Evaluating capability of a process with ordinal responses

Abstract

Evaluating the capability of a manufacturing process is an important initial step in any quality improvement program. Methodologies have been reported in literature for evaluating capability of processes with quantitative characteristics of different natures. However, quantifying capability of a process with qualitative responses remains a difficult task. In this paper, a novel method is presented for measuring capability of a process with ordinal responses involving three ordered categories. The proposed method makes use of the process area of proportions and specification area of proportions defined in a two-dimensional plane. Extensive simulation studies reveal that in general, the defined process area does not always follow a normal distribution. However, by using Johnson transformation, it can be transformed to normal distribution and thus capability of a process with ordinal responses can be evaluated easily. Application of the proposed method to a real life problem is presented.

Keywords:

• Process capability index
• Ordinal response
• Process area of proportions
• Specification area of proportions
• Johnson transformation