MEWMA) control chart, the Modified Weighted Standard Deviation Exponentially Weighted Moving Average (MWSD-EWMA) control chart, and the Modified Weighted Variance Exponentially Weighted Moving Average (MWV-EWMA) control chart. A comparison of the performance measures is the average run length (ARL) were compared with the traditional EWMA control chart in various situations via simulation. The results show that for Gamma distribution, the MWSD-EWMA control chart is performs well for small sample size (gif.latex?n=5), low levels of gif.latex?\kappa&space;_{3}, gif.latex?(\kappa&space;_{3}=1) and gif.latex?\delta are low gif.latex?(\delta&space;=0.10,&space;0.25) in all levels of gif.latex?\lambda. The MEWMA control chart is the better than other charts for moderate levels of  gif.latex?\delta gif.latex?(\delta&space;=&space;0.50) on all levels of gif.latex?\kappa&space;_{3},&space;\lambda,&space;n  and relatively small differences with the MWV-EWMA control chart. When the process distribution is Weibull, the MWSD-EWMA control chart is performs well for small sample size gif.latex?(n=5) and gif.latex?\delta are low gif.latex?(\delta&space;=&space;0.10,&space;0.25) in all values of  gif.latex?\kappa&space;_{3}  and gif.latex?\lambda. If the sample sizes are moderate and large gif.latex?(n&space;=&space;10,&space;20), the MWSD-EWMA control chart is better than other charts for very low level of gif.latex?\delta gif.latex?(\delta&space;=&space;0.10) in all values of gif.latex?\kappa&space;_{3}  and  gif.latex?\lambda. For lognormal distribution, we found that the results as well as the Weibull distribution in all levels of gif.latex?\kappa&space;_{3},&space;\lambda and gif.latex?n.  Finally, all charts are similar performances for all values of gif.latex?\kappa&space;_{3},&space;\lambda and gif.latex?n when high levels of gif.latex?\delta  in all skewed distribution processes.

References

Atta AMA, Ramli R. A comparison study on the performances of EWMA, and CUSUM control charts for skewed distributions using weighted standard deviation methods. J Sci Tech. 2011; 3: 77-88.

Champ CW, Woodall WH. Exact results for Shewhart control charts with supplementary runs rules. Technometrics. 1987; 29: 393-399.

Chan LK, Cui HJ. Skewness correction and R charts for skewed distributions. Nav Res Logist. 2003; 50: 1-19.

Chang YS, Bai DS. Control charts for positively popultions with weighted standard deviation. Qual Reliab Eng Int. 2001; 17: 397-406.

Choobinech F, Ballard JL. Control-limits of QC charts for skewed distributions using weighted-variance. IEEE Trans Reliab. 1987; 36: 473-477.

Crowder SV. A simple method for studying run-length distributions of exponentially weighted moving average charts. Technometrics. 1987; 29: 401-417.

Crowder SV. Design of exponentially weighted moving average schemes. J Qual Tech. 1989; 21: 155-162.

Derya K, Canan H. Control charts for skewed distributions: Weibull, gamma, and lognormal. Metodoloski. 2012; 9: 95-106.

Derya K. Robust control chart for monitoring the skewed and contaminated process. Hacettepe J Math Stat. 2016; 46: 1-19.

Khoo MBC, Atta AMA. An EWMA control chart for monitoring the mean of skewed populations using weighted variance. Proceeding of the 2008 IEEE International Conference on Industrial Engineering and Engineering Management; 2008 Dec 8-11; Singapore. IEEE; 2008. p. 218-223.

Khoo MBC, Atta AMA, Chen CH. Proposed and S control charts for skewed distributions. Proceeding of the 2009 IEEE International Conference on Industrial Engineering and Engineering Management; 2009 Dec 8-11; Singapore. IEEE; 2009. p. 389-393.

Lucas JM, Saccucci MS. Exponentially weighted moving average control schemes: properties and enhancements. Technometrics. 1990; 32(1): 1-12.

Montgomery DC. Introduction to statistical quality control. 5th ed. New York: John Wiley & Sons; 2005.

Muhammad A, Osama-H A, Chi-Hyuck J. A control chart for gamma distribution using multiple dependent state sampling. Ind Eng Manag Syst. 2017; 16: 109-117.

Page ES. Control charts with warning lines. Biometrics. 1955; 42: 243-257.

Roberts SW. Properties of control chart zone tests. Bell Syst Tech J. 1958; 37: 83-114.

Roberts SW. Control chart tests based on geometric moving averages. Technometrics. 1959; 42: 97-102.

Downloads

Published

2018-12-27

How to Cite

Noiplab, T., & Mayureesawan, T. (2018). Modified EWMA Control Chart for Skewed Distributions and Contaminated Processes. Thailand Statistician, 17(1), 16–29. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/163164

Issue

Section

Articles