New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion

A statistical quality control chart is widely recognized as a potentially powerful tool that is frequently used in many manufacturing and service industries to monitor the quality of the product or manufacturing processes. In this paper, we propose new synthetic control charts for monitoring the process mean and the process dispersion. The proposed synthetic charts are based on ranked set sampling (RSS), median RSS (MRSS), and ordered RSS (ORSS) schemes, named synthetic-RSS, synthetic-MRSS, and synthetic-ORSS charts, respectively. Average run lengths are used to evaluate the performances of the control charts. It is found that the synthetic-RSS and synthetic-MRSS mean charts perform uniformly better than the Shewhart mean chart based on simple random sampling (Shewhart-SRS), synthetic-SRS, double sampling-SRS, Shewhart-RSS, and Shewhart-MRSS mean charts. The proposed synthetic charts generally outperform the exponentially weighted moving average (EWMA) chart based on SRS in the detection of large mean shifts. We also compare the performance of the synthetic-ORSS dispersion chart with the existing powerful dispersion charts. It turns out that the synthetic-ORSS chart also performs uniformly better than the Shewhart-R, Shewhart-S, synthetic-R, synthetic-S, synthetic-D, cumulative sum (CUSUM) ln S2, CUSUM-R, CUSUM-S, EWMA-ln S2, and change point CUSUM charts for detecting increases in the process dispersion. A similar trend is observed when the proposed synthetic charts are constructed under imperfect RSS schemes. Illustrative examples are used to demonstrate the implementation of the proposed synthetic charts. Copyright © 2014 John Wiley & Sons, Ltd.

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

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

[3]  P. Masson,et al.  Quality control techniques for routine analysis with liquid chromatography in laboratories. , 2007, Journal of chromatography. A.

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

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

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

[7]  William H. Woodall,et al.  Evaluating and Improving the Synthetic Control Chart , 2002 .

[8]  Philippe Castagliola,et al.  A Synthetic Scaled Weighted Variance Control Chart for Monitoring the Process Mean of Skewed Populations , 2009, Commun. Stat. Simul. Comput..

[9]  CESAR A. Acosta-Mejia,et al.  A comparison of control charting procedures for monitoring process dispersion , 1999 .

[10]  Zhang Wu,et al.  A SYNTHETIC CONTROL CHART FOR MONITORING THE PROCESS MEAN OF SKEWED POPULATIONS BASED ON THE WEIGHTED VARIANCE METHOD , 2008 .

[11]  Maria E. Calzada,et al.  THE ROBUSTNESS OF THE SYNTHETIC CONTROL CHART TO NON-NORMALITY , 2001 .

[12]  Emmanuel Yashchin,et al.  Weighted Cumulative Sum Technique , 1989 .

[13]  H. A. David.  Miscellanea: Gini's mean difference rediscovered , 1968 .

[14]  Deepak George Pazhayamadom,et al.  Self-starting CUSUM approach for monitoring data poor fisheries , 2013 .

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

[16]  Narayanaswamy Balakrishnan,et al.  Ordered ranked set samples and applications to inference , 2008 .

[17]  Stephen V. Crowder,et al.  An EWMA for Monitoring a Process Standard Deviation , 1992 .

[18]  Thomas A. Budne.  The Application of Random Balance Designs , 1959 .

[19]  Philippe Castagliola,et al.  A synthetic double sampling control chart for the process mean , 2010 .

[20]  Fah Fatt Gan,et al.  A CUMULATIVE SUM CONTROL CHART FOR MONITORING PROCESS VARIANCE , 1995 .

[21]  Sheue-Ling Hwang,et al.  Application control chart concepts of designing a pre-alarm system in the nuclear power plant control room , 2008 .

[22]  Jean-Jacques Daudin,et al.  Double sampling X charts , 1992 .

[23]  Fah Fatt Gan,et al.  Optimal designs of one-sided ewma charts for monitoring a process variance , 1994 .

[24]  E. S. Page.  Controlling the Standard Deviation by Cusums and Warning Lines , 1963 .

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

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

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

[28]  Cesar A. Acosta-Mejia.  Monitoring reduction in variability with the range , 1998 .

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

[30]  S. Stokes,et al.  Ranked set sampling with concomitant variables , 1977 .

[31]  H. J. Huang,et al.  A synthetic control chart for monitoring process dispersion with sample standard deviation , 2005, Comput. Ind. Eng..

[32]  Narayanaswamy Balakrishnan,et al.  BLUEs of Parameters of Generalized Geometric Distribution Using Ordered Ranked Set Sampling , 2005 .

[33]  William H. Woodall,et al.  The Use of Control Charts in Health-Care and Public-Health Surveillance , 2006 .

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

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

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