
Measurement Systems


Introduction 
We use measurements to understand and control our parts and processes. Our measurements are never exact. It is critical, therefore, to understand, quantify, and control the errors introduced by the measurement system itself. Excessive gage Variation (i.e. poor gage R&R) makes it very difficult to see (and control) what is really happening within a process.
The amount of potential error in the measurement is statistically quantified through a Gage R&R study. The result of a gage R&R study is a comparison of the variation in the measurement system compared to the specification and the corresponding percentage of the tolerance consumed by measurement system variation.
Repeatability refers to the variation present when one person measures the same part several times with the same gage.
Reproducibility is the variation resulting from different operators measuring the same parts with the same gage.
If Repeatability is large compared to Reproducibility, some of the reasons may be:
Instrument needs maintenance
The clamping or location for the gaging needs improvement
There is excessive within part variation (tapered bores, surface which are not flat, etc)
The Gage/Fixture should be redesigned to be more rigid.
If Reproducibility is large compared with Repeatability, some of the reasons may be:
The appraisers need to be better trained on how to use and read the gage instrument
The gage is hard to read
Fixturing to obtain more consistent measurement process are needed.
Gage R&R:
R&R of less than 20%  Measurement System Acceptable
R&R 20% to 30%  Measurement System May Be Acceptable. Make your decision based on the classification of characteristics , operator training issues, hardware application, parttopart variation, customer input, realistic tolerancing, etc. Do not automatically assume that a new measurement system is needed.
R&R over 30%  Measurement System Unacceptable. Find the problem and remove the root cause. Evaluate other measurement systems after attempting to correct the current system.
Number of Distinct Categories:
The number of distinct Categories is another indicator of the measurement systems capability. An acceptable system should have a minimum of 5 distinct categories. This indicates that the measurement system is able to divide the data into 5 or more groups and it can tell the difference between parts falling into one of those groups.

Variable Gauge R & R 
Study Format
4 operators, 20Samples, 4 trials
Method
The provided data was processed using the MINITAB computer software.
The data provided appears to follow a normal distribution, with a mean of 9.613 and a standard deviation of 0.05199.
The X bar and R chart for Operator #1 shows a few points that appear to be out of control. The X bar chart depicts a downward trend. However, the R chart is quite consistent. This may be an indication that the operator is using the measuring device correctly, but it is not taking accurate measurements.
Besides point 5, this operator’s measurements seem to be a very stable and incontrol. Operator #2 seems to be taking very accurate and precise data with his/her vernier calipers. Point 5 lies well about the upper control limit on the R chart and perhaps it should be investigated why this point lies so far off.
The data from Operator #3 appears to have some trends in variability, but mainly incontrol. Point 11 seems out of the ordinary and perhaps actions should be taken to see the cause of this widespread variability. The X bar chart shows a slight cyclic pattern to it. This may be due to factors such as changes in temperature or operator fatigue.
The X bar chart for Operator #4 depicts an upward shift in the process level. The R chart, on the other hand, is quite consistent. This may lead us to believe that the operator is using the calipers correctly, but something may be changing with the caliper that is causing the measurements to change.

Gage R&R Study  XBar/R Method 
A close look at the X double bar chart for all operators shows that operator 1 had a lot of out of control data near the end of his run compared to the other three operators. This may be due to operator fatigue or perhaps machine tool wear. From this X double bar chart, it appears that there is quite a bit of variability in the measurements taken between operators. From the output data for our study, 62.22% of the variability was from Repeatability, whereas only 24.60% was from reproducibility. What this indicates is that the variability caused by the gauge itself is greater than variability due to different operators using the gauge. This is a very good indication that a new measuring device is desperately needed.

ANOVA: measurement versus product, operator 
The variance due to reproducibility is the sum of the operator variance and the product*operator variance (0.00053 + 0.00065). The repeatability variance is listed as the Error variability (0.00163). This ANOVA output displays that the repeatability variance is higher than the reproducibility variance. This again indicates that the gauge is causing more variance in our process than the operator.

