A generalization of Clements’ method for non‐normal Pearsonian processes with asymmetric tolerances

Abstract

For non‐normal Pearsonian processes, Clements proposed a method for calculating estimators of the two basic process capability indices Cp and Cpk. Pearn and Kotz applied Clements’ method to obtain estimators for the other two more advanced process capability indices Cpm and Cpmk. Their considerations on those indices, however, are restricted to processes with symmetric tolerances. Recently, Pearn and Chen proposed a generalization of the index Cpk to handle cases with asymmetric tolerances. The generalization takes into account the asymmetry of the manufacturing specifications, which is shown to be superior to the other existing methods. In this paper, we apply this approach and consider a generalization of Clements’ method for non‐normal Pearsonian processes where the manufacturing tolerances are asymmetric. Comparisons between the original Clements’ method and the proposed generalization are provided. The results indicate that the generalization is more accurate than the original Clements’ method in measuring process capability.