R&R Analysis Using ANOVA



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R&R Analysis Using ANOVA

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R&R Analysis Using ANOVA

Analysis of Variance, or ANOVA for short, is an experimental design technique that looks at a number of variables at the same time.

  • It is used to help determine which of the variables under study have a statistically significant impact on the process output.

  • With measurement systems, we can explore how the test equipment and appraiser variables affect the measurement system output.

ANOVAs allow us to study four measurement system components:

  • Variation between parts or samples.

  • Reproducibility between operators or appraisers.

  • Repeatability of the measurement equipment.

  • Interaction between the samples and the appraisers.

The use of ANOVA does have some advantages over standard GR&R studies:

  • ANOVAs provide information on interactions between samples and appraisers.

  • With an ANOVA, we can vary the number of samples, appraisers, trials, and even the number of measurement devices to get a more accurate picture of the variation in the measurement system.

  • ANOVAs allow us to get an accurate estimate of variances.

  • ANOVA techniques are the preferred method for analyzing measurements for destructive testing.

Disadvantage of ANOVA:

  • Calculations using ANOVA are more complex than those with other techniques. It is best to use a computer with DOE software for the calculations.

ANOVA Data Format

  • A standard 2-factor ANOVA format is used for analyzing measurement systems.

  • Factor A is used to designate the parts or samples. Factor B represents the appraisers.

  • The number of levels for each factor is a function of the number of samples and the number of appraisers.



a = number of levels of a

b = number of levels of b

n = sample size per cell

N = total number of measurements made

Mean Square Values

  • Mean square values are calculations of variance. The variance is the standard deviation squared.

  • Mean square values are calculated for the Parts (MSParts), Appraisers (MSAppraisers), the Parts x Appraisers Interaction (MSPxA), the Error (MSError), and a “Pooled” term MSPool, if appropriate.

PxA Interaction

  • We will evaluate the significance of the Parts x Appraisers Interaction using the F-test.

    • If this interaction is significant, we will need to investigate the reasons for it.

    • If it is not significant, we will assume it is really part of the experimental error and pool the PxA Interaction value in with the Error Value.

Calculating Repeatability

  • If the PxA Interaction is not significant, then the Repeatability statistic, sE, is determined by pooling the MSError and MSPxA.

  • If the interaction is significant, then the Repeatability statistic, sE, is determined from the MSError

Calculating Reproducibility

  • The Reproducibility, sA, is determined by the MSAppraisers with a correction term to account for confounding from the instrument variation.

  • If the PxA Interaction is not significant:

  • If the PxA Interaction is significant:

R&R Calculations

  • If the PxA Interaction is not significant, the R&R is simply:

  • If the PxA Interaction is statistically significant, the R&R calculation is more involved:


r=number of trials

R&R as a % of the Total Tolerance (TT)

  • We prefer the measurement system to take up less than 10% of the Total Tolerance. If it takes up 30% or more of the TT, the measurement system needs work.

R&R as a % of the Total Variation (TV):

  • If the %GR&R is greater than 30% of the total variation, then the measurement system should be improved.

  • To calculate the percentage of the total variation taken up by the measurement system, we need to know both the Part Variation (PV) and the Total Variation, TV.

  • If the PxA Interaction is significant:

  • If the PxA Interaction is not significant:

  • With PV known, TV can be calculated:

Contribution of MSA to Total Variation:

  • We can also calculate the contribution that the measurement system actually makes to the total variation. The formula for the % Contribution is:

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