Functional capability space and optimum process adjustments for manufacturing processes with in-specs failure

This paper introduces a methodology for functional capability analysis and optimal process adjustment for products with failures that occur when design parameters and process variables are within tolerance limits (in-specs). The proposed methodology defines a multivariate functional capability space (FC-Space) using a mathematical morphology operation, the Minkowski sum, in order to represent a unified model with (i) multidimensional design tolerance space; (ii) in-specs failure region(s); and, (iii) non-parametric, multivariate process measurements represented as Kernel Density Estimates (KDEs). The defined FC-Space allows the determination of a desired process fallout rate in the case of products with field failures that occur within design tolerances (in-specs). The outlined process adjustment approach identifies the optimum position of the process mean in order to minimize the overlap between the KDEs and in-specs failure regions, i.e., achieve the minimum possible process fallout rate for current process variation. The FC-Space-based process adjustment methodology is illustrated using a case study from the electronics industry where the in-specs failure region is identified based on warranty information analysis.