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128 Part II: Metrology
Continued
Step 5: Calculate the average range (R – ) for operators:
R R +
=
R + R
1 2 3
3
300 . + 250 . + 300 .
=
= 283 .
3
Part II.G
Step 6: Calculate repeatability (this value is also referred to as equipment
variation [EV]) and the estimate of the standard deviation of repeatability
(s Repeatability ):
Repeatability( EV)= R × K1 = 283 . × 305 . = 863 .
where from Appendix F for three trials and n (# of parts × # of operators)
= 30, we have K 1 = 3.05.
EV 863 .
sˆ
Repeatability
= = = 167 . .
515 . 515 .
Step 7: Calculate reproducibility (this value is also referred to as appraiser
or operator variation [AV]) and the estimate of the standard deviation of
repeatability (s Reproducibility ):
( ) ( ) ×
2
Reproducibility( AV)= Rx
× K
EV 2 m r
2
/
where from Appendix G for three operators, we have K 2 = 2.70, # of
parts = m = 10 , and # of trials = r = 3. Thus, we have
2 2
Reproducibility( AV)= ( 066 . × 270 . )
( 863 . ) / 10×
3
= 083 . .
Note that if the number under the radical is negative, then AV is zero.
The estimate of the standard deviation of reproducibility (s Reproducibility ) is
084 .
sˆ
Reproducibility
= = 016 . .
515 .
Since, using this method, the reproducibility is calculated by ignoring the
interaction term, the standard deviation of reproducibility may merely
be looked upon as the operator standard deviation.
Step 8: Calculate GR&R (that is, repeatability and reproducibility) and the estimate of
GR&R standard deviation:
Continued