vdoc

Chapter 13: G. Measurement System Analysis 129
Continued
2 2
GageR&R = ( Repeatability) + ( Reproducibility)
2 2
= ( 863 . ) + (.
83)
= 867 .
The estimate of GR&R standard deviation is given by
867 .
sˆ
Gage
= = 168 . .
515 .
The ANOVA Method
Measurement system analysis using the ANOVA method is done by using two
types of experimental designs; crossed and nested, or hierarchical, designs. The
crossed designs are used when each operator measures the same parts, whereas
nested or hierarchical designs are used when each operator measures different
parts, in which case we say that the parts are nested within operators. In this chapter
we discuss the case when each operator measures the same parts and thus use
crossed designs only.
Gage R&R Study—ANOVA Method
Interpretation of Two-Way ANOVA Table with Interaction. In the ANOVA table
in Figure 13.4, we test three hypotheses:
• H 0 : All parts are similar versus H 1 : All parts are not similar
• H 0 : All operators are equally good versus H 1 : All operators are not
equally good
• H 0 : Interactions between parts and operators are negligible versus H 1 :
Interactions between parts and operators are not negligible
The decision whether to reject or not to reject any of these hypotheses depends
on the p-value (shown in the last column) and the corresponding value of the
level of significance. If the p-value is less than or equal to the level of significance
Part II.G
Source DF SS MS F P
Part Numbers 9 6135.73 681.748 165.532 0.000
Operators 2 6.76 3.378 0.820 0.456
Part Numbers*Operators 18 74.13 4.119 1.477 0.131
Repeatability 60 167.33 2.789
Total 89 6383.96
Alpha to remove interaction term = 0.25
Figure 13.4 Two-way ANOVA table with interaction (Minitab printout).