# 32. MSA – Gage R&R X Bar Method

For readers who are not familiar with Gage R&R, please refer to the **MSA introduction link** for Gage R&R’s background introduction application. And X Bar Method is used to execute the type II when we have different appraisers to operate the measurement system.

In order to initiate the gage R&R analysis with X Bar method, there are 3 constants which is critical because it will decide you relative constants to calculate the gage R&R.

- Number of Samples (n)
- Number of Appraisers (a)
- Number of Trials per Sample (k)
- Specification (Median, USL and LSL)

In this example, there will be 12 samples (**n = 12**) and 4 appraisers (**a = 4**) and 4 trials per samples (**k = 4**). And before collect the gage R&R data and evaluate the measurement system, the following d2 table and constant calculation will be primary used for the reference.

*d2 constant table*

*Variance Calculation Equation and Applications*

And based on the table and calculation equation with the above description, K1 will be roughly 0.486 while K2 is 0.447 and K3 is 0.299 respectively.

Once the constants are determined, then it’s the time to collect the data and calculate the critical inputs for Gage R&R.

*Demonstrated Data Input*

Where

*Data Input Constant Calculation*

The tables below will be the final GR&R indicator definition and how to execute the calculation to understand the indicators.

*Gage R&R Factor Calculation*

*Gage R&R Variance % Calculation*

And by analyzing the GR&R and %PV, the results can be described by the criteria listed below

*% Gage R&R Criteria*

*% Part Variance Criteria*