Kamran Paynabar

Characterization of non-linear profiles variations using mixed-effect models and wavelets

There is an increasing research interest in the modeling and analysis of complex non-linear profiles using the wavelet transform. However, most existing modeling and analysis methods assume that the total inherent profile variations are mainly due to the noise within each profile. In many practical situations, however, the profile-to-profile variation is often too large to be neglected. In this article, a new method is proposed to model non-linear profile data variations using wavelets. For this purpose, a wavelet-based mixed-effect model is developed to consider both within- and between-profile variations. The utilization of wavelets not only simplifies the computational complexity of the mixed-effect model estimation but also facilitates the identification of the sources of the between-profile variations. In addition, a change-point model involving the likelihood ratio test is applied to ensure that the collected profiles used in the model estimation follow an identical distribution. Finally, the performance of the proposed model is evaluated using both Monte Carlo simulations and a case study.

Monitoring and diagnosis of multichannel nonlinear profile variations using uncorrelated multilinear principal component analysis

In modern manufacturing systems, online sensing is being increasingly used for process monitoring and fault diagnosis. In many practical situations, the output of the sensing system is represented by time-ordered data known as profiles or waveform signals. Most of the work reported in the literature has dealt with cases in which the production process is characterized by single profiles. In some industrial practices, however, the online sensing system is designed so that it records more than one profile at each operation cycle. For example, in multi-operation forging processes with transfer or progressive dies, four sensors are used to measure the tonnage force exerted on dies. To effectively analyze multichannel profiles, it is crucial to develop a method that considers the interrelationships between different profile channels. A method for analyzing multichannel profiles based on uncorrelated multilinear principal component analysis is proposed in this article for the purpose of characterizing process variations, fault detection, and fault diagnosis. The effectiveness of the proposed method is demonstrated by using simulations and a case study on a multi-operation forging process.

Identifying the period of a step change in high-yield processes

Quality control charts have proven to be very effective in detecting out-of-control states. When a signal is detected a search begins to identify and eliminate the source(s) of the signal. A critical issue that keeps the mind of the process engineer busy at this point is determining the time when the process first changed. Knowing when the process first changed can assist process engineers to focus efforts effectively on eliminating the source(s) of the signal. The time when a change in the process takes place is referred to as the change point. This paper provides an estimator for a period of time in which a step change in the process non-conformity proportion in high-yield processes occurs. In such processes, the number of items until the occurrence of the first non-conforming item can be modeled by a geometric distribution. The performance of the proposed model is investigated through several numerical examples. The results indicate that the proposed estimator provides a reasonable estimate for the period when the step change occurred at the process non-conformity level. Copyright

An overview and perspective on social network monitoring

ABSTRACT In this expository article we give an overview of some statistical methods for the monitoring of social networks. We discuss the advantages and limitations of various methods as well as some relevant issues. One of our primary contributions is to give the relationships between network monitoring methods and monitoring methods in engineering statistics and public health surveillance. We encourage researchers in the industrial process monitoring area to work on developing and comparing the performance of social network monitoring methods. We also discuss some of the issues in social network monitoring and give a number of research ideas.

Image-Based Process Monitoring Using Low-Rank Tensor Decomposition

Image and video sensors are increasingly being deployed in complex systems due to the rich process information that these sensors can capture. As a result, image data play an important role in process monitoring and control in different application domains such as manufacturing processes, food industries, medical decision-making, and structural health monitoring. Existing process monitoring techniques fail to fully utilize the information of color images due to their complex data characteristics including the high-dimensionality and correlation structure (i.e., temporal, spatial and spectral correlation). This paper proposes a new image-based process monitoring approach that is capable of handling both grayscale and color images. The proposed approach models the high-dimensional structure of the image data with tensors and employs low-rank tensor decomposition techniques to extract important monitoring features monitored using multivariate control charts. In addition, this paper shows the analytical relationships between different low-rank tensor decomposition methods. The performance of the proposed method in quick detection of process changes is evaluated and compared with existing methods through extensive simulations and a case study in a steel tube manufacturing process.

A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis

Process monitoring and fault diagnosis using profile data remains an important and challenging problem in statistical process control (SPC). Although the analysis of profile data has been extensively studied in the SPC literature, the challenges associated with monitoring and diagnosis of multichannel (multiple) nonlinear profiles are yet to be addressed. Motivated by an application in multioperation forging processes, we propose a new modeling, monitoring, and diagnosis framework for phase-I analysis of multichannel profiles. The proposed framework is developed under the assumption that different profile channels have similar structure so that we can gain strength by borrowing information from all channels. The multidimensional functional principal component analysis is incorporated into change-point models to construct monitoring statistics. Simulation results show that the proposed approach has good performance in identifying change-points in various situations compared with some existing methods. The codes for implementing the proposed procedure are available in the supplementary material.

Monitoring Temporal Homogeneity in Attributed Network Streams

Network modeling and analysis has become a fundamental tool for studying various complex systems. This paper proposes an extension of statistical monitoring to network streams, which is crucial for effective decision-making in various applications. To this end, a model for the probability of edge existence as a function of vertex attributes is constructed and a likelihood method is developed to monitor the underlying network model. The method is flexible to detect any form of anomaly that arises from different network edge-formation mechanisms. Experiments on simulated and real network streams depict the properties and benefits of the method compared with existing methods in the literature.

On the conditional decision procedure for high yield processes

Cumulative Count of Conforming (CCC) items chart has shown to be an effective tool for monitoring high yield processes. However, this chart uses a single count value to determine whether a change in a process has occurred. This makes the chart relatively insensitive to process shifts. To improve the performance of the chart, values of the previous runs or observations were incorporated into the decision rule using conditional probability. This paper investigates the performance of the modified decision rule and shows that the results obtained for the average run length are only true for the case of independent observations. An appropriate relationship for the average run length is developed and the results are compared to the modified decision rule mathematically and numerically. The results indicate that the average run length values obtained from the modified decision rule always underestimates the true values.

Multiscale monitoring of autocorrelated processes using wavelets analysis

This article proposes a new method to develop multiscale monitoring control charts for an autocorrelated process that has an underlying unknown ARMA(2, 1) model structure. The Haar wavelet transform is used to obtain effective monitoring statistics by considering the process dynamic characteristics in both the time and frequency domains. Three control charts are developed on three selected levels of Haar wavelet coefficients in order to simultaneously detect the changes in the process mean, process variance, and measurement error variance, respectively. A systematic method for automatically determining the optimal monitoring level of Haar wavelet decomposition is proposed that does not require the estimation of an ARMA model. It is shown that the proposed wavelet-based Cumulative SUM (CUSUM) chart on Haar wavelet detail coefficients is only sensitive to the variance changes and robust to process mean shifts. This property provides the separate monitoring capability between a variance change and a mean shift, which shows its advantage by comparison with the traditional CUSUM monitoring chart. For the purpose of mean shift detection, it is also shown that using the proposed wavelet-based Exponentially Weighted Moving Average (EWMA) chart to monitor Haar wavelet scale coefficients will more successfully detect small mean shifts than direct-EWMA charts.

Repeatability of Cerebral Perfusion Using Dynamic Susceptibility Contrast MRI in Glioblastoma Patients

OBJECTIVES This study evaluates the repeatability of brain perfusion using dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) with a variety of post-processing methods. METHODS Thirty-two patients with newly diagnosed glioblastoma were recruited. On a 3-T MRI using a dual-echo, gradient-echo spin-echo DSC-MRI protocol, the patients were scanned twice 1 to 5 days apart. Perfusion maps including cerebral blood volume (CBV) and cerebral blood flow (CBF) were generated using two contrast agent leakage correction methods, along with testing normalization to reference tissue, and application of arterial input function (AIF). Repeatability of CBV and CBF within tumor regions and healthy tissues, identified by structural images, was assessed with intra-class correlation coefficients (ICCs) and repeatability coefficients (RCs). Coefficients of variation (CVs) were reported for selected methods. RESULTS CBV and CBF were highly repeatable within tumor with ICC values up to 0.97. However, both CBV and CBF showed lower ICCs for healthy cortical tissues (up to 0.83), healthy gray matter (up to 0.95), and healthy white matter (WM; up to 0.93). The values of CV ranged from 6% to 10% in tumor and 3% to 11% in healthy tissues. The values of RC relative to the mean value of measurement within healthy WM ranged from 22% to 42% in tumor and 7% to 43% in healthy tissues. These percentages show how much variation in perfusion parameter, relative to that in healthy WM, we expect to observe to consider it statistically significant. We also found that normalization improved repeatability, but AIF deconvolution did not. CONCLUSIONS DSC-MRI is highly repeatable in high-grade glioma patients.