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Autocorrelation in Process Data

/****************************************************************/
/*          S A S   S A M P L E   L I B R A R Y                 */
/*                                                              */
/*    NAME: SHWARIEW                                            */
/*   TITLE: Autocorrelation in Process Data                     */
/* PRODUCT: QC                                                  */
/*  SYSTEM: ALL                                                 */
/*    KEYS: Shewhart Charts, Autocorrelation,                   */
/*   PROCS: SHEWHART ARIMA                                      */
/*    DATA:                                                     */
/*                                                              */
/*     REF: SAS/QC Software:  Usage and Reference, Version 6,   */
/*          First Edition, Volume 1 and Volume 2                */
/*                                                              */
/****************************************************************/

data Chemical;
   input xt @@;
   t = _n_;
   datalines;
96  90  89  89  94  91  89  93  87  85
84  84  87  90  88  92  91  93  91  92
85  88  89  89  92  91  85  86  89  88
88  91  95 101  92  97  92  89  90  84
82  86  87  82  82  87  86  86  81  89
91  92  99  91  90  84  79  76  77  74
78  83  81  86  84  79  76  81  78  78
81  78  78  82  81  81  83  80  78  73
71  74  73  68  70  72  70  68  72  81
91  82  85  80  80  81  83  83  86  88
;

symbol h=2.0 pct;
title 'Individual Measurements Chart';
proc shewhart data=Chemical;
   irchart xt*t / npanelpos = 100
                  split     = '/';
   label xt = 'Observed/Moving Range'
          t = 'Time';
run;

ods graphics on;
ods select ChiSqAuto SeriesACFPlot SeriesPACFPlot;
proc arima data=Chemical plots(only)=series(acf pacf);
   identify var = xt;
run;
quit;

ods select ParameterEstimates;
proc arima data=Chemical;
   identify var=xt;
   estimate p=1 method=ml;
run;

proc arima data=Chemical;
   identify var=xt;
   estimate p=1 method=ml;
   forecast out=Results id=t;
run;

title 'Residual Analysis Using AR(1) Model';
symbol h=2.0 pct;
proc shewhart data=Results(firstobs=4 obs=100);
   xchart xt*t / npanelpos = 100
                 split     = '/'
                 trendvar  = forecast
                 xsymbol   = xbar
                 ypct1     = 40
                 vref2     = 70 to 100 by 10
                 lvref     = 2
                 nolegend;
   label xt = 'Residual/Forecast'
          t = 'Time';
run;

title ;
proc arima data=Chemical;
   identify var=xt(1);
   estimate q=1 method=ml noint;
   forecast out=EWMA id=t;
run;

data EWMA;
   set EWMA(firstobs=2 obs=100);
run;

data EWMAtab;
   length _var_ $ 8 ;
   set EWMA (rename=(forecast=_mean_ xt=_subx_));
   _var_    = 'xt';
   _sigmas_ = 3;
   _limitn_ = 1;
   _lclx_   = _mean_ - 3 * std;
   _uclx_   = _mean_ + 3 * std;
   _subn_   = 1;
run;

symbol h=2.0 pct;
title 'EWMA Center Line Control Chart';
proc shewhart table=EWMAtab;
   xchart xt*t / npanelpos = 100
                 xsymbol   = 'Center'
                 nolegend;
   label _subx_ = 'Observed'
              t = 'Time' ;
run;