Model-based process capability indices: The dry-etching semiconductor case study

Process capability indices are widely used to check quality standards both at the production level and for business activity. They consider the location and the deviation from specification limits and targets. The literature contains many contributions on this topic both in the univariate and the multivariate context. Motivated by a real semiconductor case study, we discuss the role of rational subgroups and the challenge they present in the computation of capability indices, especially when data refer to lots of products. In addition, our context involves a mix of problems: unilateral specification limit, nonsymmetric distribution of the data, evidence of data from a mixture of distributions, and the need to filter one component of the mixture. After solving the previous issues and because of the peculiar characteristics of semiconductor processes based on the so called “wafers,” we contribute to the literature a proposal on how to compute capability indices in the case of heteroscedastic spatial processes. With a generalized additive model, we show that it is possible to estimate a capability surface that allows the identification of regions expected to not be fully compliant with the desired quality standards.