Repeatability and Reproducibility ( R & R) -- Basic Knowledge - Part 1

 What is gauge repeatability and reproducibility?

Gage repeatability and reproducibility (GR&R) is defined as the process used to evaluate a gauging instrument's accuracy by ensuring its measurements are repeatable and reproducible.

 

What is meant by repeatability?

·        Repeatability is defined as the closeness of agreement between independent test results, obtained with the same method, on the same test material, in the same laboratory, by the same operator, and using the same equipment within short intervals of time.

·        Repeatability is the variation due to the measurement device. It is the variation that is observed when the same operator measures the same part many times, using the same gage, under the same conditions.

 

What is reproducibility of a measurement system?

·        Reproducibility is the deviation of the results obtained when the same sample is measured continuously for multiple times with changed measuring conditions.

·        Reproducibility is mainly used to evaluate the long-term stability of the instrument, the reliability of the sampling method, and the effect of different operators, and so on.

 

 

THE THREE TYPES OF GR&R STUDIES

·        There are three GR&R studies—crossed, nested, and expanded—each with a different objective.

·        Choosing which GR&R study to perform depends on how much data are available and whether the measurement test is destructive.

Crossed GR&R Study

In this study, the same parts are measured multiple times by each operator (Figure 1). It’s used to determine how much process variation is due to measurement system variation.

Crossed GR&R is used in nondestructive scenarios—when parts are not destroyed during measurement and can be measured twice. For example, when measuring the length of a part, the part is not changed during the measurement.

Figure 1: Crossed Gage Repeatability and Reproducibility (GR&R) Study

Nested GR&R Study

This method is used when only one operator measures each part, usually because the test destroys the part (Figure 2). This study is called nested because one or more factors are nested under another factor and not crossed with the other factors.

Nested GR&R is used in destructive testing scenarios. For example, testing the amount of force required to open a bag of potato chips, heat-treating steel tubes, and testing the strength of a rope until it breaks. In these examples, the sample is destroyed during testing, making it impossible to test the sample again.

A critical factor of a nested GR&R study is to identify a batch of material that is so close to the original it reasonably can be assumed the parts in the batch are the same part. The key to being able to run a destructive GR&R study is the assumption that a batch is homogeneous.

Figure 2: Nested Gage Repeatability and Reproducibility (GR&R) Study

Expanded GR&R Study

Standard GR&R studies (crossed and nested) assess the effects of two factors in the measurement system—typically operator and part (Figure 3). In many cases, the effects of operator and part are not sufficient to provide a complete understanding of the measurement system, so a third variable (typically gage) is added to the standard GR&R study.

Figure 3: Standard Gage Repeatability and Reproducibility (GR&R) Study

When three or more factors are included in the analysis, the study is called expanded GR&R (Figure 4). An expanded GR&R study can be done if one or more of the following conditions exists:

More than two factors are being assessed. The study analyzes not just parts and operators, but also up to eight additional factors, such as gage, lab, or location.

There are missing data points. An expanded GR&R study can be performed even with incomplete data and unbalanced studies.

There are fixed or random factors for greater flexibility.

Figure 4: Expanded Gage Repeatability and Reproducibility (GR&R) Study

Differences between a standard and expanded GR&R study include:

The expanded GR&R study allows additional factors to be evaluated.

Interactions between the additional factors and the operator and part also can be assessed.

The expanded GR&R study allows analysis of the data—even if there are missing data points.

The data collection plan commonly is adjusted for the expanded GR&R. Repeating the standard plan for each additional factor is costly, so the number of parts is often reduced. For example, five parts are to be measured by three operators using three randomly selected gages, and each operator will measure each part twice. Thus, the total sample will be 5 × 3 × 3 × 2 = 90. In a standard GR&R study, more parts can be selected, but this is an unacceptably large sample size for expanded GR&R.

When there isn’t enough data for a standard GR&R study, an expanded GR&R is an ideal tool to comprehensively characterize the measurement system