Process Analysis Gage Repeatability and Reproducibility - Plots of Repeatability and Reproducibility
There are several ways to summarize via graphs the findings from a repeatability and reproducibility experiment. For example, suppose we are manufacturing small kilns that are used for drying materials for other industrial production processes. The kilns should operate at a target temperature of around 100 degrees Celsius. In this study, 5 different engineers (operators) measured the same sample of 8 kilns (parts), three times each (three trials). We can plot the mean ratings of the 8 parts by operator. If the measurement system is reproducible, then the pattern of means across parts should be quite consistent across the 5 engineers who participated in the study.
R and S charts
Quality Control discusses in detail the idea of R (range) and S (Sigma) plots for controlling process variability. We can apply those ideas here and produce a plot of ranges (or
Sigmas) by operators or by parts; these plots will allow us to identify outliers among operators or parts. If one operator produced particularly wide ranges of measurements, we may want to find out why that particular person had problems producing reliable measurements (e.g., perhaps he or she failed to understand the instructions for using the measurement gage). Analogously, producing an R chart by parts may allow us to identify parts that are particularly difficult to measure reliably; again, inspecting that particular part may give us some insights into the weaknesses in our measurement system.
Repeatability and reproducibility summary plot
The summary plot shows the individual measurements by each operator; specifically, the measurements are shown in terms of deviations from the respective average rating for the respective part. Each trial is represented by a point, and the different measurement trials for each operator for each part are connected by a vertical line. Boxes drawn around the measurements give us a general idea of a particular operator's bias. A more detailed description of how to interpret and use the information provided by this plot is presented the Examples.