The EXPAND Procedure

## Example 14.3 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 14.3.1.

```   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 14.3.1 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 14.3.2.

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

Output 14.3.2 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 14.3.3.

Output 14.3.3 Interpolated Defects Rate Curve

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