Estimating process capability indices based on subsamples for asymmetric tolerances

Chen and Pearn (2001) proposed a new generalization of process capability indices (PCIs) for processes with asymmetric tolerances. C-p(") (u, v), is superior to the original index C,,(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 mu and sigma(2), 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 delta" and the precision index gamma". We investigate the relationships of delta" and gamma" with the process yield. We obtain the exact cumulative distribution functions and explicit forms of probability density functions of the natural estimators of delta", gamma", 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 gamma" and;(u, v) and the expected values and the variances for delta", gamma", and C-p(")(u, v). We also analyze the statistical properties of the estimated indices and delta", gamma", and C-p(")(u, v) assuming the process is normally distributed.