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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