Measuring process yield based on the capability index Cpm

Process capability indices Cp, Ca, Cpk and Cpm have been proposed to the manufacturing industry as capability measures based on various criteria including variation, departure, yield, and loss. It has been noted in recent quality research and capability analysis literature that both the Cpk and Cpm indices provide the same lower bounds on process yield, that is, Yield≤2Φ(3Cpk)-1=2Φ(3Cpm)-1. In this paper, we investigate the behaviour of the actual process yield in terms of the number of nonconformities (in ppm) for processes with a fixed index value of Cpk=Cpm, but with different degrees of process centring, which can be expressed as a function of the capability index Ca. The results illustrate that it is advantageous to use the index Cpm over the index Cpk when measuring process capability, since Cpm provides better customer protection.