Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts

Distribution-free (nonparametric) control charts can play an essential role in process monitoring when there is dearth of information about the underlying distribution. In this paper, we study various aspects related to an efficient design and execution of a class of nonparametric Phase II exponentially weighted moving average (denoted by NPEWMA) charts based on exceedance statistics. The choice of the Phase I (reference) sample order statistic used in the design of the control chart is investigated. We use the exact time-varying control limits and the median run-length as the metric in an in-depth performance study. Based on the performance of the chart, we outline implementation strategies and make recommendations for selecting this order statistic from a practical point of view and provide illustrations with a data-set. We conclude with a summary and some remarks.

[1]  Sven Knoth.  Run length quantiles of EWMA control charts monitoring normal mean or/and variance , 2015 .

[2]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[3]  Wilbert C.M. Kallenberg,et al.  Parametric control charts , 2003 .

[4]  Lloyd S. Nelson,et al.  Tables for a Precedence Life Test , 1963 .

[5]  Darrell Radson,et al.  Graphical Representation of Run Length Distributions , 2005 .

[6]  Subhabrata Chakraborti,et al.  Robustness of the EWMA control chart for individual observations , 2011 .

[7]  Amitava Mukherjee,et al.  Design and implementation of CUSUM exceedance control charts for unknown location , 2014 .

[8]  S. Steiner.  EWMA Control Charts with Time-Varying Control Limits and Fast Initial Response , 1999 .

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

[10]  K. E. Case,et al.  Development and Evaluation of Control Charts Using Exponentially Weighted Moving Averages , 1989 .

[11]  J. Macgregor,et al.  The exponentially weighted moving variance , 1993 .

[12]  C. Burns.  Quality management and business excellence. , 2006 .

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

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

[15]  Sven Knoth,et al.  On ARL-Unbiased Control Charts , 2015 .

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

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

[18]  Stephen V. Crowder,et al.  Exponentially Weighted Moving Average (EWMA) Control Chart , 2008 .

[19]  Seven Knoth,et al.  Fast initial response features for EWMA control charts , 2005 .

[20]  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..

[21]  W. H. Deitenbeck.  Introduction to statistical process control. , 1995, Healthcare facilities management series.

[22]  Saddam Akber Abbasi,et al.  Nonparametric Progressive Mean Control Chart for Monitoring Process Target , 2013, Qual. Reliab. Eng. Int..

[23]  Wen-Chih Chiu,et al.  Economic-statistical Design of Maximum Exponentially Weighted Moving Average Control Charts , 2013, Qual. Reliab. Eng. Int..

[24]  Longcheen Huwang,et al.  New EWMA control charts for monitoring process dispersion , 2010, Comput. Stat. Data Anal..

[25]  Sven Knoth,et al.  EWMA Schemes with Nonhomogeneous Transition Kernels , 2003 .

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

[27]  Muhammad Riaz,et al.  Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring , 2013, Qual. Reliab. Eng. Int..

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

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

[30]  Muhammad Riaz,et al.  On designing a new Tukey-EWMA control chart for process monitoring , 2016 .

[31]  Philippe Castagliola,et al.  Computational Statistics and Data Analysis an Ewma Chart for Monitoring the Process Standard Deviation When Parameters Are Estimated , 2022 .

[32]  M. D. Martínez-Miranda,et al.  Computational Statistics and Data Analysis , 2009 .

[33]  Philippe Castagliola,et al.  Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length , 2011, Qual. Reliab. Eng. Int..

[34]  Amitava Mukherjee,et al.  Distribution-Free Exceedance CUSUM Control Charts for Location , 2013, Commun. Stat. Simul. Comput..

[35]  Abdul Haq,et al.  A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean , 2013, Qual. Reliab. Eng. Int..

[36]  Douglas C. Montgomery,et al.  Statistical quality control : a modern introduction , 2009 .

[37]  Amitava Mukherjee,et al.  A distribution-free phase-II CUSUM procedure for monitoring service quality , 2017 .

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

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

[40]  Yan Su,et al.  Adaptive EWMA procedures for monitoring processes subject to linear drifts , 2011, Comput. Stat. Data Anal..

[41]  Fah Fatt Gan,et al.  An optimal design of cumulative sum control chart based on median run length , 1994 .

[42]  Muhammad Riaz,et al.  Mixed Cumulative Sum–Exponentially Weighted Moving Average Control Charts: An Efficient Way of Monitoring Process Location , 2015, Qual. Reliab. Eng. Int..

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

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

[45]  Muhammad Riaz,et al.  An EWMA-Type Control Chart for Monitoring the Process Mean Using Auxiliary Information , 2014 .

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

[47]  Amitava Mukherjee,et al.  Editorial to the Special Issue: Nonparametric Statistical Process Control Charts , 2015, Qual. Reliab. Eng. Int..