Gauge
Repeatability and Reproducibility (GR&R)

Gauge
Repeatability and Reproducibility,
or
GR&R,
is a measure of the capability of a gauge or gage to obtain the same measurement
reading every time the measurement process is undertaken
for the same characteristic or parameter. In other words, GR&R
indicates the consistency and stability of a measuring equipment. The ability of a measuring
device to provide consistent measurement data is important in the
control of any process.

Mathematically, GR&R is actually a measure of
the variation of a gage's measurement, and not of its stability. An
engineer must therefore strive to minimize the GR&R numbers of his or
her measuring equipment, since a high GR&R number indicates instability
and is thus undesirable.

As its name
implies,
GR&R (or simply 'R&R') has two major components, namely, repeatability and
reproducibility.
Repeatability
is the ability of the same gage to give consistent measurement readings no matter how
many times the same operator of the gage repeats the measurement
process.
Reproducibility,
on the other hand, is the ability of the same gage to give consistent
measurement readings regardless of who performs the measurements.
The evaluation of a gage's reproducibility, therefore, requires
measurement readings to be acquired by different operators under the
same conditions.

Of course, in
the real world, there are no existing gages or measuring devices that
give exactly the same measurement readings all the time for the same
parameter. There are five (5) major
elements
of a
measurement system, all of which contribute to the variability of a
measurement process: 1) the standard; 2) the workpiece; 3) the
instrument; 4) the people; and 5) the environment.

All of these
factors affect the measurement reading acquired during each measurement
cycle, although to varying degrees. Measurement errors, therefore,
can only be minimized if the errors or
variations
contributed individually by each of these factors can also be minimized.
Still, the gage is at the center of any measurement process, so its
proper design and usage must be ensured to optimize its repeatability
and reproducibility.

There are
various ways by which the R&R of an instrument may be assessed, one of
which is outlined below. This method, which is based on the method
recommended by the Automotive Industry Action Group (AIAG), first
computes for variations due to the measuring equipment and its operators. The over-all GR&R is then computed from these
component variations.

Equipment
Variation,
or EV,
represents the repeatability of the measurement process. It is
calculated from measurement data obtained by the same operator from
several cycles of measurements, or trials, using the same equipment.
Appraiser
Variation
or AV,
represents the reproducibility of the measurement process. It is
calculated from measurement data obtained by different operators or
appraisers using the same equipment under the same conditions. The
R&R,
is just the combined effect of EV and AV.

It must be
noted that measurement variations are caused not just by EV and AV, but
by Part
Variation
as well,
or PV.
PV represents the effect of the variation of parts being measured on the
measurement process, and is calculated from measurement data obtained
from several parts.

Thus, the
Total
Variation (TV),
or the over-all variation exhibited by the measurement system,
consists of the effects of both R&R and PV. TV is equal to the
square root of the sum of (R&R)^{2}
and (PV)^{2}
square, i.e.,

TV = √
(R&R)^{2} + PV^{2}.

In a GR&R
report, the final results are often expressed as %EV, %AV, %R&R, and %PV,
which are simply the ratios of EV, AV, R&R, and PV to TV expressed
in %. Thus,
%EV=(EV/TV)x100%;
%AV=(AV/TV)x100%; %R&R=(R&R/TV)x100%;
and %PV=(PV/TV)x100%.
The gage is good if its %R&R is
less than 10%.
A %R&R between 10% to 30% may also be acceptable, depending on what it
would take to improve the R&R. A %R&R of more than 30%, however,
should prompt the process owner to investigate how the R&R of the gage
can be further improved.

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