Families of capability indices for one-sided specification limits

We study, when the specification interval is one-sided, two new classes of indices, which are based on the classes of indices for asymmetric tolerances earlier defined by Vannman. These classes generalize indices for one-sided specification limits earlier suggested in the literature. By varying the parameters of the classes various indices with suitable properties can be obtained. Under the assumption of normality explicit forms of the distributions of the two new classes of the estimated indices are provided. Numerical investigations are made to explore the behavior of the estimators of the indices for different values of the parameters. Based on the estimators a decision rule that can be used to determine whether the process can be considered capable or not is provided and suitable criteria for choosing an index from the families are suggested.