چكيده به لاتين
Abstract:
In some statistical process control applications, quality of a process or product is characterized by a relationship between a response variable and one or more explanatory variables which is referred to as profile by researchers. In certain cases, quality of a process or a product can be effectively characterized by two or more simultaneous profiles in which response variables are correlated. In this situations use of methods which consider the multivariate structure between response variables is inevitable. In this dissertation, structure of multivariate multiple linear regression is used to model these kind of processes. In the field of multivariate multiple linear profiles, it is assumed that observations are independent from each other, while often due to the proximity of the samples to each other in terms of time, this assumption is violated, and observations are correlated with each other. In this research, it is assumed that the quality of process is modeled using a multivariate multiple linear profiles when independence assumption of observations within profile is violated via the first order class of autoregressive moving average (ARMA(1,1)) models. Generally control charts are used to monitoring profile over a time. The time that a control chart gives an out of control signal is to different with real time that process changed. This actual time of the change in a process is called the change point. In this research after removing autocorrelation, the step change point and drift change point in the regression parameters is estimated by using maximum likelihood method after getting a signal from the control chart in Phase II. Then, the accuracy and precision performance of the proposed estimators is evaluated and compared through a Monte Carlo simulation studies under different shift types.
Keywords: Change point, Autocorrelated multivariate multiple linear profiles, control chart, Maximum likelihood estimator
