Effects of Model Estimation on Control Charts for Ordinal Response Profiles

The quality of some complex manufacturing or service processes might be characterized by the functional relationship referred to as a profile. To monitor the ordinal response profile, a generalized likelihood ratio control chart was proposed based on a nonparametric regression model. In practice, the in-control(IC) model was usually unknown and needed to be estimated. Three model estimation methods, including the local linear kernel estimation, spline, and Newton Raphson, were proposed to study the effects of model estimation on the performance of the control chart, considering different sample sizes and different parameter settings of the estimation method. The simulation results and case study show that, the sample size has a significant effect on the IC performance of the control chart, but when the sample size exceeds a certain value, the performance of the control chart no longer changes with the sample size. When the IC model is a generalized linear model, all three estimation methods have a significant impact on the out-of-control performance of the control chart, where the Newton Raphson method performs better. When the IC model is unknown, the local linear kernel estimation method is better. © 2022, China Mechanical Engineering Magazine Office. All right reserved.