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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 2factor 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 (MS_{Parts}),
Appraisers (MS_{Appraisers}), the Parts x Appraisers Interaction
(MS_{PxA}), the Error (MS_{Error}), and a “Pooled” term MS_{Pool}, if
appropriate.
PxA Interaction
Calculating Repeatability

If the PxA Interaction is not significant, then the Repeatability
statistic, s_{E}, is determined by pooling the MS_{Error} and MS_{PxA}.
 If the interaction is significant, then the Repeatability
statistic, s_{E}, is determined from the MS_{Error}
Calculating Reproducibility
 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:


