Nonparametric control chart using auxiliary information for smallest extreme value distribution

Abstract

Traditionally, in using an auxiliary variable for quality control applications, the response and auxiliary variables are often assumed to follow a bivariate normal distribution. Given that the response variable and an auxiliary variable are linearly related, a novel process monitoring method is proposed to scrutinize the shifts of the model parameter when the response and auxiliary variables follow the smallest extreme value distributions. Utilizing the estimates of the model parameters as input variables, auxiliary information based (AIB) multivariate sign exponential weighted moving average (AIB-MSEWMA) control chart is proposed. Because the AIB-MSEWMA control chart doesn’t require the multivariate normality distribution assumption for the estimators of model parameters, the AIB-MSEWMA control chart is more reliable than the competitors of the AIB-Hotelling T 2 and AIB multivariate EWMA control charts in terms of the false alarm rate. Finally, the operation of the AIB-MSEWMA control chart is illustrated through a regenerated data set of the car brake system.