The pitfalls of the unconventional process capability indices

Abstract

For assessing capability of a normal process with upper specification limit (USL) conventionally C_pu index is estimated to facilitate better decision making in product and process management. But, in practice, many quality characteristics having USL only, e.g. count data, proportion defective etc. are discrete and follow Poisson or binomial distributions. Some unconventional indices (e.g. C_u , C_fu ¸ C_pcu and C_pyu) are proposed in literature for assessing capability of Poisson or binomial processes. Due to legacy of usages of Cpu index and its interpretations, a user of an unconventional index often tends to interpret its values with reference to the values of C_pu for the bad, good or highly capable normal processes, and get a false impression about the capability of the concerned Poisson or binomial process. In this paper, the key features of those unconventional indices are highlighted and then some numerical analysis is carried out for assessing the interpretation issues associated with these unconventional indices. The results of these analyses reveal that although there is no interpretation issue for the unconventional index Cu , there are serious interpretation issues with all other unconventional indices. The mathematical relationships of estimates of other unconventional indices with the estimate of C_u index are established. It is recommended to convert the estimates of other unconventional indices into estimated C_u value using those relationships before any decision making. Otherwise, users of the other unconventional indices may inadvertently be led to erroneous decision making.