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AbstractAs the complexity of production processes increases, the diversity of data types drives the development of network monitoring technology. This paper mainly focuses on an online algorithm to detect serially correlated directed networks robustly and sensitively. First, we consider a transition probability matrix to resolve the double correlation of primary data. Further, since the sum of each row of the transition probability matrix is one, it standardizes the data, facilitating subsequent modeling. Then we extend the spring length based method to the multivariate case and propose an adaptive cumulative sum (CUSUM) control chart on the strength of a weighted statistic to monitor directed networks. This novel approach assumes only that the process observation is associated with nearby points without any parametric time series model, which is in line with reality. Simulation results and a real example from metro transportation demonstrate the superiority of our design.

AbstractMost modern processes involve multiple quality characteristics that are all measured on attribute levels, and their overall quality is determined by these characteristics simultaneously. The characteristic factors usually correlate with each other, making multivariate categorical control techniques a must. We study Phase I analysis of multivariate categorical processes (MCPs) to identify the presence of change‐points in the reference dataset. A directional change‐point detection method based on log‐linear models is proposed. The method exploits directional shift information and integrates MCPs into the unified framework of multivariate binomial and multivariate multinomial distributions. A diagnostic scheme for identifying the change‐point location and the shift direction is also suggested. Numerical simulations are conducted to demonstrate the detection effectiveness and the diagnostic accuracy.© 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

AbstractNonparametric control charts are useful in statistical process control when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate self‐starting methodology for monitoring location parameters. It is based on adapting the multivariate spatial rank to on‐line sequential monitoring. The weighted version of the rank‐based test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control scheme. It is robust to non‐normally distributed data, easy to construct, fast to compute and also very efficient in detecting multivariate process shifts, especially small or moderate shifts which occur when the process distribution is heavy‐tailed or skewed. As it avoids the need for a lengthy data‐gathering step before charting and it does not require knowledge of the underlying distribution, the proposed control chart is particularly useful in start‐up or short‐run situations. A real‐data example from white wine production processes shows that it performs quite well. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 91–110, 2012

AbstractIn various modern statistical process control applications that involve high‐dimensional data streams (HDDS), accurate fault diagnosis of out‐of‐control (OC) streams is becoming crucial. The existing diagnostic approaches either focus on moderate‐dimensional processes or are unable to determine the shift direction accurately, especially when the signal‐to‐noise ratio is low. In this paper, we conduct a bold trial and consider the fault classification problem of the mean vector of HDDS where determining the shift direction of the OC streams is important to perform customized repairs. To this end, under the basic assumptions that the in‐control data streams are normal with mean 0 and variance 1, and that the high‐dimensional observations after the alarm are solely OC, the problem is formulated into a three‐classification multiple testing framework, and an efficient data‐driven diagnostic procedure is developed to minimize the expected number of false positives and to control the missed discovery rate at given level. The procedure is statistically optimal and computationally efficient, and improves the diagnostic effectiveness by considering directional information, which provides insights to guide further decisions. Both theoretical and numerical results reveal the superiority of the new method.