This document discusses methods for performing gauge repeatability and reproducibility (GR&R) tests on surface metrology equipment. It finds that GR&R values are often over 100% due to within-part variation rather than instrument error. Using a uniform sinusoidal specimen eliminates much of the within-part variation, resulting in more accurate GR&R values typically under 10%. The document also provides a method to determine the optimal number of measurements needed per part based on the surface variation and tolerance.

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How to perform GR&Rs using
surface-finish metrology
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%GR&R INSTRUMENT VAR.
%GR&R W/IN SPEC VAR.
%GR&R INSTRUMENT VAR.
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Performing gage repeatability and
reproducibility (GR&R) tests on surface-
finsih equipment can be a very frustrating
experience. It is not uncommon to obtain
GR&R’s that are in excess of 100 percent
on certain types of parameters and toler-
ances. Understandably, this leaves the
evaluator with serious concerns about
the integrity of his surface-finish instru-
ment. In most cases, the cuprit turns out
to be within the part variation, not in the
instrument.
A GR&R procedure was carefully
developed to eliminate such variables as
part-to-part variation, and to separate ap-
praiser-caused variation from equipment
caused variation. For most applications,
however, there was no need to include
a methodology to eliminate within part
variation.
In a classic GR&R test for example, an
QD gage - within part-variation effects
from out-of-round, taper, and straight-
ness - can be significantly minimized
by ensuring that the measurements are
conducted on about the same position
each time the part is measured. You may
conclude that a similar procedure would
be sufficient for surface-finish evaluation.
There’s a catch though. Errors of form
change quite gradually. On the other
hand, surface finish can change dramati-
cally, even between traces that are only
5 micrometers (200 micro inches) apart.
If you were to develop a part-orienting
fixture such that you could position the
part within ±0.0001mm each time, you
would be measuring a surface similar to
that shown in Fig. 1.
It is therefore not surprising that
the resulting GR&R’s for that surface,
as shown in Fig. 2, are extremely high.
Through elaborate test procedures, we
were able to isolate true instrument varia-
tion from within-part variation. It is clear
that the major contributor to GR&R value
is the within-part variation.
The measuring instrument itself, in
this case a Hommel-Etamic Form4004,
is capable of replicating a single trace to
a high degree of precision (see Fig. 3).
the changes depicted are the result of a
gradual change in the surface as the stylus
continues to traverse the same position
on the steel part. Changes in parameter
calculations were in the order of 0.001 to
0.004 micrometers per trace.
Sinusoidal Specimen
Conducting traces on exactly the same
position on the part may produce more re-
producible results, but it doesn’t allow the
opportunity to test such variables as equip-
ment setup and other operator variables. If
you want to determine instrument capabil-
ity with precision, the use of a sinusoidal
specimen as shown in Fig. 4 will result in a
more fair evaluation of the test instrument.
The sinusoidal specimen is much more
uniform than a typical surface. Within
specimen variation is much lower than
that found in common machined surfaces.
Compare the differences between Fig. 1
and Fig. 4.
Those GR&R tests conducted with the
instrument that produced results in Fig. 2
produced the results in Fig. 5 when testes
were conduced on a high precision sur-
face-finish specimen. The major distinction
between testes was elimination of within-
part variation by using a very uniform test
specimen.
Less Than Actual
I should be noted that because si-
nusoidal specimens have very gradual
transitions through peaks and valleys, the
variability of the instrument is less than
what would really occur on an actual part
by about a factor of 2 on peak-to-valley
parametesr such as Rt, Rmax, Rz, Rp and
Rpm. Actual parts may have much sharper
valleys and peaks. In any case, even when
factoring in the 2X factor, GR&Rs were less
than 10 percent.
It should be obvious from the preded-
ing information that when you are actually
measuring production parts, you need to
perform more than on trace on a surface,
and then average the results to determine
a value more representative of the surface.
The next issue is one of determining the
number of traces required for a particular
surface.
Economically, you don’t want to run
any more traces than necessary to achieve
a set level of precision. We have developed
a procedure to deal with issues, using
“Student T” theory to establish the opti-
mum number of traces for certain level of
precision. The procedure is as follows:
Establish the standard deviation of the1.
surface under evaluation. About 20 to 30
traces should be enough to determine
the standard deviation of a surface. It is
necessary to do this calculation only once
with a particular part or process, since the
standard deviation varies only slightly from
part to part offer time for a given process.
Divide the standard deviation obtained from2.
STep 1 by the total tolerance.
Determine the acceptable P value. This is3.
the probability that average values of sam-
ples from the same part will agree within 10
percent of each other. For example a P value
of 80 means 80 percent of the time average
values from the same part will agree with
each other wvithin 10 percent.
The selected P value will vary depend-
ing on three criteria:
How close actual values are to the•
tolerance
the criticality of the parameter•
the difficulty or cost of making multiple•
traces
Fig. 7 depicts the standard deviation
to tolerance ratios for a fin-ground steel
surface, and the resulting traces per part
that would be needed for a precision of 10
percent of the tolerance. The number of
traces was derived from the chart in Fig. 6.
Need better methods
Exisiting GR&R methods are inadequate
for determining the capability of surface-
finish instruments. Measurements on high-
quality reference specimens will produce
more representiative GR&R numbers. You
should be aware however, that they will
tend to be lower than what will occur on
an actual part surface.
Surface finish callouts will have to be
accompanied by sample-size requirements.
These should be in the form of number of
traces per part, or else there will be con-
tinued problems between departments,
customers, and suppliers in correlating
measured results on the same part.
How to perform GR&Rs using
surface-finish metrology
Fig. 3 - This represents
50 consecutive traces on
exactly the same position
on a ground steel surface.
Fig. 4 - This is the
topography of a Hommel-
Etamic (RND) roughness
reference specimen.
Fig. 5 - Typical GR&Rs using a
sinusoidal surface specimen,
where the measuring zone was
limited to 0.25mm by 4.8mm.
Fig. 6 - A method for determining the
optimum number of traces for a precision
of 10 percent of the tolerance.
NUMBER OF TRACES
%GR&R
Surface Roughness Parameter
Fig. 7 - Variation of
relative to tolerance, as
measured on a finely
ground surface with
25 readings of 4-8mm,
evenly spaced.
Fig. 2 - This chart represents
the percent of GR&Rs you
may expect to obtain if tests
were conducted on the sur-
face shown in Fig. 1.
Fig. 1 - Ground steel surface patch 0.25mm wide by 4.8mm
long. This topography depicts the variablility of a ground steel
surface in a zone that is only 0.25mm (0.010”) wide.
SURFACE ROUGHNESS PARAMETER
SURFACE ROUGHNESS PARAMETER
STD. DEV./TOLERANCE TRACES REQ’D PER PART
STD. DEV
TOT. TOL
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