Developing loss-based functional process capability indices for simple linear profile

Abstract

Process capability of simple linear profiles (SLPs) has been already measured by functional process capability indices ( and ), which are unable to distinguish between on-target and off-target processes. Hence, in this paper, we develop traditional loss-based indices for simple linear profiles using a functional approach. These new indices are based on the Taguchi loss function and can adequately reflect process mean deviations from the target value. The performance of the proposed indices and existing ones are studied using simulation studies. The simulation results show that the proposed methods outperform the existing functional indices regarding smaller mean absolute error (MAE) and mean square error (MSE) metrics. Also, a procedure is introduced to determine minimum number of profile samples for the estimation of proposed indices. In addition, bootstrap confidence intervals are constructed for the proposed indices. Finally, a real case study is given to show the application of the proposed indices.