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.

中文翻译：

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基于模型的工艺能力指数：干法蚀刻半导体案例研究

流程能力指数被广泛用于检查生产水平和业务活动的质量标准。他们考虑位置以及与规格限制和目标的偏差。在单变量和多变量上下文中，文献都包含许多关于该主题的贡献。在一个真实的半导体案例研究的推动下，我们讨论了有理子群的作用以及它们在计算能力指数时所面临的挑战，尤其是当数据涉及大量产品时。此外，我们的情况还涉及一系列问题：单方面的规格限制，数据的非对称分布，来自混合分布的数据证据以及需要过滤混合物的一种成分。解决了先前的问题之后，由于基于所谓的“晶圆”的半导体工艺的特殊特性，我们为文献提供了关于在异方差空间工艺中如何计算能力指数的建议。利用广义的加性模型，我们表明可以估计一个能力面，该能力面允许识别预期不完全符合所需质量标准的区域。