Encyclopedia and Handbook of Process Capability Indices: A Comprehensive Exposition of Quality Control Measures

The C p and C pk indices are appropriate measures of "progress" for quality improvement paradigms in which reduction of variability is the guiding principle and process yield is the primary measure of success. However, these indices are not taking into account the cost of failing to meet customers' requirements. A world-renown Japanese quality central expert, G. Taguchi, on the other hand, focus on the loss in a product's worth when one of its characteristics departs from the customers' ideal value T. To handle this situation, Hsiang and Taguchi (1985) introduced the index C pm, independently proposed by Chan et al. (1988). The index is based on the idea of the squared error loss and it is sometimes called the Taguchi index. It concentrates on measuring the ability of the process to cluster around the target, which reflects the degrees of process targeting (centering). The index C pm involves the variation of production items with respect to the target value and the specification limits that are preset in the factory. It is defined as:
where as above USL LSL is the allowable tolerance range of the process, d = (USL LSL) /2 is the half length of the specification interval, and ? is a measure of the average product deviation from the target value T. The term ? 2 = ? 2 + (