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126 Part II: Metrology
Note that the AIAG recommends using the factor 6 instead of 5.15, since it covers
almost 100 percent, or to be exact 99.74 percent, of the range. Values of K 1 for
various sample sizes (that is, the number of trials or the number of measurements
taken on the same part by the same operator) are given in Appendix F. As noted
by Barrenstine, Duncan (1986) points out that this estimation procedure should be
slightly modified if N = r × n = (# operators) × (# parts) is less than 16. Thus, if N is
less than 16, then K 1 is defined as
K
1
515
= . .
(13.7)
*
d
2
Part II.G
The values of d * 2 are listed in Duncan (1986), Table D 3 . The values of K 1 listed in
Appendix F are determined according to the value of N.
Again, using Barrentine’s notation (2003, page 57) the Reproducibility = AV,
ignoring the interaction term, is defined as
Reproducibility = = ( ) ( )
2
2 EV
AV K R
2 x
( r×
n)
. (13.8)
where r is the number of trials, n the number of parts, EV is as given in equation
(13.5), R x
– is the range of the operator’s means, and the factor K2 is defined as
K
2
515
= . .
(13.9)
*
d
The values of K 2 are listed in Appendix G. The value of d * 2 can be found from
Duncan’s Table D 3 by selecting g = 1 and m = n (# operators). Thus, for example, if
we have five operators, then from Duncan’s Table D 3 for g = 1, m = 5, we have
K = 515 .
2
248 .
= 2077 . .
We now illustrate the range and the ANOVA methods with the following
example.
2
EXAMPLE 13.1
A manufacturer of bolts used in automotive applications has installed a new measuring
gage. In order to perform the measurement system analysis on the new gage the
quality manager randomly selected three operators from the department of quality control,
who decided to take a random sample of ten bolts. Each operator took three measurements
on each bolt, which were selected randomly. The data obtained is shown in
Table 13.1.
Continued