A New Measure of Process Capability:C_pm

On the reliability of the estimated incapability index

“…However, we can show that MSE(C ia ) = 4C ip C ia /n + [2/n(n − 1)](C ip ) 2 , and so 2 , which is greater than 0 for n = 2, equal to 0 for n = 3, and less than 0 for n ≥ 4. Therefore, the UMVUEC ia has smaller mean squared error than the MLEĈ ia , and is more reliable for applications with n ≥ 4.…”

“…Since c n < 1, thenĈ ip = c nĈip underestimates C ip but with smaller variance. In fact, we may calculate 2 and obtain…”

“…We note that the mathematical relationships C ip = 1/(C p ) 2 , and C ia = 9(1−C a ) 2 can be established, where C p and C a are two basic process capability indices considered by Kane [3] and Pearn et al [4].…”

“…If we define C ip = (σ/D) 2 , and C ia = [(µ − T )/D] 2 , then C pp can be expressed as C pp = C ip + C ia . Since C ip measures the process variation relative to the specification tolerance, it has been referred to as the process imprecision index.…”

“…The index C pp is a simple transformation of C * pm , a general form of the capability index C pm considered by Chan et al [2], which provides an uncontaminated separation between information concerning the process precision and the process accuracy. The index C pp is defined as follows:…”