Optimal confidence intervals on the variation for operators and gauge in manufacturing process with repeated measurements

It is necessary to measure the attributes of the parts in any manufacturing process. It is also important to monitor measurement system in the manufacturing process because repeated measurements of the attributes include variability as well as target value. This paper considers variabilities due to repeated measurements, operators, and gauge in a measurement system. The measurement system is statistically modeled as a two-factor mixed model with one covariate and interaction. That is, this model employs J operators randomly chosen to conduct measurements on I randomly selected parts from a manufacturing process. In this experiment each operator measures each part K times. This paper aims to provide engineering practitioners with statistically optimal confidence intervals on the variation due to operators and gauge resulted from a measurement system statistically modeled. The optimal confidence intervals are based on a moderate large sample method (MLS) and a generalized p-value method (GEN). The confidence intervals proposed can be useful tools to determine whether a manufacturing process is adequate for monitoring a measurement system.