Change point detection in univariate and multivariate processes

In this proposal, we present several methodologies for change point detection in univariate and multivariate processes, identifying fault variables in multivariate processes, and detecting changes in multistage processes. We first propose an adaptive runs rule, which is motivated by the concept of supplementary runs rule, in order to make univariate control charts more sensitive to small mean shifts. The adaptive runs rule assigns scores to consecutive runs based on the estimated shift size of the mean. We supplement the Adaptive CUSUM (ACUSUM) chart with the adaptive runs rule to enhance its sensitivity in detecting small mean shifts. We then present two new multivariate SPC procedures, MASC and AMASC, for detecting general mean shift vectors based on the approximate sequential test, which uses an approximate likelihood ratio of a central and a noncentral distribution. Similar to the univariate CUSUM chart, a multivariate CUSUM chart can be designed to detect a particular size of the mean shift optimally based on the scheme of a sequential likelihood ratio test for noncentrality. However, in multivariate case, the probability ratio of a sequential test is intractable mathematically and the test statistic based on the ratio does not have a closed form expression which makes it impractical for real application. We drive an approximate log-likelihood ratio and propose a multivariate SPC chart based on the sequential test. We propose an adaptive step-down procedure using conditional statistics for the identification of fault variables. In a process with massive process variables (high-dimensional process), identifying which variable or a subset of variables causes an out-of-control signal is a challenging issue for quality engineers. The proposed step-down procedure selects a variable having no significant evidence of a change at each step based on the variables that are selected in previous steps. When the number of fault variables is small, the selected variables are useful to construct powerful conditional test statistics for identifying the shifted components of the mean vector. The proposed procedure yields a reasonable computational complexity in a high-dimensional process, since it is based on polynomial time algorithm. Finally, we model an autocorrelated multistage process as VAR(1) model and derive the propagation models of mean shifts to subsequent stages under the state space model. Further, we propose a new conditional multivariate EWMA (CMEWMA) chart to detect the shift of mean in a multistage process by incorporating unchanged stage information. The simulation results show that the proposed MEWMA chart is efficient in detecting a wide range of small mean shifts compared with the observation-based and residual-based MEWMA charts.Ph.D.Includes bibliographical referencesby Jinho Ki