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## About this lesson

Attribute data Gage R&R Studies generate a number of metrics that are used for judging the performance of the measurement system used to evaluate pass/fail attribute data. In this lesson, each of these metrics is described and the method of calculation is explained.

## Exercise files

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Attribute Data Gage R&R Calculations.xlsx11.7 KB Attribute Data Gage R&R Calculations - Solution.xlsx

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## Quick reference

### Attribute Data Gage R&R Calculations

The formulas and calculations for attribute data Gage R&R Studies are simple counts of comparisons between appraisers and the reference standard with answers converted to a percentage.

### When to use

The attribute data Gage R&R calculations are done once all data is collected in order to determine the Gage R&R measurements.

### Instructions

Attribute data Gage R&R Studies rely upon data that is in the form of pass/fail, yes/no or good/bad. There are only two states possible, the desired state and an undesirable state.

Attribute data Gage R&R studies have many of the components seen in variable data Gage R&R Studies. These include two or three appraisers and two or three trials. One difference is that attribute data studies require a minimum of 30 items and 30 is definitely better.

- In order to assess the system performance, some items need to be acceptable and some unacceptable. Ideally these would be split 50% of one type and 50% of the other type – although a 70-30 split will still provide excellent study results. And of course inspections of items are done in a random order.
- One other input that is normally used with attribute data Gage R&R Studies, although it does not help in the calculation of repeatability and reproducibility, is a reference standard of the true value for each item in the study. This reference will be used for some accuracy calculations that are done in parallel with GRR. The results are analysed by comparing results across trials, across the appraisers and with the standard. Minitab will also use the Chi-Square statistical analytical tool to gain evern more insight.
- Repeatability is the within appraiser measure. An individual repeatability score is determined for each appraiser. This is the number of items in which they matched their score across all trials divided by the total number of items. The system repeatability is the average of all the individual repeatability scores. The target for repeatability is 90% or better with the marginal range being 80% to 90%.
- Reproducibility is the between appraiser measure. In this case it is a check of two aspects of the assessment. First, did an appraiser agree on all assessments for an item and second, did that appraiser agree with another appraiser on all their assessments of the item. Determine how many times this condition exists and then divide that value by the number of items and the number of appraiser pairs. The target percentage and marginal zone are the same as for Repeatability.

Attribute data Gage R&R studies include the reference value for each item. This allows the study to examine both precision (repeatability and reproducibility) but also to assess accuracy measurements.

- Accuracy is the percentage of times an appraiser made the correct assessment of an item. It is the total number of correct assessments divided by the number of items, trials, and appraisers. Once again we will use a target of greater than 90% and a marginal zone of 80% to 90%.
- False Alarm is the condition when an appraiser assessed something to be a “Fail” that the reference standard has rated to be a “Pass.” This means an appraiser is rejecting a good item. The acceptable rate for this is only 5% or less and the marginal rate is %5 to 10%.
- Miss Rate is the opposite condition. It occurs when an appraiser assesses something to be a “Pass” when its true value is a “Fail". This is more dangerous to the customer since it means a flawed output could be delivered to a customer who is expecting the product or service to correct. The acceptable rate for this is only less than 2% and the marginal zone is 2% to 5%.
- Effectiveness is the final accuracy and precision measurement. It is done at the item level and is determined by counting the number of items where all appraiser’s assessment agreed on all trials with the true value from the reference standard. And this is divided by the number of items to create a percentage effectiveness. The target is once again greater than 90% and the marginal zone is 80% to 90%.

### Hints & tips

- You can see how important it is that the data is recorded for the correct item.
- Be sure to get at least a 70-30 split or better for the items – however, those that are bad should not be so obviously bad that the appraiser does not even need to assess the item with the measurement system.
- Basic repeatability and reproducibility do not need the reference standard, but every time I have run this type of study, I have included the reference standard so I could calculate the accuracy measurements also.

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