R&R Analysis Using ANOVA

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R&R Analysis Using ANOVA

### 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.

• 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.

#### ANOVA Table

Where:

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:

where:

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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