This paper presents a study of a new procedure, which is based on integrating a powerful nonparametric test for the two-sample problem and EWMA control scheme to online sequential monitoring. The proposed procedure, based on individual observation per sample, can be used to monitor the location and the scale parameters of a univariate continuous distribution, simultaneously. An iterative computation procedure is developed for computing the monitoring statistics. A search algorithm for the control limit based on Monte-Carlo simulation and bisection method is derived and a table is provided. The sensitivity analysis on the procedure is studied in detail. Monte-Carlo simulation results show that the proposed procedure is quite robust to nonnormally distributed data, and moreover, it is efficient in detecting various process shifts. A real data example from a chemical reaction process is shown to illustrate the application of our proposed procedure.

This paper develops a new multivariate nonparametric statistical process control (SPC) control chart for monitoring shape parameters, which is based on integrating a powerful multivariate spatial-sign test and exponentially weighted moving average (EWMA) control scheme to on-line sequential monitoring. It has a strictly distribution-free property over a broad class of population models, which implies the in-control run-length distribution can attain or is always very close to the nominal one when using the same control limit designed for the multivariate normal distribution. This proposed control chart possesses some other positive features: its computation speed is fast with a similar computation effort to the parametric multivariate EWMA (MEWMA) counterpart; it is easy to implement because only the multivariate median and the associated transformation matrix need to be estimated from the historical data before monitoring; it is efficient in detecting small or moderate shifts, when the process distribution is heavy tailed or skewed; it is also able to handle the case when the sample size is one and is effective in downward shifts. Simulation comparisons and a real-data example from a white-wine production process show that it performs quite well in applications.

The presence of outliers would inevitably lead to distorted analysis and inappropriate prediction, especially for multiple outliers in high-dimensional regression, where the high dimensionality of the data might amplify the chance of an observation or multiple observations being outlying. Noting that the detection of outliers is not only necessary but also important in high-dimensional regression analysis, we, in this paper, propose a feasible outlier detection approach in sparse high-dimensional linear regression model. Firstly, we search a clean subset by use of the sure independence screening method and the least trimmed square regression estimates. Then, we define a high-dimensional outlier detection measure and propose a multiple outliers detection approach through multiple testing procedures. In addition, to enhance efficiency, we refine the outlier detection rule after obtaining a relatively reliable non-outlier subset based on the initial detection approach. By comparison studies based on Monte Carlo simulation, it is shown that the proposed method performs well for detecting multiple outliers in sparse high-dimensional linear regression model. We further illustrate the application of the proposed method by empirical analysis of a real-life protein and gene expression data.

An outlier is defined as an observation that is significantly different from the others in its dataset. In high-dimensional regression analysis, datasets often contain a portion of outliers. It is important to identify and eliminate the outliers for fitting a model to a dataset. In this paper, a novel outlier detection method is proposed for high-dimensional regression problems. The leave-one-out idea is utilized to construct a novel outlier detection measure based on distance correlation, and then an outlier detection procedure is proposed. The proposed method enjoys several advantages. First, the outlier detection measure can be simply calculated, and the detection procedure works efficiently even for high-dimensional regression data. Moreover, it can deal with a general regression, which does not require specification of a linear regression model. Finally, simulation studies show that the proposed method behaves well for detecting outliers in high-dimensional regression model and performs better than some other competing methods.

In many practical situations, multiple variables often need to be monitored simultaneously to ensure the process is in control. In this article, we develop a feasible multivariate monitoring procedure based on the general multivariate exponentially weighted moving average (MEWMA) to monitor the multivariate count data. The multivariate count data is modeled using Poisson log-normal distribution to characterize their interrelations. We systematically investigate the effects of different charting parameters and propose an optimization procedure to identify the optimal charting parameters. In particular, we provide a design table to the quality engineers as a simple tool to design the optimal MEWMA chart. To further improve the efficiency, we integrate the variable sampling intervals (VSI) in the monitoring scheme. We use simulation studies and an example to elicit the application of the proposed scheme. The results are encouraging and demonstrate effectiveness of the proposed methods well.