Nonparametric EWMA-Type Control Charts for Monitoring Industrial Processes: An Overview

In the present paper we provide an up-to-date overview of nonparametric Exponentially Weighted Moving Average (EWMA) control charts. Due to their nonparametric nature, such memory-type schemes are proved to be very useful for monitoring industrial processes, where the output cannot match to a particular probability distribution. Several fundamental contributions on the topic are mentioned, while recent advances are also presented in some detail. In addition, some practical applications of the nonparametric EWMA-type control charts are highlighted, in order to emphasize their crucial role in the contemporary online statistical process control. KeywordsDistribution-free statistical methods, Rank-based procedures, Nonparametric statistical process control, Exponentially weighted moving average (EWMA) control charts, Sign statistics.

[1]  H. A. Muttlak,et al.  Statistical quality control based on ranked set sampling , 2003 .

[2]  P. Castagliola,et al.  An EWMA-type chart based on signed ranks with exact run length properties , 2020 .

[3]  R. Meyer,et al.  The Fundamental Theorem of Exponential Smoothing , 1961 .

[4]  M. A. Graham,et al.  A Nonparametric EWMA Sign Chart for Location Based on Individual Measurements , 2011 .

[5]  Christos Koukouvinos,et al.  A nonparametric triple exponentially weighted moving average sign control chart , 2020, Qual. Reliab. Eng. Int..

[6]  Robert E. Sherman,et al.  Design and Evaluation of a Repetitive Group Sampling Plan , 1965 .

[7]  Amitava Mukherjee,et al.  Distribution-free exponentially weighted moving average control charts for monitoring unknown location , 2012, Comput. Stat. Data Anal..

[8]  K. K. Kamalja,et al.  Parameter estimation of Cambanis-type bivariate uniform distribution with Ranked Set Sampling , 2021 .

[9]  Abdul Haq,et al.  A nonparametric EWMA chart with auxiliary information for process mean , 2018, Communications in Statistics - Theory and Methods.

[10]  Zhang Wu,et al.  A control scheme for monitoring the frequency and magnitude of an event , 2009 .

[11]  Xin Lai,et al.  An adaptive nonparametric exponentially weighted moving average control chart with dynamic sampling intervals , 2020, Stat. Anal. Data Min..

[12]  N. Balakrishnan,et al.  Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics , 2009 .

[13]  Fugee Tsung,et al.  Likelihood Ratio-Based Distribution-Free EWMA Control Charts , 2010 .

[14]  Amal K. Shamma,et al.  Development and Evaluation of Control Charts Using Double Exponentially Weighted Moving Averages , 1992 .

[15]  I. Triantafyllou Wilcoxon-type rank-sum control charts based on progressively censored reference data , 2019, Communications in Statistics - Theory and Methods.

[16]  Muhammad Riaz,et al.  Control charts for location based on different sampling schemes , 2013 .

[17]  M. A. Graham,et al.  Nonparametric (distribution-free) control charts: An updated overview and some results , 2019, Quality Engineering.

[18]  Shin-Li Lu,et al.  An Extended Nonparametric Exponentially Weighted Moving Average Sign Control Chart , 2015, Qual. Reliab. Eng. Int..

[19]  Joseph L. Gastwirth,et al.  Percentile Modifications of Two Sample Rank Tests , 1965 .

[20]  Jennifer Brown,et al.  Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes , 2015 .

[21]  Philippe Castagliola,et al.  An EWMA signed ranks control chart with reliable run length performances , 2020, Qual. Reliab. Eng. Int..

[22]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[23]  J. L. Clutter,et al.  Ranked Set Sampling Theory with Order Statistics Background , 1972 .

[24]  Muhammad Riaz,et al.  Mixed Tukey EWMA-CUSUM control chart and its applications , 2017 .

[25]  M. A. Graham,et al.  Nonparametric Statistical Process Control , 2019 .

[26]  William H. Woodall,et al.  Controversies and Contradictions in Statistical Process Control , 2000 .

[27]  Nikolaos I. Panayiotou,et al.  A new distribution-free monitoring scheme based on ranks , 2020, Commun. Stat. Simul. Comput..

[28]  Bin Chen,et al.  Adaptive Phase II Nonparametric EWMA Control Chart with Variable Sampling Interval , 2015, Qual. Reliab. Eng. Int..

[29]  Shey-Huei Sheu,et al.  The Generally Weighted Moving Average Control Chart for Detecting Small Shifts in the Process Mean , 2003 .

[30]  Philippe Castagliola,et al.  A CUSUM chart for detecting the intensity ratio of negative events , 2018, Int. J. Prod. Res..

[31]  Saddam Akber Abbasi,et al.  An enhanced nonparametric EWMA sign control chart using sequential mechanism , 2019, PloS one.

[32]  Raid W. Amin,et al.  A nonparametric exponentially weighted moving average control scheme , 1991 .

[33]  Patrick D. Bourke,et al.  Detecting a shift in fraction nonconforming using runlength control charts with 100% inspection , 1991 .

[34]  Dong Hee Kim,et al.  Wilcoxon signed rank test using ranked-set sample , 1996 .

[35]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[36]  Ioannis S. Triantafyllou,et al.  Recent Advances on Univariate Distribution-Free Shewhart-Type Control Charts , 2020 .

[37]  Rudra Sen,et al.  Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes , 2015 .

[38]  Frederick Mosteller,et al.  Tables of the Freeman-Tukey Transformations for the Binomial and Poisson Distributions , 1961 .

[39]  Philippe Castagliola,et al.  Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length , 2019 .

[40]  Peihua Qiu,et al.  On Nonparametric Statistical Process Control of Univariate Processes , 2011, Technometrics.

[41]  Liu Liu,et al.  A Sequential Rank-Based Nonparametric Adaptive EWMA Control Chart , 2013, Commun. Stat. Simul. Comput..

[42]  Peihua Qiu,et al.  Nonparametric Dynamic Curve Monitoring , 2018, Technometrics.

[43]  Muhammad Riaz,et al.  Use of ranked set sampling in nonparametric control charts , 2016 .

[44]  Peihua Qiu,et al.  Some perspectives on nonparametric statistical process control , 2018 .

[45]  Amitava Mukherjee,et al.  Distribution-free phase-II exponentially weighted moving average schemes for joint monitoring of location and scale based on subgroup samples , 2017 .

[46]  S. W. Roberts,et al.  Control Chart Tests Based on Geometric Moving Averages , 2000, Technometrics.

[47]  J. Ledolter,et al.  A Control Chart Based on Ranks , 1991 .

[48]  Zhi Song,et al.  An efficient approach of designing distribution-free exponentially weighted moving average schemes with dynamic fast initial response for joint monitoring of location and scale , 2020 .

[49]  Peihua Qiu,et al.  Distribution-free monitoring of univariate processes , 2011 .

[50]  Smiley W. Cheng,et al.  A new nonparametric EWMA Sign Control Chart , 2011, Expert Syst. Appl..

[51]  Muhammad Azam,et al.  A new exponentially weighted moving average sign chart using repetitive sampling , 2014 .

[52]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[53]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[54]  S. Chakraborti,et al.  Nonparametric Control Charts: An Overview and Some Results , 2001 .

[55]  C. Jun,et al.  Design of a sign chart using a new EWMA statistic , 2020, Communications in Statistics - Theory and Methods.

[56]  Philippe Castagliola,et al.  Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature , 2021, Qual. Reliab. Eng. Int..

[57]  Chi-Hyuck Jun,et al.  Repetitive group sampling procedure for variables inspection , 2006 .

[58]  Amer Ibrahim Al-Omari,et al.  Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods , 2012 .

[59]  Douglas M. Hawkins,et al.  A Nonparametric Change-Point Control Chart , 2010 .

[60]  Jan Kalina,et al.  Nonparametric multivariate rank tests and their unbiasedness , 2012, 1203.0450.

[61]  Eeva Maria Rapoo,et al.  An EWMA control chart based on the Wilcoxon rank-sum statistic using repetitive sampling , 2018 .

[62]  Giovanni Celano,et al.  An EWMA-type sign chart with exact run length properties , 2019, Journal of Quality Technology.

[63]  J. Stuart Hunter,et al.  The exponentially weighted moving average , 1986 .

[64]  Giovanna Capizzi,et al.  An Adaptive Exponentially Weighted Moving Average Control Chart , 2003, Technometrics.

[65]  Robert L. Mccornack,et al.  Extended Tables of the Wilcoxon Matched Pair Signed Rank Statistic , 1965 .

[66]  Robert V. Hogg,et al.  A Two-Sample Adaptive Distribution-Free Test , 1975 .

[67]  Jun Yang,et al.  Distribution-free EWMA schemes for simultaneous monitoring of time between events and event magnitude , 2018, Comput. Ind. Eng..

[68]  Peihua Qiu,et al.  Distribution-free multivariate process control based on log-linear modeling , 2008 .

[69]  Jafar Ahmadi,et al.  Sign control chart based on ranked set sampling , 2018 .

[70]  Sunil K. Mathur,et al.  A new nonparametric bivariate test for two sample location problem , 2009, Stat. Methods Appl..

[71]  Li Xue,et al.  A nonparametric CUSUM chart for monitoring multivariate serially correlated processes , 2020, Journal of Quality Technology.

[72]  Michael B. C. Khoo,et al.  Comparisons of some distribution-free CUSUM and EWMA schemes and their applications in monitoring impurity in mining process flotation , 2019, Comput. Ind. Eng..

[73]  Muhammad Riaz,et al.  An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location , 2017, Qual. Reliab. Eng. Int..

[74]  Johannes Ledolter,et al.  A new nonparametric quality control technique , 1992 .

[75]  Lianjie Shu,et al.  An adaptive exponentially weighted moving average control chart for monitoring process variances , 2008 .

[76]  Maria E. Calzada,et al.  The Generalized Synthetic Chart , 2009 .

[77]  William G. Cochran,et al.  Sampling Techniques, 3rd Edition , 1963 .

[78]  G. McIntyre,et al.  A method for unbiased selective sampling, using ranked sets , 1952 .

[79]  Szu Hui Ng,et al.  Nonparametric CUSUM and EWMA Control Charts for Detecting Mean Shifts , 2010 .

[80]  Saddam Akber Abbasi,et al.  A new nonparametric EWMA sign control chart , 2012, Expert Syst. Appl..

[81]  Francisco J. Samaniego,et al.  Nonparametric Maximum Likelihood Estimation Based on Ranked Set Samples , 1994 .

[82]  Muhammad Riaz,et al.  On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process , 2020, Mathematics.

[83]  Mu'azu Ramat Abujiya,et al.  Quality Control Chart for the Mean using Double Ranked Set Sampling , 2004 .

[84]  Giovanni Celano,et al.  A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data , 2020 .

[85]  Zhi Song,et al.  A Class of Distribution-Free Exponentially Weighted Moving Average Schemes for Joint Monitoring of Location and Scale Parameters , 2020 .

[86]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Small Shifts in the Process Mean , 2000 .

[87]  P. Maravelakis,et al.  The Shewhart Sign Chart with Ties: Performance and Alternatives , 2020 .

[88]  Subha Chakraborti,et al.  A nonparametric exponentially weighted moving average signed-rank chart for monitoring location , 2011, Comput. Stat. Data Anal..

[89]  Philippe Castagliola,et al.  A new nonparametric adaptive EWMA control chart with exact run length properties , 2019, Comput. Ind. Eng..

[90]  Philippe Castagliola,et al.  Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions , 2019, Quality Engineering.

[91]  Amitava Mukherjee,et al.  Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts , 2017, Int. J. Prod. Res..

[92]  Jesse Frey,et al.  Robust confidence intervals for a proportion using ranked-set sampling , 2021 .

[93]  Philippe Castagliola,et al.  A new memory-type monitoring technique for count data , 2015, Comput. Ind. Eng..

[94]  Tahir Nawaz,et al.  A new nonparametric double exponentially weighted moving average control chart , 2019, Qual. Reliab. Eng. Int..

[95]  Peihua Qiu Introduction to Statistical Process Control , 2013 .

[96]  Y. Lepage A combination of Wilcoxon's and Ansari-Bradley's statistics , 1971 .

[97]  Abdul Haq,et al.  A new nonparametric synthetic EWMA control chart for monitoring process mean , 2019, Commun. Stat. Simul. Comput..

[98]  Zhensheng Huang,et al.  A Nonparametric Repetitive Sampling DEWMA Control Chart Based on Linear Prediction , 2020, IEEE Access.

[99]  Mahmoud A. Mahmoud,et al.  Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts , 2017, Commun. Stat. Simul. Comput..

[100]  Muhammad Riaz,et al.  A sensitive non-parametric EWMA control chart , 2015 .

[101]  Thomas P. Hettmansperger The ranked-set sample sign test , 1995 .

[102]  Douglas C. Montgomery,et al.  Research Issues and Ideas in Statistical Process Control , 1999 .

[103]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[104]  D. A. Evans,et al.  An approach to the probability distribution of cusum run length , 1972 .

[105]  J. A. Nachlas,et al.  X charts with variable sampling intervals , 1988 .

[106]  Jean-Claude Malela-Majika,et al.  New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic , 2020 .

[107]  Christos Koukouvinos,et al.  A nonparametric double generally weighted moving average signed‐rank control chart for monitoring process location , 2020, Qual. Reliab. Eng. Int..

[108]  P. Qiu,et al.  A Nonparametric Control Chart for Dynamic Disease Risk Monitoring , 2020 .