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The SHEWHART Procedure

Step 2: Modeling the Trend

The next step is to model the trend as a function of hour. The chart in Figure 13.43.48 suggests that the mean level of the process (saved as DiameterX in the OUTLIMITS= data set SUBMEANS) grows as the log of HOUR. The following statements fit a simple linear regression model in which DiameterX is the response variable and LOGHOUR (the log transformation of HOUR) is the predictor variable. Part of the printed output produced by PROC REG is shown in Figure 13.43.49.

data submeans;
   set submeans;
   loghour=log(hour);
run;
proc reg data=submeans ;
   model Diameterx=loghour;
   output out=regdata predicted=fitted ;
run;

Output 13.43.49 Trend Analysis for Diameter from PROC REG
X and s Chart for Diameter

The REG Procedure
Model: MODEL1
Dependent Variable: DiameterX Mean of Diameter

Parameter Estimates
Variable Label DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept Intercept 1 9.99056 0.02185 457.29 <.0001
loghour   1 0.13690 0.00967 14.16 <.0001

Figure 13.43.49 shows that the fitted equation can be expressed as

     

where is the fitted subgroup average.1 A partial listing of the OUT= data set REGDATA created by the REG procedure is shown in Figure 13.43.50.

Output 13.43.50 Partial Listing of the Output Data Set regdata from the REG Procedure
X and s Chart for Diameter

hour DiameterX DiameterS DiameterN loghour fitted
1 9.9992 0.09726 8 0.00000 9.9906
2 10.1060 0.07290 8 0.69315 10.0855
3 10.1428 0.06601 8 1.09861 10.1410
4 10.1565 0.08141 8 1.38629 10.1803
5 10.1583 0.15454 8 1.60944 10.2109


Footnotes

  1. Although this example does not check for the existence of a trend, you should do so by using the hypothesis tests provided by the REG procedure.
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