Establishing Multivariate Specification Regions for Incoming Raw Materials Using Projection to Latent Structure Models: Comparison Between Direct Mapping and Model Inversion

Increasing raw material variability is challenging for many industries since it adversely impacts final product quality. Establishing multivariate specification regions for selecting incoming lot of raw materials is a key solution to mitigate this issue. Two data-driven approaches emerge from the literature for defining these specifications in the latent space of Projection to Latent Structure (PLS) models. The first is based on a direct mapping of good quality final product and associated lots of raw materials in the latent space, followed by selection of boundaries that minimize or best balance type I and II errors. The second rather defines specification regions by inverting the PLS model for each point lying on final product acceptance limits. The objective of this paper is to compare both methods to determine their advantages and drawbacks, and to assess their classification performance in presence of different levels of correlation between the quality attributes. The comparative analysis is performed using simulated raw materials and product quality data generated under multiple scenarios where product quality attributes have different degrees of collinearity. First, a simple case is proposed using one quality attribute to illustrate the methods. Then, the impact of collinearity is studied. It is shown that in most cases, correlation between the quality variable does not seem to influence classification performance except when the variables are highly correlated. A summary of the main advantages and disadvantages of both approaches is provided to guide the selection of the most appropriate approach for establishing multivariate specification regions for a given application.