## General

As we discuss in Measurement System Analysis (MSA) that we can take actions to improve our manufacturing process. These actions are based on the data we measure from process. Every manufacturing process is monitored by using the tool Statistical process Control (SPC), in which regularly data to be collected. For that the measurement system should have the acceptable level of variation to get the accurate data. Therefore we preferred the measurement system which has no error / variation. To calculate the process variation & measurement system variations, there is an effective tool is Gage Repeatability and Reproducibility (Gage R&R).

**What is Gage Repeatability & Reproducibility?**

Gage repeatability & Reproducibility (Gauge R&R) is define as the method to discover how much of the process variation is due to the measurement equipment and measurement method. This method is design to evaluate the effects of repeatability & reproducibility separately, and as a combine overall error of measurement. Also to initiate appropriate actions to minimize the measurement system variation contributed in total process variation.

**Repeatability** – It is the variation in obtained while measuring a given characteristic repeatedly on the same part

- With one measuring instrument

- By one appraiser

**Reproducibility** – finally It is the variation in the average of the measurement system made

- By different appraisers
- Using the same measuring instrument
- On identical characteristic of the same part

**How to perform Gage R&R study?**

There is 1 gage (Instrument / equipment), 3 different operators, total of 3 trials and 10 components (ideally covering the Full range of the process spread) should be used.

### Method:

- Identify the operators who inspect the parts as A, B & C.
- Select 10 components & identify them through numbering from 1 to 10.
- Select the Gage which is calibrated before taken for trail if appropriate.
- Then Let operator A measures the 10 components and enter the results in worksheet.
- Let operator B measures the 10 components and enter the result in the worksheet in same order without seeing the operator A results.
- Let operator C measures the 10 components and enters the result in the worksheet in same order without seeing the operator A & operator B results.
- The one cycle is completed; repeat the cycle 2 times again until each operator has measured 10 components a total of 3 times. Record all results in the worksheet.
- Complete the calculation as per the standard.

### Gage R&R Calculation’s

Let us take an example by putting the values from actual data. We have the data from measurement then we add this data in the worksheet as shown above.

calculate the basic terms from above data,

**R = ****(r _{a} + r_{b} + r**

_{c}**) / No. of operators**=(0.151+0.221+0.253)/3 =0.2083

**UCL _{R }= R * D4** = 0.2083 * 2.58 = 0.538

**(D4 For 2 Trials=3.27 & 3 Trials=2.58)**

Now from the above example we have to calculate the following terms

- Equipment Variation (EV)
- Appraiser / Operator Variation (AV)
- Repeatability & Reproducibility (GRR)
- Part Variation (PV)
- Total Variation (TV)
- No. of distinct categories (ndc)

#### 1) **Equipment variation (EV): Repeatability**

It calculates the variation one operator has when measuring the same part using the same Gage more than one time.

**EV = R * K _{1}** =0.2083 * 0.5908 = 0.12306

**(K1 for 2 Trials=0.8862 & 3 Trials=0.5908)**

#### 2) **Appraiser Variation (AV): Reproducibility**

It is the variation in the average of measurement by different operators measure the same part using same Gage.

#### 3) **Repeatability & Reproducibility (GRR)**

This is the combination of operator variation & Equipment variation….

For this example

**Part Variation (PV)**

It is calculated by range of the parts average, as below

For this example

#### 5) **Total Variation (TV)**

Total variation is calculated for interpreting the above analysis.

For this example

#### 6) **Number of distinct categories (ndc)**

The number of distinct categories (ndc) is a measure of the number of distinct categories that can be distinguished by the measurement system, so this can show that the how much your data is categorized in terms of control charts.

ndc = 1.41 (PV / GRR) =1.41 (1.101/0.208) =7

For acceptance level “ndc” value should be greater then 5.

**Now finally to comparing the above data with variation in the parts,**

1. %EV = 100*(EV / TV) =100*(0.123 / 1.121) =10.98%

2. %AV = 100*(AV / TV) =100*(0.68 / 1.121) =15.05%

**3. %GRR = 100*(GRR / TV) =100*(0.208 / 1.121) =18.64%**

4. %PV = 100*(PV / TV) =100*(1.101 / 1.121) =98.25%

**GRR Acceptance
Criteria**

- Now If %GRR < 10% – Measurement system is acceptable
- If 10% <%GRR < 30% – Measurement system is conditionally accepted
- Then if %GRR > 30% – Measurement system is not acceptable

**Interpretation from Gage Repeatability & Reproducibility (Gage R&R) study**

**When repeatability is
large compare to reproducibility**

- Instrument need maintenance
- Redesign Gage for more rigidity
- Improve location / clamping of gauging
- Excessive within part variation

**When reproducibility
is large compare to repeatability **

- Training need to operator for better Gage measurement
- Incremental division on instrument are not readable
- Need fixture to provide consistency in Gage use.