The density control chart: a general approach for constructing a single chart for simultaneously monitoring multiple parameters

References

• Bischak , DP and Trietsch , D . 2007 . The rate of false signals in control charts with estimated limits . Journal of Quality Technology , 39 : 54 – 65 .
   Web of Science ®Google Scholar
• Chao , MT and Cheng , SW . 1996 . Semicircle control chart for variables data . Quality Engineering , 8 : 441 – 446 .
   Google Scholar
• Chen , G and Cheng , SW . 1998 . Max-chart: Combining chart and S chart . Statistica Sinica , 8 : 263 – 271 .
   Web of Science ®Google Scholar
• Chen , G , Cheng , SW and Xie , H . 2001 . Monitoring process mean and variability with one EWMA chart . Journal of Quality Technology , 33 : 223 – 233 .
   Web of Science ®Google Scholar
• Chen , G , Cheng , SW and Xie , H . 2004 . A new EWMA control chart for monitoring both location and dispersion . International Journal of Quality and Quantitative Management , 1 : 217V – 231 .
   Google Scholar
• Chen , G , Cheng , SW and Xie , H . 2005 . A new multivariate control chart for monitoring both location and dispersion . Communications in Statistics: Computations and Simulations , 34 : 203 – 217 .
   Web of Science ®Google Scholar
• Cheng , SW and Li , GY . 1993. A single variables control chart, Technical Report, University of Manitoba, Winnipeg, Canada
   Google Scholar
• Cheng , SW and Thaga , K . 2005 . Multivariate Max-CUSUM chart . Quality Technology and Quantitative Management International , 2 : 191 – 206 .
   Google Scholar
• Cheng , SW and Thaga , K . 2006 . On single variables control charts: an overview . Quality and Reliability Engineering International , 22 : 811 – 820 .
   Web of Science ®Google Scholar
• Costa , AFB . 1993 . Joint economic design of and R control charts for processes subject to two independent assignable causes . IIE Transactions , 25 : 27 – 33 .
   Web of Science ®Google Scholar
• Costa , AFB . 1998 . Joint and R charts with variable parameters . IIE Transactions , 30 : 505 – 514 .
   Web of Science ®Google Scholar
• Costa , AFB and Rahim , MA . 2000 . Economic design of and R charts under Weibull shock models . Quality and Reliability Engineering International , 16 : 143 – 156 .
   Web of Science ®Google Scholar
• Costa , AFB and Rahim , MA . 2002. Joint and R charts with two stage sampling. In: IIE Research Conference, Orlando
   Google Scholar
• Costa , AFB and Rahim , MA . 2004 . Joint and R charts with two stage samplings . Quality and Reliability Engineering International , 20 : 699 – 708 .
   Web of Science ®Google Scholar
• Costa , AFB , De Magalhães , MS and Epprecht , EK . 2009 . Monitoring the process mean and variance using a synthetic control chart with two-stage testing . International Journal of Production Research , 47 ( 18 ) : 5067 – 5086 .
   Web of Science ®Google Scholar
• De Magalhaes , MS and Moura Neto , F . 2005. Joint economic model for totally adaptive and R charts. European Journal of Operational Research, 161, 148–161
   Google Scholar
• Domangue , R and Patch , SC . 1991 . Some omnibus exponentially weighted moving average statistical process monitoring schemes . Technometrics , 33 : 299 – 313 .
   Web of Science ®Google Scholar
• Gan , FF . 1995 . Joint monitoring of mean and variance using exponentially weighted moving average control charts . Technometrics , 37 : 446 – 453 .
   Web of Science ®Google Scholar
• Gan , FF . 2000 . “ Joint monitoring of process mean and variance based on the exponentially weighted moving averages ” . In Statistical Process Monitoring and Optimisation , 189 – 208 . New York : Marcel Dekker .
   Google Scholar
• Hawkins , DM and Deng , Q . 2009 . Combined charts for mean and variance information . Journal of Quality Technology , 41 : 415 – 425 .
   Web of Science ®Google Scholar
• Hawkins , DM and Zamba , KD . 2005 . Statistical process control for shifts in mean or variance using a change point formulation . Technometrics , 47 : 164 – 173 .
   Web of Science ®Google Scholar
• He , D and Grigoryan , A . 2006 . Joint statistical design of double sampling and S charts . European Journal of Operational Research , 168 : 122 – 142 .
   Web of Science ®Google Scholar
• Levinson , WA and Polny , A . 1999 . SPC for tool particle counts . Semiconductor International , 22 : 117 – 122 .
   Google Scholar
• Li , Z , Zhang , J and Wang , Z . 2010 . Self-starting control chart for simultaneously monitoring process mean and variance . International Journal of Production Research , 48 : 4537 – 4553 .
   Web of Science ®Google Scholar
• Jensen , WA . 2006 . Effects of parameter estimation on control chart properties: A literature review . Journal of Quality Technology , 38 : 349 – 364 .
   Web of Science ®Google Scholar
• Jones , LL and Case , KE . 1981 . Economic design of a joint and R-control chart . IIE Transactions , 13 : 182V – 195 .
   Web of Science ®Google Scholar
• MacGregor , JF and Harris , TJ . 1993 . The exponentially weighted moving variance . Journal of Quality Technology , 25 : 106 – 118 .
   Web of Science ®Google Scholar
• Machado , MAG , Costa , AFB and Marins , FAS . 2009 . Control charts for monitoring the mean vector and the covariance matrix of bivariate processes . The International Journal of Advanced Manufacturing Technology , 45 : 772 – 785 .
   Web of Science ®Google Scholar
• Montgomery , DC , Runger , GC and Hubele , NF . 2004 . Engineering statistics , New York : Wiley .
   Google Scholar
• Ohta , H , Kimura , A and Rahim , MA . 2002 . An economic model for and R charts with timevarying parameters . Quality and Reliability Engineering International , 18 : 131V – 139 .
   Web of Science ®Google Scholar
• Rahim , MA . 1989 . Determination of optimal design parameters of joint X and R charts . Journal of Quality Technology , 21 : 65V – 70 .
   Web of Science ®Google Scholar
• Rahim , MA and Costa , AFB . 2000 . Joint economic design of and R charts under Weibull shock models . International Journal of Production Research , 38 ( 13 ) : 2871 – 2889 .
   Web of Science ®Google Scholar
• Reynolds , MR Jr and Chao , G-Y . 2006 . Multivariate control charts for monitoring the mean vector and covariance matrix . Journal of Quality Technology , 38 : 230 – 253 .
   Web of Science ®Google Scholar
• Reynolds , MR Jr and Stoumbos , ZG . 2001 . Monitoring the process mean and variance using individual observations and variable sampling intervals . Journal of Quality Technology , 33 : 181 – 205 .
   Web of Science ®Google Scholar
• Saniga , EM . 1989 . Economic statistical control charts designs with an application on and R charts . Technometrics , 31 : 313 – 320 .
   Web of Science ®Google Scholar
• Saniga , EM . 1991 . Joint statistical design of and R control charts . Journal of Quality Technology , 23 : 156 – 162 .
   Web of Science ®Google Scholar
• Sheu , S-H . 2009 . Monitoring process mean and variability with generally weighted moving average control charts . Computers and Industrial Engineering , 57 : 401 – 407 .
   Web of Science ®Google Scholar
• Shewhart , WA . 1925 . The applications of statistics as an aid in maintaining quality of a manufacturing product . Journal of American Statistical Association , 20 : 546 – 548 .
   Google Scholar
• Spiring , FA and Cheng , SW . 1998 . An alternative variables control chart: the univariate and multivariate cases . Statistica Sinica , 8 : 273 – 287 .
   Web of Science ®Google Scholar
• Sweet , AL . 1986 . Control charts using coupled exponential weighted moving average . IIE Transactions , 18 : 26 – 33 .
   Web of Science ®Google Scholar
• Takemoto , Y , Watakabe , K and Arizono , I . 2003 . A study of cumulative sum control charts . International Journal of Production Research , 41 ( 9 ) : 1873 – 1886 .
   Web of Science ®Google Scholar
• Thaga , K . 2003 . Contributions to statistical process control tools. Thesis (PhD) University of Manitoba, Winnipeg, Canada
   Google Scholar
• White , EM and Schroeder , R . 1987 . A simultaneous control chart . Journal of Quality Technology , 19 : 1 – 10 .
   Web of Science ®Google Scholar
• Wu , Z and Tian , Y . 2005 . Weighted-loss-function CUSUM chart for monitoring mean and variance of a production process . International Journal of Production Research , 43 ( 14 ) : 3027 – 3044 .
   Web of Science ®Google Scholar
• Xie , H . 1999 . Contributions to qualimetry. Thesis (PhD) University of Manitoba, Winnipeg, Canada
   Google Scholar
• Yeh , AB , Huwang , L and Wu , Y-F . 2005 . A likelihood ratio based EWMA control chart for monitoring variability of multivariate normal processes . IIE Transactions on Quality and Reliability Engineering , 36 : 865 – 879 .
   Web of Science ®Google Scholar
• Yeh , AB and Lin , DK-J . 2002 . A new variables control chart for simultaneously monitoring multivariate process mean and variability . International Journal of Reliability, Quality and Safety Engineering , 9 : 41 – 59 .
   Google Scholar
• Zhang , J , Zou , C and Wang , Z . 2010 . A Control Chart Based on Likelihood Ratio Test for Monitoring Process Mean and Variability . Quality and Reliability Engineering International , 26 : 63 – 73 .
   Web of Science ®Google Scholar
• Zhou , Q , Luo , Y and Wang , Z . 2010 . A control chart based on likelihood ratio test for detecting patterned mean and variance shifts . Computational Statistics and Data Analysis , 54 : 1634 – 1645 .
   Web of Science ®Google Scholar