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:

⇒ 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:

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 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:

⇒ 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:

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 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.

→ 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.

→ 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 the average range of the three appraisers.

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

→ 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).

→ 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

→ 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?

→ 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.

➥ 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.

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