Concepedia

Process capability analysis—a robustness study

International Journal of Production Research · 1993 · 75 citations · 17 references

TL;DR

The study examines the robustness of Cp and Cpk process capability ratios when the underlying process distribution departs from normality. The authors aim to extend their analysis by applying the Taguchi loss function to generalize process capability assessment beyond normal distributions. They derive the distributions of estimated Cp and Cpk ratios and use them to validate large‑scale simulations, while also applying the Taguchi loss function to generalize capability analysis. Simulation and analytical results show that Cp and Cpk lack robustness to non‑normality, leading to recommendations that process distribution effects be considered before using these indices.

Abstract

Abstract The robustness of two popular process capability ratios, Cp and Cpk, when the random process being observed departs from normality is analysed. The distributions of estimated process capability ratios are derived and used as a basis for validation of large-scale simulation studies in an examination of departures from normality. The simulation studies and analytical results provide a basis for recommended procedures. It is recommended that the impact of process distributions be considered before using popular process capability indexes, due to the lack of robustness when departures from normality are ecountered. As an extension of our findings, we consider the Taguchi loss function as a generalization to process capability analysis regardless of the underlying population distribution.