Measurement System Analysis An evaluation of the measurement system MUST be undertaken to ensure effective analysis of any subsequent data generated for a given process/product characteristic Measurement error is a statistical term meaning the net effect of all sources of measurement variability that cause an observed value to deviate from the true value Both process and measurement variability must be evaluated and improved together If we work on process variability first and our measurement variability is large, we can never conclude that the improvement made was significant, or correct Observed Value = True Value +/- Measurement Error True Variability = Process Variability + Measurement Variability

Types of Measurement Errors Measurement System Bias - Calibration Study Measurement System Variation - GRR Study µ total = µ process +/- µ measurement σ2 total = σ2 process + σ2 measurement

Observed Process Variation Sources of Variation Observed Process Variation Actual Process Variation Measurement Variation Long-term Process Variation Short-term Process Variation Variation within a Sample Variation due to Operators Variation due to Gage Reproducibility Accuracy Repeatability Stability Linearity

Measurement system Error Sources of Variation Measurement system Error Precise Accurate Repeatability Reproducibility Accuracy can be taken care by Calibration Precision can be taken care by GRR Accuracy Stability Linearity

Component of GRR Study 1 2 1 2 1 2 Trial Reading #1 3 4 3 4 3 4 5 6 5 Difference leads to Reproducibility 1 2 1 2 1 2 Trial Reading #1 3 4 3 4 3 4 5 6 5 6 5 6 Difference leads to Repeatability Six Parts / Conditions 1 2 1 2 1 2 Trial Reading #2 3 4 3 4 3 4 5 6 5 6 5 6 Operator A Operator B Operator C

Methods of Performing GRR: ANOVA Method ANOVA not only separates the equipment & operator variation, but also elaborates on combined effect of operator & part ANOVA uses the ‘standard deviation’ instead of ‘range’, & hence gives a better estimate of the measurement system variation ANOVA also may not need the ‘tolerance’ value as an input