## What is a Gauge R&R study in MSA?

### 1) What is a Gauge R&R study in MSA?

→ Gauge R&R study or “Gauge Repeatability and Reproducibility Study” is a term
which is commonly used in MSA.
→ To calculate the GR&R %, following five contributors are to be calculated:
1. Equipment Variation (EV)
2. Appraiser Variation (AV)
3. Gauge Repeatability & Reproducibility (GRR)
4. Part Variation (PV)
5. Total Variation (TV)

#### ➤ [1] Equipment Variation (EV) in GRR study in MSA:

➧ This is the "within appraiser" variation.
➧ It measures the variation one appraiser has when measuring the same part
(and the same characteristic) using the same gauge more than one time.
➧ The calculation is given below.
⇒ Where K1 is a constant that depends on the number of trials.
For 2 trials, K1 is 0.8862.
For 3 trials, K1 is 0.5908.

#### ➤ [2] Appraiser Variation (AV) in GRR study in MSA:

➧ This is the "between appraisers" variation.
➧ It is the variation in the average of the measurements made by the different appraisers
when measuring the same characteristic on the same part.
➧ The calculation is given below.

Where K2 is a constant that depends on the number of appraisers.
For 2 appraisers, K2 is 0.7071.
For 3 appraisers, K2 is 0.5231

#### ➤ [3] Gauge Repeatability & Reproducibility (GRR) in GRR study in MSA:

➧ GRR is the combination of AV and EV and the calculation is given below.

#### ➤ [4] Part Variation (PV) :

➧ The part variation is determined by multiplying the range of the part averages (Rp)
by a constant K3.
➧ K3 depends on the number of parts.
➧ The part variation is then given by:
⇒ Some other values of K3 for different numbers of parts:

#### ➤ [5] Total Variation (TV) :

➧ This is the total variation from the study. It is determined by the following equation:

### 2) Steps for Gauge Repeatability and Reproducibility (GR&R) Study in MSA:

1. Select 10 parts that represent the full range of long-term process variation.
2. Identify the appraisers (inspectors or part checker).
3. If appropriate, calibrate the gauge or verify that the last calibration date is valid.
4. Open the Gauge R&R worksheet to record data.
5. Have each appraiser assess each part 3 times (trials – first in order, second in reverse order, third random).
6. Input data into the Gauge R&R worksheet.
7. Enter the number of operators, trials, samples and specification limits
8. Analyze data in the Gauge R&R worksheet.
9. Assess MSA trust level.
10. Take actions for improvement if necessary.

#### ➤ Step 1: Determine the number of parts, the number of appraisers to use and the number of trials - GRR study in MSA

➧ There are several issues that must be considered when planning a gauge R&R study.
➧ The first is the number of appraisers and the number of parts to use.
➧ The number of parts (n) must be greater than or equal to 5.
➧ The number of appraisers (k) must be greater than 2.
➧ The number of trials (r) must be greater than or equal to two.
➧ This represents how often each appraiser will measure a part.
➧ In addition, the n*k should be greater than 15.
➧ This gives more confidence in the results.
➧ If possible, include all the appraisers who operate the gauge in the study.

#### ➤ Step 2: Select the parts for the study - GRR study in MSA

➧ The next step is selecting the parts to include in the study.
➧ The parts should be selected to reflect the range of variation in the process.
➧ In other words, don't just take 10 parts off the line right in a row.
➧ You need to select the parts so they reflect the variation seen in
the manufacturing process.

#### ➤ Step 4: Conduct the Measurements- GRR study in MSA

➧ The parts must be run in random order.
➧ Start with appraiser A. Appraiser A measures the parts in random order.
➧ The results are recorded.
➧ This process continues for each appraiser without the appraisers being able to see
the results from other appraisers.
➧ This cycle is continued until you have completed all trials.
➧ Be sure that an appraiser cannot see his/her results from previous trials.

#### ➤Step 5: Analyzing the Results- GRR study in MSA

➧ You select three appraisers (A, B, and C).
➧ You select five parts that represent typical variation in the length output.
➧ You have each appraiser measure each part three times.
➧ The measurement results are given below.

➧ You use the above results to perform the gauge R&R calculations.
➧ You start by determining the following:
➧ The average for each trial for each appraiser
➧ The average and range for each part for each appraiser
➧ The overall average and average range for each appraiser

➧ The overall average and the average range for the part
➧ These calculations are shown in the table below.

→ Determine the average range for the three appraisers.

Then, determine the difference between the maximum appraiser average and
the minimum appraiser average.

➧ A has the maximum average (3.157). C has the minimum average (2.695).
➧ Thus,  the difference is (3.157) - (2.695) = 0.462

→ Next, determine the range of the part averages (Rp).

➧ The largest part average is for Part 3 (4.10).
➧ The smallest part average is for Part 5 (1.94).
➧ So, Rp = (4.10) - (1.94) = 2.16

→ Putting up these values for all the 5 contributors:

#### ➤Step 6: Interpreting the results- GRR study in MSA

➧ Remember, a gauge R&R study is a study in variation.
➧ You must have variation in the parts and in the appraisers to calculate
the above numbers.
➧ To determine if the measurement system is adequate, you must compare
the results to Total Variation (TV).

➧ The number that most people focus on first is the % GRR
➧ The following guidelines can be used to determine if the measurement system
is acceptable, conditionally acceptable or not acceptable.

➧ Green: < 10% of TV (Measurement system is acceptable)
➧ Yellow: 10-30% of TV (Measurement system may be acceptable
based on the application)
➧ Red: > 30% of TV (Measurement system needs improvement)

➧ In this example, the measurement system needs improvement since
%GRR is greater than 30%.
➧ Sometimes you can look at the %AV and %EV to get insights into where to start
improving the measurement system.
➧ But the study indicates that the measurement system must be improved.

#### ➤ You can also determine the number of distinct categories (ndc).

➧ This is a measure of the number of distinct categories that can be distinguished by
the measurement system.
➧ It is similar to looking at how many possible values there are on a range control chart.
➧ The calculation is:
ndc = 1.41(PV/GRR) = 1.41(0.872/0.319) = 3.8
➧ The integer value of ndc should be greater than or equal to 5.
➧ In this case, it is 3.
➧ Again, this is an indication that the measurement system needs improvement.

#### ➤ If repeatability is large compared to reproducibility, then the reasons may be:

1. The instrument needs maintenance;
2. Other reason may be the gauge should be redesigned to be more rigid;
3. The clamping or location for gauging needs to be improved;
4. There is excessive part variation.

#### ➤ If reproducibility is large compared to repeatability, then possible causes may be:

1. The appraiser needs to be better trained in how to use and read the gauge instrument.
2. Calibrations on the gauge dial are not clear
3. A fixture of some sort may be needed to help the appraiser use the gauge more consistently.

#### ➤ Some improvement points

➧ Brainstorm with the team for improvement solutions.
➧ Determine best “practical solution” (may require some experimentation).
➧ Pilot the best solution
➧ Implement the best solution – train employees.
➧ Re-run the study to verify the improvement.

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