A unified class of process capability indices for asymmetric tolerances and non-normal data

Process capability analysis plays a critical role in quality control by evaluating how well manufacturing processes meet defined specifications. However, traditional process capability indices (PCIs) rely on assumptions of symmetric tolerances and normally distributed data, which often do not hold in real-world applications and can lead to misleading conclusions. To overcome these limitations, we propose two novel classes of PCIs designed specifically for asymmetric tolerances, complemented by parametric estimation procedures and asymptotic confidence limits. To address the issue of non-normal data, we further employ an inverse transformation via constrained B-spline regression, which removes the need for the normality assumption. We demonstrate that our proposed PCIs reduce to traditional indices under symmetric conditions and normal data while extending applicability to a broader range of cases. Numerical simulations and a real-world application in an electronics company confirm the effectiveness and practical utility of our approach.