Capability indices when tolerances are asymmetric

Different process capability indices, which have been suggested for asymmetric tolerances, are discussed and, furthermore, two new classes of appropriate indices are suggested. We study the properties of these new classes of indices. We provide, under the assumption of normality, explicit forms of the distributions of these new classes of the estimated indices. We suggest a decision rule to be used to determine if the process can be considered capable. Using the results regarding the distributions it is possible to calculate the probability that the process is to be considered capable. Based on these results we suggest criteria for choosing an index from the class under investigation.