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XCHART Statement |
See CUSCOMB in the SAS/QC Sample Library |
Lucas (1982) introduced a combined Shewhart-cusum scheme that is illustrated in this example. Also refer to Ryan (1989). The data set used here is CANS, which is created in "Creating a One-Sided Cusum Chart with a Decision Interval" .
The first step is to compute and save one-sided cusums to detect
a positive shift from the mean.
proc cusum data=cans; xchart weight*hour / nochart mu0 = 8.100 /* target mean */ sigma0 = 0.050 /* known standard deviation */ delta = 1 /* shift to be detected */ h = 3 /* decision interval */ k = 0.5 /* reference value */ scheme = onesided /* onesided scheme */ outtable = tabcus /* save the result} */ ( drop = _var_ _subn_ _exlim_ rename = ( _cusum_ = _subr_ _h_ = _uclr_ ) ) ; run;
Note that a headstart value is not used here but can be specified with the HSTART= option. Several variables in the OUTTABLE= data set are dropped or renamed so that they can later be read by the SHEWHART procedure.
The next step is to construct a Shewhart chart (not shown) for
individual measurements.
proc shewhart data=cans; irchart weight*hour / nochart mu0 = 8.100 sigma0 = 0.050 outtable = tabx ( drop = _subr_ _lclr_ _r_ _uclr_ ); id comment; run;
By default, limits are computed, but the multiple of can be modified with the SIGMAS= option. As before, the results are saved in an OUTTABLE= data set.
Next, the two OUTTABLE= data sets are merged.
data combine; merge tabx tabcus; by hour; _lclr_ = 0.0; _r_ = 0.5 * _uclr_; run;
The data set COMBINE has the structure required for a TABLE= data set used with the IRCHART statement in the SHEWHART procedure (see "TABLE= Data Set" in Chapter 34, "IRCHART Statement").
Finally, the combined scheme is displayed with the SHEWHART procedure.
title "Combined Shewhart-Cusum Analysis for Weight"; symbol v=dot c=salmon; proc shewhart table=combine; irchart weight*hour / ypct1 = 50 noctl2 ucllabel2 = 'h=0.3' outlabel = ( comment ) outlabel2 = ( comment ) cframelab = ligr cframe = bigb split = '/' cinfill = ywh cconnect = salmon; label _subi_ = 'Shewhart/Cusum'; run;
The chart is shown in Output 12.3.1.
Output 12.3.1: Combined Shewhart -Cusum SchemeLucas (1982) tabulates average run lengths for combined Shewhart-cusum schemes. The scheme used here has an ARL of 111.1 for and an ARL of 6.322 for .
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