On the actual and observed process capability indices: A signal-to-noise ratio model

In the evaluation of process capability, gauge measurement errors usually distort the measured data yielding two dissimilar capability indices, particularly, the actual and the observed process capability indices (ACp and OCp). Gauge measurement errors result in underestimation of the actual process capability, consequently, the variance of gauge errors has to be assessed to better chart the relationship between the ACp and OCp. The different variance components of a measurement system can be assessed by a gauge repeatability and reproducibility (GR&R) study. This paper presents novel relationships between the ACp and OCp by means of a signal-to-noise ratio (SNR) model. The probability density functions of both indices will be presented in terms of SNR and a procedure to find the critical values of ACp and OCp is established. In contrast to literature studies, a measurement system can now be described by a novel α-β characteristic curve. Different SNR values will result in different α-β curves, hence, the acceptance of a measurement system depends on the specified significance values of α and β and not solely on strict SNR values. Since measured data yields two different ACp and OCp distributions, type I and type II error analysis can be performed. Different case studies are presented to validate the resulting relationships and distributions.