What is a Gauge R&R study in MSA? | GRR Study | Variable MSA Study

GRR Study | Variable MSA Study

What is a Gauge R&R study in MSA?

→ Gauge R&R study or “Gauge Repeatability and Reproducibility Study (GRR Study)” is a term which is commonly used in Measurement System Analysis.

→ 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. 
→ Equipment Variation measures the variation of an appraiser when measuring the same part (and the same characteristic) using the same instrument more than one time.
→ Calculation of Equipment Variation:
Equipment Variation (EV) in GRR study in MSA

⇒ 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.
→ Appraiser Variation is the variation in the different appraisers when measuring the same characteristic on the same part with the same instrument more than one time.
→ Calculation of Appraiser Variation:
Appraiser Variation (AV) in GRR study in MSA

 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.
Gauge Repeatability & Reproducibility (GRR) in GRR study in MSA

➤ [4] Part Variation (PV) :

→ The part variation is calculated 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:
Part Variation (PV)

⇒ Some other values of K3 for different numbers of parts:

values of K3 in MSA


➤ [5] Total Variation (TV) :

→ This is the total variation from the study. It is determined by the following equation:
Total Variation (TV)

Steps for GR&R Study in MSA with Excel Template:

  1. Determine the number of parts, the number of appraisers to use and the number of trials
  2. Select the parts & measuring instrument for the study
  3. Label the parts from 1 to n and designate the appraisers A, B, etc.
  4. Conduct the Measurements & Put data into the Excel Template
  5. Analyzing the Results
  6. Interpreting the results

➤ Step 1: Determine the number of parts, the number of appraisers to use and the number of trials

→ 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.


➤ Step 2: Select the parts & measuring instrument for the study

→ 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.
→ The parts should be selected in the proper method that they cover all possible variants of the manufacturing process.
→ If appropriate, calibrate the gauge or verify that the last calibration date is valid.


➤ Step 3: Label the parts from 1 to n & designate appraisers A,B, etc.


➤ Step 4: Conduct the Measurements & Put data into the Excel Template

→ The parts must be run in random order.
→ All appraiser measures the reading each part 3 times.
→ Example trial1 – first in order, trial2 - second in reverse order, trial3 - third random).
→ 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.


👉 Click here: GRR Study Excel Template Download

→ Open the Gauge R&R worksheet to record data.
→ Write data into the Gauge R&R worksheet.
→ Enter the number of operators, trials, samples and specification limits



 ➤ Step 5: Analyzing the Results

→ Analyze data in the Gauge R&R worksheet.
→ In this study, we have selected three appraisers (A, B, and C) and five parts that represent typical variation in the length output. 
→ All appraiser measures the reading each part 3 times.
→ The Calculation is mentioned in the below picture.


Analyzing the Results - GRR study in MSA

👉 Click here: GRR Study Excel Template Download

→ We use the above results to perform the gauge R&R calculations.
→ We start by determining the following:
→ The average for each trial for each appraiser
→  Average & Range of each part with each appraiser.
→ The average range for the part
 These calculations are shown in the table below.

Calculation of recorded data


→ Calculation of the average range of the three appraisers.

Determine the average range for the three appraisers

 Then, calculate the difference between the maximum and minimum of appraiser average.

determine the difference

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

→ Next, we will calculate the range of the part averages (Rp). 

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:

Putting up these values for all the 5 contributors

 Step 6: Interpreting the results

→ 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.
→ We have to check Total Variation to decide that our measurement system is applicable or not?


Calculation of TV

👉 Click here: GRR Study Excel Template Download

→ 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 (Conditionally 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.




➦ Also, we will check the number of distinct categories (ndc) in Gauge R&R Study

→ 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.


 Correction Criteria of Measurement System Analysis:

➥ 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 may require to use the gauge in an appripriate manner.

➤ Some improvement points in Gauge R&R study in MSA

→ Brainstorm with the team for improvement solutions.
→ Determine the best “practical solution” (may require some experimentation).
→ Pilot the best solution
→ Implement the best solution – train employees.
→ Again conduct the study to verify the Improvement.