The EXPAND Procedure

Example 15.3 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 15.3.1.

data samples;
  input date : date9. defects @@;
  label defects = "Defects per 1000 Units";
  format date date9.;
datalines;

   ... more lines ...

title "Sampled Defect Rates";
proc print data=samples;
run;

Output 15.3.1 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
            plots=(input output);
  id date;
  convert defects / observed=(beginning,average);
run;

The following PROC PRINT step prints the results, as shown in Output 15.3.2.

title "Estimated Monthly Average Defect Rates";
proc print data=monthly;
run;

Output 15.3.2 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

The plots produced by PROC EXPAND are shown in Output 15.3.3.

Output 15.3.3 Interpolated Defects Rate Curve

Interpolated Defects Rate Curve, continued