Phase II monitoring of auto-correlated linear profiles using linear mixed model

In many circumstances, the quality of a process or product is best characterized by a given mathematical function between a response variable and one or more explanatory variables that is typically referred to as profile. There are some investigations to monitor auto-correlated linear and nonlinear profiles in recent years. In the present paper, we use the linear mixed models to account autocorrelation within observations which is gathered on phase II of the monitoring process. We undertake that the structure of correlated linear profiles simultaneously has both random and fixed effects. The work enhanced a Hotelling's T2 statistic, a multivariate exponential weighted moving average (MEWMA), and a multivariate cumulative sum (MCUSUM) control charts to monitor process. We also compared their performances, in terms of average run length criterion, and designated that the proposed control charts schemes could effectively act in detecting shifts in process parameters. Finally, the results are applied on a real case study in an agricultural field

The analysis of residuals variation and outliers to obtain robust response surface

In this paper, the main idea is to compute the robust regression model, derived by experimentation, in order to achieve a model with minimum effects of outliers and fixed variation among different experimental runs. Both outliers and nonequality of residual variation can affect the response surface parameter estimation. The common way to estimate the regression model coefficients is the ordinary least squares method. The weakness of this method is its sensitivity to outliers and specific residual behavior, so we pursue the modified robust method to solve this problem. Many papers have proposed different robust methods to decrease the effect of outliers, but trends in residual behaviors pose another important issue that should be taken into account. The trends in residuals can cause faulty estimations and thus faulty future decisions and outcomes, so in this paper, an iterative weighting method is used to modify both the outliers and the residuals that follow abnormal trends in variation, like descending or ascending trends, so they will have less effect on the coefficient estimation. Finally, a numerical example illustrates the proposed approach