A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X¯ control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X¯ chart integrates the VSI X¯ chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic X¯ chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic X¯ chart and the existing X¯, synthetic X¯, VSI X¯ and EWMA X¯ charts, in terms of ATS, are made. The ATS results show that the VSI synthetic X¯ chart outperforms the other X¯ type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic X¯ chart.

[1]  Michael B. C. Khoo,et al.  The run sum t control chart for monitoring process mean changes in manufacturing , 2014 .

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

[3]  Athanasios C. Rakitzis,et al.  Control charts with switching and sensitizing runs rules for monitoring process variation , 2014 .

[4]  Marion R. Reynolds,et al.  Evaluating properties of variable sampling interval control charts , 1995 .

[5]  Wu Zhang,et al.  Optimal np Control Charts with Variable Sample Sizes or Variable Sampling Intervals , 2002 .

[6]  F L Chen,et al.  VARIABLE SAMPLING INTERVAL SYNTHETIC CONTROL CHARTS FOR JOINTLY MONITORING PROCESS MEAN AND STANDARD DEVIATION , 2006 .

[7]  Douglas C. Montgomery,et al.  Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[8]  이경택,et al.  Variable Sampling Interval x Control Charts with An Improved Switching Rule , 1997 .

[9]  Morton Klein.  Composite Shewhart-EWMA statistical control schemes , 1996 .

[10]  Fang Yen Yen,et al.  Synthetic-Type Control Charts for Time-Between-Events Monitoring , 2013, PloS one.

[11]  Eugenio K. Epprecht,et al.  Performance Comparisons of EWMA Control Chart Schemes , 2010 .

[12]  Sotiris Bersimis,et al.  A compound control chart for monitoring and controlling high quality processes , 2014, Eur. J. Oper. Res..

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

[14]  Afb Costa.  (X)OVER-BAR CHARTS WITH VARIABLE SAMPLE-SIZE , 1994 .

[15]  Philippe Castagliola,et al.  The synthetic [Xbar] chart with estimated parameters , 2011 .

[16]  Raid W. Amin,et al.  A Robustness Study of Charts with Variable Sampling Intervals , 1993 .

[17]  Philippe Castagliola,et al.  Optimal design of the synthetic chart for the process mean based on median run length , 2012 .

[18]  Afb Costa.  (X)over-bar charts with variable parameters , 1999 .

[19]  Mei Yang,et al.  Optimization designs of the combined Shewhart-CUSUM control charts , 2008, Comput. Stat. Data Anal..

[20]  J. A. Nachlas,et al.  X charts with variable sampling intervals , 1988 .

[21]  Santiago Omar Caballero Morales.  Economic Statistical Design of Integrated X-bar-S Control Chart with Preventive Maintenance and General Failure Distribution , 2013 .

[22]  Antonio Fernando Branco Costa,et al.  X̄ Charts with Variable Parameters , 1999 .

[23]  Shashibhushan B. Mahadik,et al.  A Special Variable Sample Size and Sampling Interval Chart , 2009 .

[24]  Antonio Fernando Branco Costa,et al.  X̄ charts with variable sample size , 1994 .

[25]  Zhang Wu,et al.  An SPRT control chart with variable sampling intervals , 2011 .

[26]  Michael B. C. Khoo,et al.  Economic and economic statistical designs of the synthetic chart using loss functions , 2013, Eur. J. Oper. Res..

[27]  Kerrie Mengersen,et al.  Change Point Estimation in Monitoring Survival Time , 2012, PloS one.

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

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

[30]  Philippe Castagliola,et al.  On t and EWMA t charts for monitoring changes in the process mean , 2009, Qual. Reliab. Eng. Int..

[31]  Philippe Castagliola,et al.  A combined synthetic&X chart for monitoring the process mean , 2010 .

[32]  Antonio Fernando Branco Costa,et al.  X̄ Chart with Variable Sample Size and Sampling Intervals , 1997 .

[33]  James M. Lucas,et al.  Combined Shewhart-CUSUM Quality Control Schemes , 1982 .

[34]  Marion R. Reynolds,et al.  Monitoring the Process Mean and Variance Using Individual Observations and Variable Sampling Intervals , 2001 .

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

[36]  Michael B. C. Khoo,et al.  Optimal Designs of the Median Run Length Based Double Sampling X̄ Chart for Minimizing the Average Sample Size , 2013, PloS one.

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