# ANOVA Analysis

#### ANOVA test will break the random error component of a measurement into smaller pieces, allowing the NDA professional to see the random uncertainty from the operator, the NDA instrument, and the item being measure. This information allows us to see what item has the greatest contribution to the random uncertainty and tells us how repeatable the measurement is by a single person and how reproducible a measurement is by multiple of individuals. It is also a great tool to spot deficiencies in equipment and personnel measurement techniques. It is highly recommended to run routinely as a personnel and equipment performance metric.

## Definitions

#### - ANOVA is analysis of variance.

#### - Reproducibility is the variation in the average of the measurements made by different operators using the same NDA measurement device and technique when measuring identical characteristics on the same item or same process.

#### - Repeatability is the inherent variability of the NDA measurement process.

#### - A nested design requires that the same part cannot be measured twice.

#### - A crossed design is when the same item can be measured multiple times.

#### - Items are what is being measured by the NDA measurement system.

#### - Operator/appraiser are those who are performing the NDA measurement.

#### - The values measured are the numerical quantities of the items being measured.

#### - Randomize will arrange the items being measured randomly.

## ANOVA Design Criteria

#### Set the design criteria and download the .csv file using the generate run sheet button. Fill in the measurement values and upload using the upload run sheet button bellow. You must do this first. Once this is done, look at the analyze tab to the left for your results. If you don't want to make your own run sheet then use run demo sheet tab to the menu at the left and download the demo sheet and upload that sheet instead.

#### To design a ANOVA experiment you must pick a certain number of operators, items to measure, and the number of times to measure each item. Increase the number of measurements will improve your results. If you have a large team it is possible to set up a design to evaluate all members and be able to spot operators with deficiencies performing measurements.

## Upload Run Sheet

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# - Interpreting the Charts and Results Below

#### - The part to part bars must be much taller than the other bars. This means the variation is from the true differences in the items measured. If the part to part bars are shorter than the other bars, the NDA measurement system is unreliable.

#### - The points on the X-bar chart needs to be outside the control limits. This means the NDA measurement system variance is much smaller than the difference in items being measured and means the NDA measurements being performed are reproducible.

#### - The points on the R-chart needs to be inside the control limits. Any point outside of the control bars needs to be investigated. This means the NDA measurements being performed are repeatable if the control limits are not exceeded.

#### - The Measured by Item chart should show a consistent range of variation for the same parts unless there are different type items measured and they are classified according to groups.

#### - The Measured by Operator lines should be almost flat. A large slope means that at least one operator has a bias to measure larger or smaller than the other operators.

#### - The Operator Interaction Chart lines connecting the plotting averages should not diverge significantly. If there is divergence, there is a bias and a relationship between the operator making the measurement and the item being measured. You can use this as a test to see if particular operators have deficiencies in their techniques.

#### - % StudyVar is the amount of variation attributed to measurement error. This should be less than 10%. This means very little variation is due to NDA measurement system. 10% to 30% can be acceptable range, depending on your needs.