Estimating Process Capability Indices Based on Subsamples for Asymmetric Tolerances

Abstract

Chen and Pearn (2001) proposed a new generalization of process capability indices (PCIs) for processes with asymmetric tolerances. (u, v), is superior to the original index C_p (u, v) and other existing generalizations by being closely related to actual the process yield, more sensitive to the process centering for given values of μ and σ², and the on-target process characteristic with the maximal value. In this article, C_p″ (u, v) is presented as the function of the accuracy index δ″ and the precision index γ″. We investigate the relationships of δ″ and γ″ with the process yield. We obtain the exact cumulative distribution functions and explicit forms of probability density functions of the natural estimators of δ″ and C_p″ (u, v) based on small subsamples data collecting from past “in-control” and S control charts. In addition, we derive the rth moments of and (u, v) and the expected values and the variances for , , and (u, v). We also analyze the statistical properties of the estimated indices , , and (u, v) assuming the process is normally distributed.

Key Words:

• Accuracy index
• Asymmetric tolerances
• Control chart
• Precision index
• Process yield