A NEW GENERALIZATION OF Cpm FOR PROCESSES WITH ASYMMETRIC TOLERANCES

Abstract

Greenwich and Jahr-Schaffrath9 introduced the incapability index C pp , which is a simple transformation of the index [Formula: see text] proposed by Chan et al.3 Chen10 considered the incapability index [Formula: see text], a generalization of C pp , to handle processes with asymmetric tolerances. Based on the same idea on [Formula: see text], we consider a new generalization [Formula: see text], which is a modification of the process capability index C pm . In the cases of symmetric tolerances, the new generalization [Formula: see text] reduces to the original index C pm . The new generalization [Formula: see text] not only takes the proximity of the target value into consideration, like those of C pm and [Formula: see text], but also takes into account the asymmetry of the specification limits. We compare the new generalization [Formula: see text] with C pa (1, 3) and C pa (0, 4), two special cases of C pa (u, v) recommended by Vännman7 for asymmetric tolerances. We also investigate the statistical properties of the natural estimator [Formula: see text], assuming the process is normally distributed. We obtain the exact distribution and an explicit form of the probability density function of [Formula: see text]. In addition, we compute the rth moment-expected value, variance of [Formula: see text], and analyze the bias as well as the MSE of [Formula: see text].