Dongdong Xiang

Univariate Dynamic Screening System: An Approach For Identifying Individuals With Irregular Longitudinal Behavior

In our daily lives, we often need to identify individuals whose longitudinal behavior is different from the behavior of those well-functioning individuals, so that some unpleasant consequences can be avoided. In many such applications, observations of a given individual are obtained sequentially, and it is desirable to have a screening system to give a signal of irregular behavior as soon as possible after that individual’s longitudinal behavior starts to deviate from the regular behavior, so that some adjustments or interventions can be made in a timely manner. This article proposes a dynamic screening system for that purpose in cases when the longitudinal behavior is univariate, using statistical process control and longitudinal data analysis techniques. Several different cases, including those with regularly spaced observation times, irregularly spaced observation times, and correlated observations, are discussed. Our proposed method is demonstrated using a real-data example about the SHARe Framingham Heart Study of the National Heart, Lung and Blood Institute. This article has supplementary materials online.

Mixed Variables-Attributes Test Plans for Single and Double Acceptance Sampling under Exponential Distribution

The mixed variables-attributes test plans for single acceptance sampling are proposed to protect “good lots” from attributes aspect and to optimize sample sizes from variables aspect. For the single and double mixed plans, exact formulas of the operating characteristic and average sample number are developed for the exponential distribution. Numerical illustrations show that the mixed sampling plans have some advantages over the variables plans or attributes plans alone.

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.

A robust self-starting spatial rank multivariate EWMA chart based on forward variable selection

A robust self-starting control chart based on forward variable selection is proposed.The proposed chart does not need prior knowledge of the IC distribution and is robust to non-normally distributed data.The need to gather extensive data before monitoring is overcome.The sensitivity to small and moderate sparse shifts in mean vectors is remarkable. Shifts in one or a few components of process mean vectors, called sparse shifts, are monitored in many applications. To monitor sparse shifts, several control charts have recently been proposed based on the variable selection technique. These charts assume either that the in-control (IC) distribution is completely known or that a sufficiently large reference dataset is available. However, this assumption is not always valid in practice. This paper develops a self-starting control chart that integrates a multivariate spatial rank test with the EWMA charting scheme based on forward variable selection for monitoring sparse mean shifts. Both the theoretical and numerical results show that the proposed chart is robust to non-normally distributed data, fast to compute, easy to construct, and can efficiently detect sparse shifts, especially when the process distribution is heavy-tailed or skewed. The proposed control chart does not need prior knowledge of the IC distribution and can start monitoring even before considerable reference data have been collected. A real-data example from a white wine production process illustrates the effectiveness of the proposed control chart.

A Double Sequential Weighted Probability Ratio Test for One-Sided Composite Hypotheses

For sequential test plans, we propose the weighted expected sample size (WESS) to evaluate the overall performance on the parameter interval of interest. Based on minimizing the WESS to control the expected sample sizes, we develop the method of double sequential weighted probability ratio test (2-SWPRT) for one-sided composite hypotheses. It is proved that the 2-SWPRT has a finite stopping time and is the asymptotically optimal test. Simulation studies show that the 2-SWPRT not only has the smallest WESS compared with the SPRT and 2-SPRT, but also is superior to the 2-SPRT and comparable with the SPRT under the null and alternative hypotheses. Moreover, the relative mean index (RMI) also shows the 2-SWPRT is an efficient method to improve the overall performance.

A Robust Multivariate EWMA Control Chart for Detecting Sparse Mean Shifts

In multivariate statistical process control (MSPC) applications, process mean shifts sometimes occur in only a few components. To solve this MSPC problem, many control charts were proposed in the literature. Most of these charts assumed that the multivariate quality characteristics are normally distributed. Among them, the control chart proposed by Zou and Qiu (2009), incorporating the least absolute shrinkage and selection operator (LASSO) method into the EWMA scheme, has the best overall performance. In this paper, we extend the classical multivariate LASSO control chart to a robust version that has an affine-invariance property and is distribution free under the family of elliptical direction distributions, indicating that the in-control run-length distribution is the same for any continuous distribution in this family and the control limit can be acquired from the multivariate standard normal distribution. Our simulation results show that the proposed method is very efficient in detecting various sparse shifts under heavy-tailed and skewed multivariate distributions. In addition, it is easy to implement with an iterative algorithm and the least angle regression (LARS) algorithm. White-wine data illustrates that the proposed control chart performs quite well in applications.

CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid

It is often encountered in the literature that the log-likelihood ratios (LLR) of some distributions (e.g. the student t distribution) are not monotonic. Existing charts for monitoring such processes may suffer from the fact that the average run length (ARL) curve is a discontinuous function of control limit. It implies that some pre-specified in-control (IC) ARLs of these charts may not be reached. To guarantee the false alarm rate of a control chart lower than the nominal level, a larger IC ARL is usually suggested in the literature. However, the large IC ARL may weaken the performance of a control chart when the process is out-of-control (OC), compared with a just right IC ARL. To overcome it, we adjust the LLR to be a monotonic one in this paper. Based on it, a multiple CUSUM chart is developed to detect range shifts in IC distribution. Theoretical result in this paper ensures the continuity of its ARL curve. Numerical results show our proposed chart performs well under the range shifts, especially under the large shifts. In the end, a real data example is utilized to illustrate our proposed chart.

Monitoring individuals with irregular semiparametric longitudinal behaviour

In our daily life, identifying individuals whose longitudinal behaviour differs from the behaviour of those well-functioning individuals is often necessary to avoid some unpleasant consequences. For such purposes, this paper proposes a new charting scheme called semiparametric screening system in cases when the longitudinal behaviour is semiparametric, using SPC and longitudinal data analysis techniques. Various cases, including those with equally spaced data points, unequally spaced data points, temporal correlated data, non-normal data, are discussed by simulations. Also our proposed method is demonstrated using two real data examples about the SHARe Framingham Heart Study of the National Heart, Lung and Blood Institute, and the moisture content of cut tobacco at the outlet collected in Shanghai tobacco group co., LTD of China, respectively. All the numerical results show that the proposed method works well in practice.

A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions

Abstract Most existing control charts monitoring the covariance matrix of multiple variables were restricted to multivariate normal distribution. When the process distribution is non-normal, the performance of these control charts could potentially be (highly) affected, especially for heavy-tail distributions. To construct a robust multivariate control chart for monitoring the covariance matrix, we applied spatial sign covariance matrix and maximum norm to the exponentially weighted moving average (EWMA) scheme and proposed a Phase II control chart. The novel chart is distribution-free under the family of elliptical directions distributions. Comparison studies demonstrate that the novel method is very powerful in detecting various shifts, especially for heavy-tailed distributions. The implementation of the proposed control chart is demonstrated by a white wine data.

A distribution-free multivariate CUSUM control chart using dynamic control limits

ABSTRACT In modern quality control, it is becoming common to simultaneously monitor several quality characteristics of a process with rapid evolving data-acquisition technology. When the multivariate process distribution is unknown and only a set of in-control data is available, the bootstrap technique can be used to adjust the constant limit of the multivariate cumulative sum (MCUSUM) control chart. To further improve the performance of the control chart, we extend the constant control limit to a sequence of dynamic control limits which are determined by the conditional distribution of the charting statistics given the sprint length. Simulation results show that the novel control chart with dynamic control limits offers a better ARL performance, compared with the traditional MCUSUM control chart. Despite it, the proposed control chart is considerably computer-intensive. This leads to the development of a more flexible control chart which uses a continuous function of the sprint length as the control limit sequences. More importantly, the control chart is easy to implement and can reduce the computational time significantly. A white wine data illustrates that the novel control chart performs quite well in applications.