Creating EWMA Charts from Subgroup Summary Data

EWMACHART Statement

Creating EWMA Charts from Subgroup Summary Data

See MACEW1 in the SAS/QC Sample Library

The previous example illustrates how you can create EWMA charts using raw data (process measurements). However, in many applications the data are provided as subgroup summary statistics. This example illustrates how you can use the EWMACHART statement with data of this type.

The following data set (CLIPSUM) provides the data from the preceding example in summarized form:

   data clipsum;
      input day gapx gaps;
      gapn=5;
   datalines;
    1  14.904  0.18716
    2  15.014  0.09317
    3  14.866  0.25006
    4  15.048  0.23732
    5  15.024  0.26792
    6  15.126  0.12260
    7  15.220  0.23098
    8  14.902  0.17254
    9  14.910  0.19824
   10  14.932  0.24035
   11  15.096  0.25618
   12  14.912  0.16903
   13  15.138  0.15928
   14  14.798  0.26329
   15  14.944  0.20876
   16  14.896  0.09965
   17  14.734  0.22512
   18  15.046  0.24141
   19  14.702  0.17880
   20  14.788  0.16634
   ;

A listing of CLIPSUM is shown in Figure 20.3. There is exactly one observation for each subgroup (note that the subgroups are still indexed by DAY). The variable GAPX contains the subgroup means, the variable GAPS contains the subgroup standard deviations, and the variable GAPN contains the subgroup sample sizes (these are all five).

The Data Set CLIPSUM

day	gapx	gaps	gapn
1	14.904	0.18716	5
2	15.014	0.09317	5
3	14.866	0.25006	5
4	15.048	0.23732	5
5	15.024	0.26792	5
6	15.126	0.12260	5
7	15.220	0.23098	5
8	14.902	0.17254	5
9	14.910	0.19824	5
10	14.932	0.24035	5
11	15.096	0.25618	5
12	14.912	0.16903	5
13	15.138	0.15928	5
14	14.798	0.26329	5
15	14.944	0.20876	5
16	14.896	0.09965	5
17	14.734	0.22512	5
18	15.046	0.24141	5
19	14.702	0.17880	5
20	14.788	0.16634	5

Figure 20.3: The Summary Data Set CLIPSUM

You can read this data set by specifying it as a HISTORY= data set in the PROC MACONTROL statement, as follows:

   title 'EWMA Chart for Gap Measurements';
   proc macontrol history=clipsum lineprinter;
      ewmachart gap*day='*' / weight=0.3;
   run;

The resulting EWMA chart is shown in Figure 20.4. Since the LINEPRINTER ^* option is specified in the PROC MACONTROL statement, line printer output is produced. The asterisk (*) specified in single quotes after the subgroup-variable indicates the character used to plot points. This character must follow an equal sign.

Note that GAP is not the name of a SAS variable in the data set but is, instead, the common prefix for the names of the three SAS variables GAPX, GAPS, and GAPN. The suffix characters X, S, and N indicate mean, standard deviation, and sample size, respectively. Thus, you can specify three subgroup summary variables in a HISTORY= data set with a single name (GAP), which is referred to as the process. The variables GAPX, GAPS, and GAPN are all required. The name DAY specified after the asterisk is the name of the subgroup-variable.

EWMA Chart for Gap Measurements

                                                                  3 Sigma Limits    
                                                                  For n=5:          
             ---------------------------------------------------                    
      15.10 +                                                   |                   
            |                  *                                |                   
            |                 ++================================| UCL               
            |      ===========+=+                               |                   
      15.05 +    ===         +  +                               |                   
            |=====           +   +                              |                   
            |               *    *            *                 |                   
    E       |              +      ++     *   ++                 |                   
    W 15.00 +              +        *   + + +  +                |                   
    M       |             *          + +   *   +                |                   
    A       |           ++            *         +               |                   
            |     *    *                        *+              | =                 
    o 14.95 +----+-++-+---------------------------+*+-----------| X = 14.950        
    f       |   *    *                               *          |                   
            |                                         +   *     |                   
    g       |                                         +   ++    |                   
    a 14.90 +                                          + + +    |                   
    p       |                                          + +  +   |                   
            |                                           *   +   |                   
            |=====                                           *  |                   
      14.85 +    ===                                          + |                   
            |      ==============                              *|                   
            |                   ================================| LCL               
            |                                                   |                   
      14.80 +                                                   |                   
             +----+----+----+----+----+----+----+----+----+----+                    
             0    2    4    6    8   10   12   14   16   18   20                    
                                                                                    
                            Subgroup Index (day)                                    
                                                                                    
    Subgroup Sizes:  * n=5   Weight=0.3

Figure 20.4: EWMA Chart from Summary Data

In general, a HISTORY= input data set used with the EWMACHART statement must contain the following variables:

subgroup variable
subgroup mean variable
subgroup standard deviation variable
subgroup sample size variable

Furthermore, the names of subgroup mean, standard deviation, and sample size variables must begin with the process name specified in the EWMACHART statement and end with the special suffix characters X, S, and N, respectively. If the names do not follow this convention, you can use the RENAME option in the PROC MACONTROL statement to rename the variables for the duration of the MACONTROL procedure step (see "Creating Charts for Means and Ranges from Summary Data" for an example of the RENAME option).

In summary, the interpretation of process depends on the input data set.

If raw data are read using the DATA= option (as in the previous example), process is the name of the SAS variable containing the process measurements.
If summary data are read using the HISTORY= option (as in this example), process is the common prefix for the names of the variables containing the summary statistics.

For more information, see "HISTORY= Data Set" .

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