Capability assessment for processes with multiple characteristics: A generalization of the popular index Cpk

Abstract

Process capability index Cpk is the most popular capability index widely used in the manufacturing industry. Existing research on the yield-based measure index Cpk to date is restricted to processes with single characteristics. However, many manufacturing processes are commonly described with multiple characteristics, for example, the gold bumping process in the TFT-LCD (thin film transistor-liquid crystal display) manufacturing industry. In the gold bumping process, gold bumps have multiple characteristics all having effects on the process yield. Obtaining accurate gold bumping manufacturing yield is very important for quality assurance and in providing guidance toward process improvement. To obtain accurate yield assessment for processes with multiple characteristics, we propose a new overall yield-measure index Ca-Tpk, which is a generalization of the index Cpk, and a natural estimator of Ca-Tpk. For the purpose of making inferences on the process capability, we derive a quite accurate approximation of the distribution of since the distribution is analytically intractable. With this distribution, we tabulate the lower confidence bounds of the new index under various sample sizes for in-plant applications. In addition, we construct a statistical test on the new yield-measure index in order to examine whether the yield meets the customers' requirements. For illustration purpose, a real case in a gold bumping factory located in the Science-based Industrial Park at Hsinchu, Taiwan is presented. © 2011 John Wiley & Sons, Ltd.