EWMA Control Chart Performance with Estimated Parameters under Non-normality
Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are...
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| Published in | Quality and reliability engineering international Vol. 32; no. 5; pp. 1637 - 1654 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Bognor Regis
Blackwell Publishing Ltd
01.07.2016
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0748-8017 1099-1638 |
| DOI | 10.1002/qre.1896 |
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| Abstract | Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non‐normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non‐normality using skewed and heavy‐tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non‐normal observations. Copyright © 2015 John Wiley & Sons, Ltd. |
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| AbstractList | Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non-normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non-normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non-normality using skewed and heavy-tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non-normal observations. Copyright © 2015 John Wiley & Sons, Ltd. Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non-normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non-normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non-normality using skewed and heavy-tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non-normal observations. |
| Author | Noorossana, R. Nayebpour, M. R. Fathizadan, S. |
| Author_xml | – sequence: 1 givenname: R. surname: Noorossana fullname: Noorossana, R. email: Correspondence to: R. Noorossana, Industrial Engineering, Iran University of Science and Technology, Tehran, Iran., rassoul@iust.ac.ir organization: Industrial Engineering Department, Iran University of Science and Technology, Tehran, Iran – sequence: 2 givenname: S. surname: Fathizadan fullname: Fathizadan, S. organization: Industrial Engineering Department, Iran University of Science and Technology, Tehran, Iran – sequence: 3 givenname: M. R. surname: Nayebpour fullname: Nayebpour, M. R. organization: Keller Graduate School of Management, DeVry University, TX, Houston, USA |
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| References_xml | – reference: Psarakis S, Vyniou AK, Castagliola P. Some recent developments on the effects of parameter estimation on control charts. Quality and Reliability Engineering International 2013. doi:10.1002/qre.1556. – reference: Mendoza-Parra MA, Nowicka M, Van Gool W, Gronemeyer H. Characterising ChIP-seq binding patterns by model-based peak shape deconvolution. BMC Genomics 2013; 14:834. – reference: Quesenberry CP. The effect of sample size on estimated limits for X¯ and X control charts. Journal of Quality Technology 1993; 25(4):237-247. – reference: Abbasi SA, Miller A. On proper choice of variability control chart for normal and non-normal processes. Quality and Reliability Engineering International 2012; 28(3):279-296. – reference: Borror CM, Montgomery DC, Runger GC. Robustness of the EWMA control chart to non-normality. Journal of Quality Technology 1999; 31:309-316. – reference: Jones LA, Champ CW, Rigdon SE. The performance of exponentially weighted moving average charts with estimated parameters. Technometrics 2001; 43(2):156-167. – reference: Saleh NA, Mahmoud AM, Abdel-Salam GA. The performance of the adaptive exponentially weighted moving average control chart with estimated parameters. Quality and Reliability Engineering International 2012; 29:595-606. – reference: Del Castillo E. Run length distributions and economic design of X charts with unknown process variance. Metrika 1996a; 43:189-201. – reference: Montgomery DC. Introduction to statistical quality control (6th edn). Wiley: New York, 2009. – reference: Braun WJ, Park D. Estimation of σ for individuals charts. Journal of Quality Technology 2008; 40(3):332-344. – reference: Champ CW, Rigdon SE. A comparison of the Markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts. Communications in Statistics-Simulation and Computation 1991; 20(1):191-204. – reference: Sim CH, Wong WK. R-charts for the exponential, Laplace and logistic processes. Statistical Papers 2003; 44:535-554. – reference: Sim CH. Inverse Gaussian control charts for monitoring process variability. Communications in Statistics-Simulation and Computation 2003b; 32:223-239. – reference: Brook D, Evans DA. An approach to the probability distribution of CUSUM run length. Biometrika 1972; 59(3):539-549. – reference: Reiss DJ, Facciotti MT, Baliga NS. Model-based deconvolution of genome-wide DNA binding. Bioinformatics 2008; 24:396-403. – reference: DeVor RE, Chang T, Sutherland JW. Statistical quality design and control contemporary concepts and methods. Prentice-Hall, Inc., Simon and Schuster: NJ, U.S.A., 1992. – reference: Jensen WA, Jones-Farmer LA, Champ CW, Woodall WH. Effects of parameter estimation on control chart properties: a literature review. Journal of Quality Technology 2006; 38:349-364. – reference: Robson JG, Troy JB. Nature of the maintained discharge of Q, X, and Y retinal ganglion cells of the cat. Journal of the Optical Society of America A 1987; 4:2301-2307. – reference: Chen G. The run length distribution of the R, S, and S2 control charts when σ is estimated. Communications in Statistics-Simulation and Computation 1998; 26:311-322. – reference: Lucas JM, Saccucci MS. Exponentially moving average control schemes: properties and enhancements. Technometrics 1990; 32(1):1-12. – reference: Wheeler DJ. Advanced topics in statistical process control: the power of Shewhart's chart. SPC Press: Knoxville, TN, 1995. – reference: Maravelakis P, Panaretos J, Psarakis S. An examination of the robustness to non normality of the EWMA control charts for the dispersion. Communications in Statistics-Simulation and Computation 2005; 34:1069-1079. – reference: Jones LA, Champ CW, Rigdon SE. The run length distribution of the CUSUM with estimated parameters. Journal of Quality Technology 2004; 36(1):95-108. – reference: Abbasi SA, Riaz M, Miller A, Ahmad S. On the performance of phase I dispersion control charts for process monitoring. Quality and Reliability Engineering International 2013. doi:10.1002/qre.1703. – reference: Chakraborti S. Run length, average run length and false alarm rate of Shewhart X chart: exact derivations by conditioning. Communications in Statistics-Simulation and Computation 2000; 29:61-81. – reference: Sim CH. Combined X-bar and CRL charts for the gamma process. Computational Statistics 2003a; 18:547-563. – volume: 36 start-page: 95 issue: 1 year: 2004 end-page: 108 article-title: The run length distribution of the CUSUM with estimated parameters publication-title: Journal of Quality Technology – year: 2009 – volume: 24 start-page: 396 year: 2008 end-page: 403 article-title: Model‐based deconvolution of genome‐wide DNA binding publication-title: Bioinformatics – volume: 18 start-page: 547 year: 2003a end-page: 563 article-title: Combined X‐bar and CRL charts for the gamma process publication-title: Computational Statistics – volume: 25 start-page: 237 issue: 4 year: 1993 end-page: 247 article-title: The effect of sample size on estimated limits for and X control charts publication-title: Journal of Quality Technology – volume: 43 start-page: 189 year: 1996a end-page: 201 article-title: Run length distributions and economic design of X charts with unknown process variance publication-title: Metrika – volume: 4 start-page: 2301 year: 1987 end-page: 2307 article-title: Nature of the maintained discharge of Q, X, and Y retinal ganglion cells of the cat publication-title: Journal of the Optical Society of America A – volume: 43 start-page: 156 issue: 2 year: 2001 end-page: 167 article-title: The performance of exponentially weighted moving average charts with estimated parameters publication-title: Technometrics – volume: 59 start-page: 539 issue: 3 year: 1972 end-page: 549 article-title: An approach to the probability distribution of CUSUM run length publication-title: Biometrika – volume: 26 start-page: 311 year: 1998 end-page: 322 article-title: The run length distribution of the R, S, and S2 control charts when is estimated publication-title: Communications in Statistics—Simulation and Computation – year: 1992 – year: 2013 article-title: Some recent developments on the effects of parameter estimation on control charts publication-title: Quality and Reliability Engineering International – volume: 28 start-page: 279 issue: 3 year: 2012 end-page: 296 article-title: On proper choice of variability control chart for normal and non‐normal processes publication-title: Quality and Reliability Engineering International – volume: 29 start-page: 61 year: 2000 end-page: 81 article-title: Run length, average run length and false alarm rate of Shewhart X chart: exact derivations by conditioning publication-title: Communications in Statistics—Simulation and Computation – volume: 38 start-page: 349 year: 2006 end-page: 364 article-title: Effects of parameter estimation on control chart properties: a literature review publication-title: Journal of Quality Technology – volume: 32 start-page: 223 year: 2003b end-page: 239 article-title: Inverse Gaussian control charts for monitoring process variability publication-title: Communications in Statistics—Simulation and Computation – volume: 44 start-page: 535 year: 2003 end-page: 554 article-title: R‐charts for the exponential, Laplace and logistic processes publication-title: Statistical Papers – volume: 29 start-page: 595 year: 2012 end-page: 606 article-title: The performance of the adaptive exponentially weighted moving average control chart with estimated parameters publication-title: Quality and Reliability Engineering International – volume: 32 start-page: 1 issue: 1 year: 1990 end-page: 12 article-title: Exponentially moving average control schemes: properties and enhancements publication-title: Technometrics – volume: 31 start-page: 309 year: 1999 end-page: 316 article-title: Robustness of the EWMA control chart to non‐normality publication-title: Journal of Quality Technology – year: 1995 – volume: 14 start-page: 834 year: 2013 article-title: Characterising ChIP‐seq binding patterns by model‐based peak shape deconvolution publication-title: BMC Genomics – volume: 20 start-page: 191 issue: 1 year: 1991 end-page: 204 article-title: A comparison of the Markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts publication-title: Communications in Statistics—Simulation and Computation – volume: 40 start-page: 332 issue: 3 year: 2008 end-page: 344 article-title: Estimation of for individuals charts publication-title: Journal of Quality Technology – volume: 34 start-page: 1069 year: 2005 end-page: 1079 article-title: An examination of the robustness to non normality of the EWMA control charts for the dispersion publication-title: Communications in Statistics—Simulation and Computation – year: 2013 article-title: On the performance of phase I dispersion control charts for process monitoring publication-title: Quality and Reliability Engineering International |
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| SubjectTerms | average run length Control charts exponentially weighted moving average Markov chain Mathematical models non-normality Parameter estimation Performance evaluation Process parameters Robustness Standard deviation standard deviation of run length Symmetry |
| Title | EWMA Control Chart Performance with Estimated Parameters under Non-normality |
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