A Least Angle Regression Control Chart for Multidimensional Data

Knockoff procedure for false discovery rate control in high-dimensional data streams

Motivated by applications to root-cause identification of faults in high-dimensional data streams that may have very limited samples after faults are detected, we consider multiple testing in models for multivariate statistical process control (SPC). With quick fault detection, only small portion of data streams being out-of-control (OC) can be assumed. It is a long standing problem to identify those OC data streams while controlling the number of false discoveries. It is challenging due to the limited number of OC samples after the termination of the process when faults are detected. Although several false discovery rate (FDR) controlling methods have been proposed, people may prefer other methods for quick detection. With a recently developed method called Knockoff filtering, we propose a knockoff procedure that can combine with other fault detection methods in the sense that the knockoff procedure does not change the stopping time, but may identify another set of faults to control FDR. A theorem for the FDR control of the proposed procedure is provided. Simulation studies show that the proposed procedure can control FDR while maintaining high power. We also illustrate the performance in an application to semiconductor manufacturing processes that motivated this development.

Process monitoring using inflated beta regression control chart

This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher’s information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.

Critical comparison of methods for fault diagnosis in metabolomics data

Platforms like metabolomics provide an unprecedented view on the chemical versatility in biomedical samples. Many diseases reflect themselves as perturbations in specific metabolite combinations. Multivariate analyses are essential to detect such combinations and associate them to specific diseases. For this, usually targeted discriminations of samples associated to a specific disease from non-diseased control samples are used. Such targeted data interpretation may not respect the heterogeneity of metabolic responses, both between diseases and within diseases. Here we show that multivariate methods that find any set of perturbed metabolites in a single patient, may be employed in combination with data collected with a single metabolomics technology to simultaneously investigate a large array of diseases. Several such untargeted data analysis approaches have been already proposed in other fields to find both expected and unexpected perturbations, e.g. in Statistical Process Control. We have critically compared several of these approaches for their sensitivity and their correct identification of the specifically perturbed metabolites. Also a new approach is introduced for this purpose. The newly introduced Sparse Mean approach, which we find here as most sensitive and best able to identify the specifically perturbed metabolites, turns metabolomics into an untargeted diagnostic platform. Aside from metabolomics, the proposed approach may greatly benefit fault diagnosis with untargeted analyses in many other fields, such as Industrial Process Control, food Adulteration Detection, and Intrusion Detection.

Surveillance of cardiovascular diseases using a multivariate dynamic screening system

In the SHARe Framingham Heart Study of the National Heart, Lung and Blood Institute, one major task is to monitor several health variables (e.g., blood pressure and cholesterol level) so that their irregular longitudinal pattern can be detected as soon as possible and some medical treatments applied in a timely manner to avoid some deadly cardiovascular diseases (e.g., stroke). To handle this kind of applications effectively, we propose a new statistical methodology called multivariate dynamic screening system (MDySS) in this paper. The MDySS method combines the major strengths of the multivariate longitudinal data analysis and the multivariate statistical process control, and it makes decisions about the longitudinal pattern of a subject by comparing it with other subjects cross sectionally and by sequentially monitoring it as well. Numerical studies show that MDySS works well in practice.