A Nonparametric HEWMA-p Control Chart for Variance in Monitoring Processes

Control charts are considered as powerful tools in detecting any shift in a process. Usually, the Shewhart control chart is used when data follows the symmetrical property of a normal distribution. In practice, the data from the industry may follow a non-symmetrical distribution or an unknown distribution. The average run length (ARL) is a significant measure to assess the performance of the control chart. The ARL may mislead when the statistic is computed from an asymmetric distribution. To handle this issue, in this paper, an ARL-unbiased hybrid exponentially weighted moving average proportion (HEWMA-p) chart is proposed for monitoring the process variance for a non-normal distribution or an unknown distribution. The efficiency of the proposed chart is compared with the existing chart in terms of ARLs. The proposed chart is more efficient than the existing chart in terms of ARLs. A real example is given for the illustration of the proposed chart in the industry.

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

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

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

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

[5]  Peihua Qiu,et al.  A Rank-Based Multivariate CUSUM Procedure , 2001, Technometrics.

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

[7]  Muhammad Azam,et al.  Designing of a new monitoring t-chart using repetitive sampling , 2014, Inf. Sci..

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

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

[10]  T. C. Edwin Cheng,et al.  Economic design of control charts for monitoring batch manufacturing processes , 2016, Int. J. Comput. Integr. Manuf..

[11]  S. Bakir.  Distribution-Free Quality Control Charts Based on Signed-Rank-Like Statistics , 2006 .

[12]  Su-Fen Yang,et al.  An Improved Distribution-free EWMA Mean Chart , 2016, Commun. Stat. Simul. Comput..

[13]  Saddam Akber Abbasi,et al.  Mixed EWMA-CUSUM and mixed CUSUM-EWMA modified control charts for monitoring first order autoregressive processes , 2017 .

[14]  C. Jun,et al.  A HEWMA-CUSUM control chart for the Weibull distribution , 2018 .

[15]  Marion R. Reynolds,et al.  A Nonparametric Procedure for Process Control Based on Within-Group Ranking , 1979 .

[16]  N. Balakrishnan,et al.  A Generally Weighted Moving Average Signed‐rank Control Chart , 2016, Qual. Reliab. Eng. Int..

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

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

[19]  D. T. Shirke,et al.  A Nonparametric Signed-Rank Control Chart for Bivariate Process Location , 2012 .

[20]  H.-J. Huang,et al.  A synthetic control chart for monitoring process dispersion with sample range , 2005 .

[21]  Ming Ha Lee,et al.  Optimal statistical design of variable sample size multivariate exponentially weighted moving average control chart based on median run-length , 2017 .

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

[23]  Su-Fen Yang,et al.  A Simple Approach for Monitoring Business Service Time Variation , 2014, TheScientificWorldJournal.

[24]  Abdul Haq,et al.  A new synthetic control chart for monitoring process mean using auxiliary information , 2016 .

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

[26]  S. Bakir.  A Distribution-Free Shewhart Quality Control Chart Based on Signed-Ranks , 2004 .

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

[28]  Chi-Hyuck Jun,et al.  Mixed Control Charts Using EWMA Statistics , 2016, IEEE Access.

[29]  Abdul Haq,et al.  A new double sampling control chart for monitoring process mean using auxiliary information , 2018 .

[30]  Shin-Li Lu.  Non parametric double generally weighted moving average sign charts based on process proportion , 2018 .

[31]  Su Fen Yang,et al.  Signal Detection for Process with Unknown Distribution , 2012 .

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

[33]  Muhammad Riaza,et al.  Nonparametric Double EWMA Control Chart for Process Monitoring , 2016 .

[34]  Barry C. Arnold,et al.  Monitoring Process Variance Using an ARL‐unbiased EWMA‐p Control Chart , 2016, Qual. Reliab. Eng. Int..

[35]  Barry C. Arnold,et al.  A Simple Approach for Monitoring Process Mean and Variance Simultaneously , 2015 .

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

[37]  Douglas M. Hawkins,et al.  A Multivariate Change-Point Model for Statistical Process Control , 2006, Technometrics.

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

[39]  Smiley W. Cheng,et al.  A new non‐parametric CUSUM mean chart , 2011, Qual. Reliab. Eng. Int..

[40]  Smiley W. Cheng,et al.  A New Chart for Monitoring Service Process Mean , 2012, Qual. Reliab. Eng. Int..

[41]  Peihua Qiu,et al.  Nonparametric Profile Monitoring by Mixed Effects Modeling , 2010, Technometrics.

[42]  S. Khan,et al.  HEWMA Control Chart Using Auxiliary Information , 2018, Iranian Journal of Science and Technology, Transactions A: Science.

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

[44]  Changliang Zou,et al.  Nonparametric control chart based on change-point model , 2009 .

[45]  Charles W. Champ,et al.  The Performance of Control Charts for Monitoring Process Variation , 1995 .

[46]  Kanita Petcharat,et al.  Sensitive Non-Parametric Control Charts For Monitoring Process Variation , 2017 .

[47]  Chi-Hyuck Jun,et al.  A hybrid exponentially weighted moving average chart for COM-Poisson distribution , 2018, Trans. Inst. Meas. Control.

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

[49]  Muhammad Azam,et al.  A Control Chart for COM–Poisson Distribution Using Resampling and Exponentially Weighted Moving Average , 2016, Qual. Reliab. Eng. Int..

[50]  Abdul Haq,et al.  A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean: Discussion , 2017, Qual. Reliab. Eng. Int..

[51]  Abdul Haq,et al.  A New Nonparametric EWMA Control Chart for Monitoring Process Variability , 2017, Qual. Reliab. Eng. Int..

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