Linear profiles monitoring in the presence of nonnormal random errors

摘要

Profile monitoring is a technique to test the stability of the relationship between a response variable and explanatory variables over time. The most relevant linear profile monitoring methods have been constructed using the normality assumption. However, the normality assumption could be violated in many quality control applications. In this study, we consider a situation in which the random errors in a linear profile model follow a skew-normal distribution. The skew-normal distribution is a generalized version of the normal distribution. A new Shewhart-type chart and exponentially weighted moving average (EWMA) chart, named the Shewhart (R) and EWMA (R) charts, respectively, are constructed based on residuals to monitor the parameters of linear profile model. The simulation results show that the multivariate EWMA chart is sensitive to the normality assumption and that the proposed Shewhart (R) and EWMA (R) charts have good ability to detect big and small-to-moderate process shifts, respectively. An example using photo mask techniques in semiconductor manufacturing is provided to illustrate the applications of the Shewhart (R) and EWMA (R) charts.