Measuring Process Performance Based on Expected Loss with Asymmetric Tolerances

By approaching capability from the point of view of process loss similar to Cpm, Johnson (1992) provided the expected relative loss Le to consider the proximity of the target value. Putting the loss in relative terms, a user needs only to specify the target and the distance from the target at which the product would have zero worth to quantify the process loss. Tsui (1997) expressed the index Le as Le ¼ Lot þ Lpe, which provides an uncontaminated separation between information concerning the process relative off-target loss (Lot) and the process relative inconsistency loss (Lpe). Unfortunately, the index Le inconsistently measures process capability in many cases, particularly for processes with asymmetric tolerances, and thus reflects process potential and performance inaccurately. In this paper, we consider a generalization, which we refer to as L00 e , to deal with processes with asymmetric tolerances. The generalization is shown to be superior to the original index Le. In the cases of symmetric tolerances, the new generalization of process loss indices L00 e, L00 ot and L00 pe reduces to the original index Le, Lot, and Lpe, respectively. We investigate the statistical properties of a natural estimator of L00 e L00 ot and L00 pe when the underlying process is normally distributed. We obtained the rth moment, expected value, and the variance of the natural estimator ^L00 e , ^L00 ot, and ^L00 pe. We also analyzed the bias and the mean squared error in each case. The new generalization L00 e measures process loss more accurately than the original index Le.