A Nonparametric Signed-Rank Control Chart for Bivariate Process Location

Abstract A nonparametric control chart based on a bivariate signed-rank test is developed for monitoring the changes in the location of a bivariate process. The average run length performance of the proposed nonparametric chart is investigated using a simulation study and is compared with a parametric control chart under bivariate normal and bivariate double exponential distributions. Further the performance of the proposed nonparametric chart is improved by using runs rules and the concept of a synthetic control chart.

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

[2]  Francisco Aparisi,et al.  A Performance Analysis of Hotelling's χ2 Control Chart with Supplementary Runs Rules , 2004 .

[3]  K. Tsui,et al.  Identification and Quantification in Multivariate Quality Control Problems , 1994 .

[4]  Regina Y. Liu.  Control Charts for Multivariate Processes , 1995 .

[5]  S. Bakir.  Distribution-Free Quality Control Charts Based on Signed-Rank-Like Statistics , 2006 .

[6]  D. T. Shirke,et al.  A Multivariate Synthetic Control Chart for Process Dispersion , 2008 .

[7]  A Bivariate Signed Rank Test , 1964 .

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

[9]  Raid W. Amin,et al.  A nonparametric exponentially weighted moving average control scheme , 1991 .

[10]  D. T. Shirke,et al.  A Multivariate Synthetic Control Chart for Monitoring Process Mean Vector , 2008 .

[11]  D. Hawkins,et al.  A nonparametric multivariate cumulative sum procedure for detecting shifts in all directions , 2003 .

[12]  E. Jacquelin Dietz,et al.  Bivariate Nonparametric Tests for the One-Sample Location Problem , 1982 .

[13]  Alexandra Kapatou,et al.  Multivariate nonparametric control charts using small samples , 1996 .

[14]  Marion R. Reynolds,et al.  A Nonparametric Procedure for Process Control Based on Within-Group Ranking , 1979 .

[15]  S. Bakir.  A Distribution-Free Shewhart Quality Control Chart Based on Signed-Ranks , 2004 .

[16]  Serkan Eryilmaz,et al.  A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs , 2007, Commun. Stat. Simul. Comput..

[17]  M. R. Reynolds,et al.  Nonparametric quality control charts based on the sign statistic , 1995 .

[18]  S. Chakraborti,et al.  Nonparametric Control Charts: An Overview and Some Results , 2001 .

[19]  Zachary G. Stoumbos,et al.  Robustness to Non-Normality of the Multivariate EWMA Control Chart , 2002 .