A note on the generalized indices of process capability

Process capability indices are widely used to assess whether the outputs of an in-control process meet the specifications. The commonly used indices are , , and . In most applications, the quality characteristics are assumed to follow normal distribution. But, in practice, many quality characteristics, e.g. count data, proportion defective etc. follow Poisson or binomial distributions, and these characteristics usually have one-sided specification limit. In these cases, computations of  or  using the standard formula is inappropriate. In order to alleviate the problem, some generalized indices (e.g.  index,  index,   index and  index) are proposed in literature. The variant of these indices for one-sided specification are  and ,  and ¸  and ,  and  respectively. All these indices can be computed in any process regardless of whether the quality characteristics are discrete or continuous.  However, the same value for different generalized indices and  or  signifies different capabilities for a process and this poses difficulties in interpreting the estimates of the generalized indices. In this study, the relative goodness of the generalized indices is quantifying capability of a process is assessed. It is found that only   or  gives proper assessment about the capability of a process. All other generalized indices give a false impression about the capability of a process and thus usages of those indices should be avoided. The results of analysis of multiple case study data taken from Poisson and binomial processes validate the above findings.

Keywords:

Generalized PCI , Goodness of generalized PCI , normal process , Poisson Process , binomial process