Sample size determination for estimating process precision and process loss based on multiple samples with designated accuracy ratio

摘要

The process capability index C_p is defined as C_p=(USL-LST)/(6 sigma), where USL and LSL are upper and lower specification limits. The Taguchi capability index C_(pm)/(USL-LST)/(6(sigma~2+(mu-T)~2)~(1/2)) where T is the target value. The loss function is loss(X) = (X -T)~2. A routine-basis data collection procedure is executed to run X and S control charts, then to analyze the past in-control data. Li, et al. (Ref. 1) and Kirmani, et al. (Refs. 2 and 3) studied the distribution of estimating process capability indices based on the ranges of the subsamples for C_p and C_(pk) and the sample standard deviation of the subsamples for C_p, respectively. Vannman and Hubele (Ref. 4) derived the distribution properties of estimated capability indices based on multiple samples. Pearn and Yang (Ref. 5) considered the distributional and inferential properties of the estimated precision C_p based on multiple samples.