## Impact of Gage R&R on the Capability Index Cp

### Why would you want to do this?

• To see how much the measurement system is contributing to the total variation
• This helps you make an informed decision as to whether you should prioritize:
• Reducing Measurement Variation
• Reducing Process Variation
• Reducing both Measurement Variation and Process Variation
• Doing nothing

### How To Use The Online Calculators

• You will need values for:
• Observed Process Capability Index
• An estimate of Gage R&R – Either:
• Gage R&R as a % of Tolerance (also known as Precision To Tolerance)
• Gage R&R as a % of Process Variation (Note: There are multiple ways of defining Process Variation)

### Calculator #1 – Remove The Impact of Gage R&R (based on Tolerance) To Estimate Actual Process Capability

#### Formula:

${\text Cp}_{\text Act} = \dfrac{{\text Cp}_{\text Obs}}{\sqrt{1 - ( {\text Cp}_{\text Obs} \times {\text GRR}_{\text T})^2}}$

$where \qquad{\text Cp}_{\text Act} = {\text the\ \textbf{actual} \ process \ variation} \\\\where \qquad{\text Cp}_{\text Obs} = {\text the\ \textbf{observed} \ process \ variation} \\\\where \qquad{\text GRR}_{\text T} = {\text Gage \ RandR \ based \ on\ \textbf{tolerance} \ range} \\$

### Calculator #2 – Remove The Impact of Gage R&R (based on Process Variation) To Estimate Actual Process Capability

#### Formula:

${\text Cp}_{\text Act} = \dfrac{{\text Cp}_{\text Obs}}{\sqrt{1 - {\text GRR}_{\text P}^2}}$

$where \qquad{\text Cp}_{\text Act} = {\text the\ \textbf{actual} \ process \ variation} \\\\where \qquad{\text Cp}_{\text Obs} = {\text the\ \textbf{observed} \ process \ variation} \\\\where \qquad{\text GRR}_{\text P} = {\text Gage \ RandR \ based \ on\ \textbf{process} \ variation} \\$

### Reference:

AIAG Measurement System Analysis 4th Edition – Appendix B – Impact of GRR on the Capability Index Cp

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