Assessing process capability index using sampling plan in the presence of measurement system errors

Measurement system errors impact the collected data used to evaluate the process capability. The work developed in this paper aims at integrating these errors in the calculation of the threshold value of Cpused for making the decision about the process capability Cp0∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left({C}_{p0}^{\ast}\right) $$\end{document} and to propose a procedure that corrects the parameters of the sampling plan used to estimate this capability index. An expression of Cp0∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{p0}^{\ast } $$\end{document}that depends on the gauge repeatability and reproducibility (GR&R), errors type I and type II, the capability index corresponding to the rejectable quality level (CpRQL), and to the acceptable quality level (CpAQL) was developed. The effects of these parameters and their relative interactions on the difference between capability index calculations with and without integrating the measurement system error (ΔCpthreshold) and the corresponding difference in the parts per million of defects ppm (Δppm) were assessed using a response surface design. It was found that the integration of the measurement system error is essential particularly when the difference between CpAQL and CpRQL is small. Concerning the correction of the sampling plan parameters, a procedure was developed to integrate the measurement system error evaluated by the GR&R. This procedure guarantees a common decision concerning the process capability whatever the state of the measurement system is, and this decision would, therefore, depend on the sample quality only.