A Proposal for a Management-Oriented Process Capability Index

Abstract

During the past three decades, PCIs – process capability indices – have inspired hundreds of pages of scientific research. The trade-off between simplicity and precision in reproducing an overall process quality prediction is both the reason behind the criticism for Cp and Cpk and the motive for their widespread use. Indeed, their strength in simplifying the assessment of a process control status compensates for some of the statistical shortcomings largely recognized in the literature, amongst which is the normality assumption. Hence, this article aims at overcoming the main statistical problems of Cp and Cpk indices by proposing a new indicator, still compliant with the traditional PCIs approach, but applicable for cases of non-normal processes while being simple to implement and easy to interpret. The proposed indicator is composed of three sub-indices, each related to a specific process characteristic: how the process is repeatable, how much the data distribution is skewed about the mean value and how much the process data comfortably lies between the specifications limits. On top of this, a specific parameter allows designers or quality engineers to modify the index value range in order to finetune the effect of the cost of Taguchi's loss function. The article presents the theoretical structure of the new indicator and an extensive numerical test on several different processes with different distributions upon multiple specification limit combinations, along with a comparison to the Cpk index, in order to demonstrate how the new index provides a clearer indication of the process criticalities.