Synthetic control chart for monitoring the pprocess mean and variance

Purpose – The aim of this paper is to present a synthetic chart based on the non‐central chi‐square statistic that is operationally simpler and more effective than the joint X¯ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes.Design/methodology/approach – The approach used is based on the non‐central chi‐square statistic and the steady‐state average run length (ARL) of the developed chart is evaluated using a Markov chain model.Findings – The proposed chart always detects process disturbances faster than the joint X¯ and R charts. The developed chart can monitor the process instead of looking at two charts separately.Originality/value – The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately.

[1]  Antonio Fernando Branco Costa,et al.  Joint economic design of x and R charts under Weibull shock models , 2000 .

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

[3]  Kenneth E. Case,et al.  Economic Design of a Joint X- and R -Control Chart , 1981 .

[4]  Rickie J. Domangue,et al.  Some omnibus exponentially weighted moving average statistical process monitoring schemes , 1991 .

[5]  E. Saniga.  Economic Statistical Control-Chart Designs with an Application to X̄ and R Charts@@@Economic Statistical Control-Chart Designs with an Application to X and R Charts , 1989 .

[6]  Antonio Fernando Branco Costa,et al.  Monitoring Process Mean and Variability with One Non-central Chi-square Chart , 2004 .

[7]  Smiley W. Cheng,et al.  A New EWMA Control Chart for Monitoring Both Location and Dispersion , 2004 .

[8]  Smiley W. Cheng,et al.  Monitoring Process Mean and Variability with One EWMA Chart , 2001 .

[9]  Zhang Wu,et al.  Implementing Synthetic Control Charts for Attributes , 2001 .

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

[11]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals , 1999 .

[12]  Trevor A Spedding,et al.  Implementing Synthetic Control Charts , 2000 .

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

[14]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R charts with variable parameters , 1998 .

[15]  Antonio Fernando Branco Costa,et al.  Joint ―X and R Charts with Two‐stage Samplings , 2004 .

[16]  Antonio Fernando Branco Costa,et al.  JOINT ECONOMIC DESIGN OF X¯ AND R CONTROL CHARTS FOR PROCESSES SUBJECT TO TWO INDEPENDENT ASSIGNABLE CAUSES , 1993 .

[17]  Abdur Rahim,et al.  An economic model for \font\twelveit=cmti10 scaled 1600$\overline{\kern‐0.85ex\hbox{\twelveit X}}$\nopagenumbers\end and R charts with time‐varying parameters , 2002 .

[18]  Smiley W. Cheng,et al.  A New Multivariate Control Chart for Monitoring Both Location and Dispersion , 2005 .

[19]  Maysa S. De Magalhães,et al.  Joint economic model for totally adaptive X and R charts , 2005, Eur. J. Oper. Res..

[20]  Antonio Fernando Branco Costa,et al.  Economic design of ?? andR charts under Weibull shock models , 2000 .

[21]  Antonio Fernando Branco Costa,et al.  The non-central chi-square chart with two-stage samplings , 2004, Eur. J. Oper. Res..

[22]  M. A. Rahim.  Determination of Optimal Design Parameters of Joint X̄ and R Charts , 1989 .