Linear profile monitoring using EWMA structure under ranked set schemes

In many manufacturing processes, study variable is not the only quality characteristic, but there may exist some explanatory variable(s) that are associated with the study variable. This association may be linear or nonlinear depending on the nature of variables. The term profiling is used for such relationships among study and explanatory variables. Linear profiles are more common options because of their simplicity and coverage of more common scenarios. A popular proposal for the monitoring of linear profiles is EWMA − 3[SRS] chart that detect shifts in the profile parameters including slope, intercept, and error variance. The said chart is designed under simple random sampling. In this study, we have designed and investigated EWMA − 3[τ] chart under the different ranked set sampling strategies (τ) such as ranked set sampling (RSS), median ranked set sampling (MRSS), extreme ranked set sampling (ERSS), double ranked set sampling (DRSS), double median ranked set sampling (DMRSS), and double extreme ranked set sampling (DERSS). We have used average run length (ARL), extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) as performance measures for the aforementioned designs of EWMA − 3[τ] chart under different sampling schemes. The computational results of run length properties revealed that the ranked set based EWMA − 3[τ] chart offers better detection ability. More specifically, EWMA − 3[ERSS] and EWMA − 3[DMRSS] serve the purpose in a more efficient way.

[1]  Saddam Akber Abbasi,et al.  On Efficient Monitoring of Process Dispersion using Interquartile Range , 2012 .

[2]  Mahmoud A. Mahmoud,et al.  A change point method for linear profile data , 2007, Qual. Reliab. Eng. Int..

[3]  Mahmoud A. Mahmoud,et al.  On the Monitoring of Linear Profiles , 2003 .

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

[5]  Hani M. Samawi,et al.  Estimating the Population Mean Using Extreme Ranked Set Sampling , 1996 .

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

[7]  Fugee Tsung,et al.  A comparison study of effectiveness and robustness of control charts for monitoring process mean , 2012 .

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

[9]  Douglas C. Montgomery,et al.  Performance evaluation of two methods for online monitoring of linear calibration profiles , 2006 .

[10]  Chunguang Zhou,et al.  A Self-Starting Control Chart for Linear Profiles , 2007 .

[11]  Muhammad Riaz,et al.  On the Performance of Linear Profile Methodologies Under Runs Rules Schemes , 2015, Qual. Reliab. Eng. Int..

[12]  A. K. Sinha,et al.  ON SOME RECENT DEVELOPMENTS IN RANKED SET SAMPLING , 2005 .

[13]  H. Weiler,et al.  The Use of Runs to Control the Mean in Quality Control , 1953 .

[14]  Changliang Zou,et al.  A control chart based on a change-point model for monitoring linear profiles , 2006 .

[15]  M. T. Alodat,et al.  Inference about the Regression Parameters Using Median-Ranked Set Sampling , 2010 .

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

[17]  Ying Liu,et al.  An enhanced adaptive CUSUM control chart , 2009 .

[18]  Saddam Akber Abbasi,et al.  On efficient phase II process monitoring charts , 2014 .

[19]  Lloyd S. Nelson,et al.  Column: Technical Aids: The Shewhart Control Chart--Tests for Special Causes , 1984 .

[20]  Abbas Saghaei,et al.  A CUSUM-based method for monitoring simple linear profiles , 2009 .

[21]  S. W. Roberts.  Control chart tests based on geometric moving averages , 2000 .

[22]  Lan Kang,et al.  On-Line Monitoring When the Process Yields a Linear Profile , 2000 .

[23]  D. Hawkins.  Multivariate quality control based on regression-adjusted variables , 1991 .

[24]  Saddam Akber Abbasi,et al.  On artificial neural networking-based process monitoring under bootstrapping using runs rules schemes , 2014, The International Journal of Advanced Manufacturing Technology.

[25]  Carroll Croarkin.  Measurement Assurance for Dimensional Measurements on Integrated-Circuit Photomasks , 2018 .

[26]  Willis A. Jensen,et al.  Monitoring Correlation Within Linear Profiles Using Mixed Models , 2008 .

[27]  Muhammad Riaz,et al.  On the performance of different control charting rules , 2011, Qual. Reliab. Eng. Int..

[28]  Ronald J. M. M. Does,et al.  Variables control chart limits and tests for special causes , 1992 .

[29]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[30]  M. F. Al-Saleh,et al.  Double-ranked set sampling , 2000 .

[31]  William H. Woodall,et al.  The monitoring of simple linear regression profiles with two observations per sample , 2010 .

[32]  Rassoul Noorossana,et al.  Phase II monitoring of simple linear profiles with random explanatory variables , 2015 .

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

[34]  William H. Woodall,et al.  A review and analysis of cause-selecting control charts , 1993 .

[35]  B. J. Mandel.  The Regression Control Chart , 1969 .

[36]  D. Montgomery,et al.  Multivariate statistical process monitoring and diagnosis with grouped regression‐adjusted variables , 1999 .

[37]  Arthur B. Yeh,et al.  Phase I Control of Simple Linear Profiles with Individual Observations , 2013, Qual. Reliab. Eng. Int..

[38]  Charles W. Champ,et al.  Exact results for shewhart control charts with supplementary runs rules , 1987 .

[39]  Zhonghua Li,et al.  Control chart based on likelihood ratio for monitoring linear profiles , 2009, Comput. Stat. Data Anal..

[40]  Hani M. Samawi,et al.  Double Median Ranked Set Sample: Comparing To Other Double Ranked Samples For Mean And Ratio Estimators , 2002 .

[41]  Saddam Akber Abbasi,et al.  Enhancing the performance of CUSUM scale chart , 2012, Comput. Ind. Eng..

[42]  William H. Woodall,et al.  Current research on profile monitoring , 2007 .

[43]  Tahir Mahmood,et al.  Control Charts for Process Dispersion Parameter under Contaminated Normal Environments , 2016, Qual. Reliab. Eng. Int..

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

[45]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[46]  Stephen V. Crowder,et al.  Average run lengths of EWMA control charts for monitoring a process standard deviation , 1992 .

[47]  William H. Woodall,et al.  Phase I Analysis of Linear Profiles With Calibration Applications , 2004, Technometrics.

[48]  Babar Zaman,et al.  Mixed CUSUM-EWMA chart for monitoring process dispersion , 2016 .

[49]  R Nour Alsana,et al.  ENHANCEMENT OF LINEAR PROFILES MONITORING IN PHASE II , 2007 .

[50]  Rassoul Noorossana,et al.  Simple linear profiles monitoring in the presence of within profile autocorrelation , 2009, Comput. Ind. Eng..

[51]  Douglas M. Hawkins,et al.  Regression Adjustment for Variables in Multivariate Quality Control , 1993 .

[52]  Muhammad Riaz,et al.  Enhancing the performance of EWMA charts , 2011, Qual. Reliab. Eng. Int..

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

[54]  Kazumasa Wakimoto,et al.  On unbiased estimates of the population mean based on the sample stratified by means of ordering , 1968 .