Recent Advances on Univariate Distribution-Free Shewhart-Type Control Charts

In this chapter, we provide an up-to-date overview of nonparametric Shewhart-type univariate control charts. The monitoring schemes incorporated in the present literature review depict the most recent developments on the topic, since it has been chosen to discuss only the advances appeared during the last decade. For each distribution-free control chart, the general setup and several performance characteristics are presented in some detail.

[1]  Wolfgang Kössler Asymptotic Power and Efficiency of Lepage-Type Tests for the Treatment of Combined Location-Scale Alternatives , 2006 .

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

[3]  Giovanni Celano,et al.  Joint Shewhart control charts for location and scale monitoring in finite horizon processes , 2016, Comput. Ind. Eng..

[4]  Serkan Eryilmaz,et al.  Article in Press Computational Statistics and Data Analysis a Phase Ii Nonparametric Control Chart Based on Precedence Statistics with Runs-type Signaling Rules , 2022 .

[5]  Ronald W. Butler,et al.  Saddlepoint Approximations to the CDF of Some Statistics with Nonnormal Limit Distributions , 1993 .

[6]  Lucio Barabesi The computation of the distribution of the sign test statistic for ranked-set sampling , 1998 .

[7]  Amitava Mukherjee,et al.  Optimal design of Shewhart-Lepage type schemes and its application in monitoring service quality , 2018, Eur. J. Oper. Res..

[8]  U. Singh,et al.  Estimation of stress–strength reliability for inverse Weibull distribution under progressive type-II censoring scheme , 2018 .

[9]  Peihua Qiu,et al.  Some Recent Studies in Statistical Process Control , 2019, Statistical Quality Technologies.

[10]  Lonnie C. Vance,et al.  The Economic Design of Control Charts: A Unified Approach , 1986 .

[11]  Saad T. Bakir,et al.  A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution , 2012 .

[12]  Ryoji Tamura,et al.  On a Modification of Certain Rank Tests , 1963 .

[13]  Giovanni Celano,et al.  On the implementation of the Shewhart sign control chart for low-volume production , 2016 .

[14]  Thong Ngee Goh,et al.  Some effective control chart procedures for reliability monitoring , 2002, Reliab. Eng. Syst. Saf..

[15]  DavidR . Thomas,et al.  Linear Order Statistic Estimation for the Two-Parameter Weibull and Extreme-Value Distributions from Type II Progressively Censored Samples , 1972 .

[16]  H. K. Tony Ng,et al.  Precedence-Type Tests and Applications: Balakrishnan/Precedence , 2006 .

[17]  Wolfgang Kössler,et al.  Max-type rank tests, U-tests, and adaptive tests for the two-sample location problem - An asymptotic power study , 2010, Comput. Stat. Data Anal..

[18]  Douglas A. Wolfe,et al.  Some Applications of Sample Analogues to the Probability Integral Transformation and a Coverage Property , 1976 .

[19]  Gerhard-Wilhelm Weber,et al.  A Literature Review on the Fuzzy Control Chart; Classifications & Analysis , 2014 .

[20]  George Nenes,et al.  Evaluation of CUSUM Charts for Finite-Horizon Processes , 2010, Commun. Stat. Simul. Comput..

[21]  P Laanvander,et al.  A class of distribution‐free control charts , 2004 .

[22]  W. Y. Wendy Lou,et al.  Distribution Theory of Runs and Patterns and Its Applications: A Finite Markov Chain Imbedding Approach , 2003 .

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

[24]  Snigdhansu Chatterjee,et al.  Distribution-free cumulative sum control charts using bootstrap-based control limits , 2009, 0906.1421.

[25]  Giovanna Capizzi,et al.  Phase I Distribution-Free Analysis of Multivariate Data , 2013, Technometrics.

[26]  Michael B. C. Khoo,et al.  Two Improved Runs Rules for the Shewhart X¯ Control Chart , 2006 .

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

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

[29]  Tzong-Ru Tsai,et al.  Economic design of two-stage control charts with skewed and dependent measurements , 2014 .

[30]  S. Chakraborti Nonparametric (Distribution-Free) Quality Control Charts† , 2011 .

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

[32]  Ioannis S. Triantafyllou,et al.  Nonparametric control charts based on order statistics: Some advances , 2018, Commun. Stat. Simul. Comput..

[33]  Markos V. Koutras,et al.  A general class of nonparametric control charts , 2018, Qual. Reliab. Eng. Int..

[34]  Wayne B. Nelson,et al.  Applied Life Data Analysis: Nelson/Applied Life Data Analysis , 2005 .

[35]  R. Jarrett A note on the intervals between coal-mining disasters , 1979 .

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

[37]  Erich L. Lehmann,et al.  The Power of Rank Tests , 1953 .

[38]  Douglas C. Montgomery,et al.  A general model for the optimal economic design of X¯ charts used to control short or long run processes , 1996 .

[39]  George Tagaras,et al.  Dynamic control charts for finite production runs , 1996 .

[40]  N. Balakrishnan,et al.  Progressively Type-II right censored order statistics from discrete distributions , 2008 .

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

[42]  G. J. Janacek,et al.  Control charts based on medians , 1997 .

[43]  Hyo-Il Park,et al.  Median Control Charts Based on Bootstrap Method , 2009, Commun. Stat. Simul. Comput..

[44]  R. Amin,et al.  Sign control charts with variable sampling intervals , 1999 .

[45]  Narayanaswamy Balakrishnan,et al.  Interval Estimation of Parameters of Life From Progressively Censored Data , 1994 .

[46]  Amitava Mukherjee,et al.  A distribution-free Phase I monitoring scheme for subgroup location and scale based on the multi-sample Lepage statistic , 2019, Comput. Ind. Eng..

[47]  Subhabrata Chakraborti,et al.  A nonparametric control chart based on the Mann-Whitney statistic , 2003 .

[48]  Christian Paroissin,et al.  One-sided Control Charts Based on Precedence and Weighted Precedence Statistics , 2015, Qual. Reliab. Eng. Int..

[49]  N. Balakrishnan,et al.  A Distribution-Free Control Chart Based on Order Statistics , 2010 .

[50]  C. F. Smit,et al.  Nonparametric Shewhart-Type Sign Control Charts Based on Runs , 2010 .

[51]  I. Triantafyllou A new distribution-free control scheme based on order statistics , 2018, Journal of Nonparametric Statistics.

[52]  Morton Klein,et al.  Two Alternatives to the Shewhart X̄ Control Chart , 2000 .

[53]  Min Xie,et al.  Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location , 2016 .

[54]  Frantisek Rublík,et al.  The multisample version of the Lepage test , 2005, Kybernetika.

[55]  Narayanaswamy Balakrishnan,et al.  Precedence-type tests and applications , 2006 .

[56]  Nancy R. Mann,et al.  Best Linear Invariant Estimation for Weibull Parameters Under Progressive Censoring , 1971 .

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

[58]  Athanasios C. Rakitzis,et al.  The Revised m-of-k Runs Rule , 2007 .

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

[60]  M. A. Graham,et al.  Distribution-free Phase II Mann–Whitney control charts with runs-rules , 2016 .

[61]  Subhabrata Chakraborti,et al.  An overview of synthetic‐type control charts: Techniques and methodology , 2019, Qual. Reliab. Eng. Int..

[62]  Fernanda Figueiredo,et al.  The total median statistic to monitor contaminated normal data , 2016 .

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

[64]  Eeva Maria Rapoo,et al.  Distribution-free cumulative sum and exponentially weighted moving average control charts based on the Wilcoxon rank-sum statistic using ranked set sampling for monitoring mean shifts , 2016 .

[65]  Acheson J. Duncan,et al.  The Economic Design of X Charts Used to Maintain Current Control of a Process , 1956 .

[66]  D. T. Shirke,et al.  A Nonparametric Synthetic Control Chart Using Sign Statistic , 2010 .

[67]  Serkan Eryilmaz,et al.  A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs , 2007, Commun. Stat. Simul. Comput..

[68]  Amitava Mukherjee,et al.  A New Distribution‐free Control Chart for Joint Monitoring of Unknown Location and Scale Parameters of Continuous Distributions , 2014, Qual. Reliab. Eng. Int..

[69]  Feng-Chia Li,et al.  An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models , 2011 .

[70]  M. A. Graham,et al.  A Phase I nonparametric Shewhart-type control chart based on the median , 2010 .

[71]  Gutti Jogesh Babu,et al.  Sign test for ranked-set sampling , 1996 .

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

[73]  Mukund Raghavachari,et al.  Control chart based on the Hodges-Lehmann estimator , 1991 .

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

[75]  A. Mood On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests , 1954 .

[76]  Giovanni Celano,et al.  The performance of the Shewhart sign control chart for finite horizon processes , 2015 .

[77]  Hidetoshi Murakami,et al.  A nonparametric control chart based on the Mood statistic for dispersion , 2010 .

[78]  G. Masarotto,et al.  Bootstrap-based design of residual control charts , 2009 .

[79]  Subhabrata Chakraborti,et al.  Improved Shewhart-type Runs-rules Nonparametric Sign Charts , 2014 .

[80]  Amitava Mukherjee,et al.  Distribution‐free Lepage Type Circular‐grid Charts for Joint Monitoring of Location and Scale Parameters of a Process , 2017, Qual. Reliab. Eng. Int..

[81]  Marco Marozzi,et al.  Some notes on the location–scale Cucconi test , 2009 .

[82]  M. R. Reynolds,et al.  Nonparametric quality control charts based on the sign statistic , 1995 .

[83]  Amitava Mukherjee,et al.  Control Charts for Simultaneous Monitoring of Unknown Mean and Variance of Normally Distributed Processes , 2013 .

[84]  Robert O'donnell,et al.  Statistical Aspects of Quality Control , 1996 .

[85]  Giovanni Celano,et al.  Shewhart and EWMA t control charts for short production runs , 2011, Qual. Reliab. Eng. Int..

[86]  H. Büning,et al.  An adaptive two-sample location-scale test of lepage type for symmetric distributions , 2000 .

[87]  Babak Abbasi,et al.  Bootstrap control charts in monitoring value at risk in insurance , 2013, Expert Syst. Appl..

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

[89]  H. N. Nagaraja,et al.  Order Statistics, Third Edition , 2005, Wiley Series in Probability and Statistics.

[90]  R. A. Groeneveld,et al.  Practical Nonparametric Statistics (2nd ed). , 1981 .

[91]  D. T. Shirke,et al.  Nonparametric Synthetic Control Charts for Process Variation , 2012, Qual. Reliab. Eng. Int..

[92]  Hidetoshi Murakami,et al.  Lepage type statistic based on the modified Baumgartner statistic , 2007, Comput. Stat. Data Anal..

[93]  Narayanaswamy Balakrishnan,et al.  Inference for the Scaled Half-Logistic Distribution Based on Progressively Type-II Censored Samples , 2005 .

[94]  Markus Neuhäuser,et al.  Nonparametric Statistical Tests: A Computational Approach , 2011 .

[95]  A. K. McCracken,et al.  Control Charts for Joint Monitoring of Mean and Variance: An Overview , 2013 .

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

[97]  Wayne Nelson,et al.  Applied life data analysis , 1983 .

[98]  Amitava Mukherjee,et al.  Distribution-free Shewhart-Lepage type premier control schemes for simultaneous monitoring of location and scale , 2017, Comput. Ind. Eng..

[99]  Victoria S. Jordan,et al.  Distribution-Free Phase I Control Charts for Subgroup Location , 2009 .

[100]  Subha Chakraborti,et al.  Nonparametric signed‐rank control charts with variable sampling intervals , 2017, Qual. Reliab. Eng. Int..

[101]  Donghoon Han,et al.  Optimal Progressive Type-II Censoring Schemes for Nonparametric Confidence Intervals of Quantiles , 2007, Commun. Stat. Simul. Comput..

[102]  Shaul P. Ladany,et al.  Optimal Use of Control Charts for Controlling Current Production , 1973 .

[103]  Douglas A. Wolfe,et al.  Introduction to the Theory of Nonparametric Statistics. , 1980 .

[104]  Amitava Mukherjee,et al.  A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale , 2012, Qual. Reliab. Eng. Int..

[105]  Jean-Claude Malela-Majika,et al.  Distribution-free precedence control charts with improved runs-rules , 2016 .

[106]  Tiantian Wang,et al.  An economically designed Sequential Probability Ratio Test control chart for short-run production , 2014, Comput. Ind. Eng..

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

[108]  Giovanni Celano,et al.  The Economic Performance of a CUSUM t Control Chart for Monitoring Short Production Runs , 2012 .

[109]  M. A. Graham,et al.  Distribution-free precedence schemes with a generalized runs-rule for monitoring unknown location , 2019, Communications in Statistics - Theory and Methods.

[110]  Subhabrata Chakraborti Run length, average run length and false alarm rate of shewhart x-bar chart: exact derivations by conditioning , 2000 .

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