Testing process capability based on Cpm in the presence of random measurement errors

Abstract

Process capability indices have been widely used in the manufacturing industry providing numerical measures on process performance. The index Cp provides measures on process precision (or product consistency). The index Cpm, sometimes called the Taguchi index, meditates on process centring ability and process loss. Most research work related to Cp and Cpm assumes no gauge measurement errors. This assumption insufficiently reflects real situations even with highly advanced measuring instruments. Conclusions drawn from process capability analysis are therefore unreliable and misleading. In this paper, we conduct sensitivity investigation on process capability Cp and Cpm in the presence of gauge measurement errors. Due to the randomness of variations in the data, we consider capability testing for Cp and Cpm to obtain lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that the estimator with sample data contaminated by the measurement errors severely underestimates the true capability, resulting in imperceptible smaller test power. To obtain the true process capability, adjusted confidence bounds and critical values are presented to practitioners for their factory applications.