Performance of Conventional X-bar Chart for Autocorrelated Data Using Smaller Sample Sizes

Control charts are used to determine whether or not a manufacturing or business process is in a state of statistical control. Various schemes of the standard (Shewhart) X chart for autocorrelated data at sample sizes of 2 and 3 are developed and compared with the schemes of the same chart for IID data at various process shifts in the process mean. It is clear from the comparison that the in-control ARL of 370 is achieved by employing the X chart for the IID and autocorrelated data but as the level of correlation increases, the performance of conventional (Shewhart) X chart deteriorates. It is concluded that for faster detection in the process mean, the larger sample sizes (n) may be used. Thus the X chart for autocorrelated data should be used with carefully and judiciously.

[1]  Richard A. Johnson,et al.  The Effect of Serial Correlation on the Performance of CUSUM Tests II , 1974 .

[2]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[3]  Layth C. Alwan,et al.  Time-Series Modeling for Statistical Process Control , 1988 .

[4]  Ahmed Ghorbel,et al.  A survey of control-chart pattern-recognition literature (1991-2010) based on a new conceptual classification scheme , 2012, Comput. Ind. Eng..

[5]  William H. Woodall,et al.  The effect of autocorrelation on the retrospective X-chart , 1992 .

[6]  Rassoul Noorossana,et al.  Using Neural Networks to Detect and Classify Out‐of‐control Signals in Autocorrelated Processes , 2003 .

[7]  Marion R. Reynolds,et al.  EWMA and CUSUM control charts in the presence of correlation , 1997 .

[8]  Daniel W. Apley,et al.  Improved design of robust exponentially weighted moving average control charts for autocorrelated processes , 2011, Qual. Reliab. Eng. Int..

[9]  Su-Fen Yang,et al.  Effects of imprecise measurement on the two dependent processes control for the autocorrelated observations , 2005 .

[10]  Venkata S. Sarma Yadavalli,et al.  Max-EWMA chart for autocorrelated processes (MEWMAP chart) , 2012 .

[11]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[12]  Petar Cisar,et al.  EWMA Algorithm in Network Practice , 2010, Int. J. Comput. Commun. Control.

[13]  Søren Bisgaard,et al.  EWMA control chart limits for first‐ and second‐order autoregressive processes , 2008, Qual. Reliab. Eng. Int..

[14]  Anju Vyas.  Print , 2003 .

[15]  P. Goldsmith,et al.  Average Run Lengths in Cumulative Chart Quality Control Schemes , 1961 .

[16]  T. Harris,et al.  Statistical process control procedures for correlated observations , 1991 .