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 + PV2.


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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