Profile monitoring with binary data and random predictors. - Shang, Yanfen
The purpose of profile monitoring is to check the stability over time of relationships between response variables and one or more explanatory variables. In many applications, categorical response variables are common and a generalized linear model is usually utilized to model this kind of profile for quality improvement. In practice, different profiles often have random explanatory variables and these variables require careful monitoring as well. Statistical process control is important and challenging for monitoring profiles in such situations. A novel control chart is proposed by integrating an exponentially weighted moving average scheme and a likelihood ratio test for the parameters of a logistic regression model. This new scheme not only monitors the functional relationship of the profile but also the mean of the explanatory variables. The proposed chart has reasonable computational and implementation complexity and is efficient in detecting shifts. The simulation results show that it performs better than the standard benchmarks in the literatures for the array of simulation examples that we consider. A real example from the electronic industries is used to illustrate the implementation of the proposed approach.
Keywords: Categorical response; Exponential weighted moving average; Generalized linear model; Profile monitoring; Random Explanatory Variables; Statistical Process Control