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The EXPAND Procedure

Example 11.2: Interpolating Irregular Observations

This example shows the interpolation of a series of values measured at irregular points in time. The data are hypothetical. Assume that a series of randomly timed quality control inspections are made and defect rates for a process are measured. The problem is to produce two reports: estimates of monthly average defect rates for the months within the period covered by the samples, and a plot of the interpolated defect rate curve over time.

The following statements read and print the input data, as shown in Output 11.2.1.

   data samples;
     input date : date9. defects @@;
     label defects = "Defects per 1000 units";
     format date date9.;
   datalines;
   13jan1992    55    27jan1992   73    19feb1992   84    8mar1992   69
   27mar1992    66     5apr1992   77    29apr1992   63   11may1992   81
   25may1992    89     7jun1992   94    23jun1992  105   11jul1992   97
   15aug1992   112    29aug1992   89    10sep1992   77   27sep1992   82
   ;
   
   title "Sampled Defect Rates";
   proc print data=samples;
   run;

Output 11.2.1: Measured Defect Rates
 
Sampled Defect Rates

Obs date defects
1 13JAN1992 55
2 27JAN1992 73
3 19FEB1992 84
4 08MAR1992 69
5 27MAR1992 66
6 05APR1992 77
7 29APR1992 63
8 11MAY1992 81
9 25MAY1992 89
10 07JUN1992 94
11 23JUN1992 105
12 11JUL1992 97
13 15AUG1992 112
14 29AUG1992 89
15 10SEP1992 77
16 27SEP1992 82

To compute the monthly estimates, use PROC EXPAND with the TO=MONTH option and specify OBSERVED=(BEGINNING,AVERAGE). The following statements interpolate the monthly estimates.

   proc expand data=samples out=monthly to=month;
     id date;
     convert defects / observed=(beginning,average);
   run;
   
   title "Estimated Monthly Average Defect Rates";
   proc print data=monthly;
   run;

The results are printed in Output 11.2.2.

Output 11.2.2: Monthly Average Estimates
 
Estimated Monthly Average Defect Rates

Obs date defects
1 JAN1992 59.323
2 FEB1992 82.000
3 MAR1992 66.909
4 APR1992 70.205
5 MAY1992 82.762
6 JUN1992 99.701
7 JUL1992 101.564
8 AUG1992 105.491
9 SEP1992 79.206

To produce the plot, first use PROC EXPAND with TO=DAY to interpolate a full set of daily values, naming the interpolated series INTERPOL. Then merge this data set with the samples so you can plot both the measured and the interpolated values on the same graph. PROC GPLOT is used to plot the curve. The actual sample points are plotted with asterisks. The following statements interpolate and plot the defects rate curve.

   proc expand data=samples out=daily to=day;
     id date;
     convert defects = interpol;
   run;
   
   data daily;
     merge daily samples;
     by date;
   run;
   
   title "Plot of Interpolated Defect Rate Curve";
   proc gplot data=daily; 
      axis2 label=(a=-90 r=90 );
      symbol1 v=none i=join;
      symbol2 v=star i=none;
      plot interpol * date = 1 defects * date = 2  / 
           vaxis=axis2 overlay;
   run;
   quit;

The plot is shown in Output 11.2.3.

Output 11.2.3: Interpolated Defects Rate Curve
expex02c.gif (4625 bytes)

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