When separate populations exhibit similar reliability as a function of multiple explanatory variables, combining them into a single population is tempting. This can simplify future predictions and reduce uncertainty associated with estimation. However, combining these populations may introduce bias if the underlying relationships are in fact different. The probability of agreement formally and intuitively quantifies the similarity of estimated reliability surfaces across a two-factor input space. An example from the reliability literature demonstrates the utility of the approach when deciding whether to combine two populations or to keep them as distinct. New graphical summaries provide strategies for visualizing the results.
Stevens, N.T., & Anderson-Cook, C.M. (2017). Quantifying Similarity in Reliability Surfaces Using the Probability of Agreement. Quality Engineering, 29(3), 395-408. http://dx.doi.org/10.1080/08982112.2017.1312004