A Copula Markov CUSUM Chart for Monitoring the Bivariate Auto‐correlated Binary Observations

Although in the statistical process control (SPC) literature, there are considerable number of researches related to the multivariates variables control charting (focusing on the variable quality characteristics), fewer investigations could be found regarding the multivariate attributes control charts (relying on the attribute quality characteristics). More specifically considering the multivariate attributes control charting, it would be more interesting to monitor the auto‐correlated data, since the real‐world processes usually include the data based on an auto‐correlation structure. Ignoring the auto‐correlation structure in developing a multivariate control chart increases the type I and type II errors simultaneously and consequently reduces the performance of the chart. The most important difficulty with developing multivariate attributes control charts is the absence of the joint distribution for the quality characteristics. This deficiency can be dispelled through the use of the copula approach for developing the joint distribution. In this paper, we use the Markov approach for modeling the auto‐correlated data. Then, the copula approach is used to make the joint distribution of two auto‐correlated binary data series. Finally, based on this joint distribution, we develop a cumulative sum (CUSUM) chart. Hence, the proposed chart is entitled the copula Markov CUSUM chart. The proposed control chart is compared with the most recent and effective existing one in the literature. Based on the average number of observations to signal (ANOS) measure, it is considered that the developed control chart performs better than the other one. In addition, a real case study related to two correlated diseases such as the Type 2 Diabetes Mellitus and the Obesity, in which each has an auto‐correlated structure, is investigated to verify the applicability of the control chart. Copyright © 2012 John Wiley & Sons, Ltd.     

A Statistical Control Chart for Monitoring High‐dimensional Poisson Data Streams

Multivariate count data are popular in the quality monitoring of manufacturing and service industries. However, seldom effort has been paid on high‐dimensional Poisson data and two‐sided mean shift situation. In this article, a hybrid control chart for independent multivariate Poisson data is proposed. The new chart was constructed based on the test of goodness of fit, and the monitoring procedure of the chart was shown. The performance of the proposed chart was evaluated using Monte Carlo simulation. Numerical experiments show that the new chart is very powerful and sensitive at detecting both positive and negative mean shifts. Meanwhile, it is more robust than other existing multiple Poisson charts for both independent and correlated variables. Besides, a new standardization method for Poisson data was developed in this article. A real example was also shown to illustrate the detailed steps of the new chart. Copyright © 2016 John Wiley & Sons, Ltd.     

Change‐point Detection in Phase I for Profiles with Binary Data and Random Predictors

In some applications, the quality of a process must be characterized by a profile, which describes the relationship between the response variable and explanatory variables. Moreover, for some processes, especially service processes, categorical response variables are common, making statistical process control techniques for profiles with categorical response data a must. We study Phase I analysis of profiles with binary data and random explanatory variables to identify the presence of change‐points in the reference profile dataset. The change‐point detection method based on logistic regression models is proposed. The method exploits directional shift information and integrates change‐point algorithm with the generalized likelihood ratio. 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. A real example is used to illustrate the implementation of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Monitoring a fraction with easy and reliable settings of the false alarm rate

Monitoring a fraction arises in many manufacturing applications and also in service applications. The traditional p‐chart is easy to use and design but is difficult to achieve the desired false alarm rate. We propose a two‐sided CUSUM Arcsine method that achieves both large and small desired false alarm rates for an in‐control probability anywhere between 0 and 1. The parameters of the new method are calculated easily, without tables, simulation, or Markov chain analysis used by many of the existing methods. The proposed method detects increases and decreases and works for constant and Poisson distributed sample sizes. The CUSUM Arcsine also has a superior sensitivity compared with other easily designed existing methods for monitoring Binomial distributed data. This paper includes an extensive literature review and a taxonomy of the existing monitoring methods for a fraction. Copyright © 2009 John Wiley & Sons, Ltd.     

A Spatiotemporal Method for the Monitoring of Image Data

Machine vision systems are increasingly being used in industrial applications because of their ability to quickly provide information on product geometry, surface defects, surface finish, and other product and process characteristics. Previous research for monitoring these visual characteristics using image data has focused on either detecting changes within an image or between images. Extending these methods to include both the spatial and the temporal aspects of image data would provide more detailed diagnostic information, which would be of great value to industrial practitioners. Therefore, in this article, we show how image data can be monitored using a spatiotemporal framework that is based on an extension of a generalized likelihood ratio control chart. The performance of the proposed method is evaluated through computer simulations and experimental studies. The results show that our proposed spatiotemporal method is capable of quickly detecting the emergence of a fault. The computer simulations also show that our proposed generalized likelihood ratio control charting method provides a good estimate of the change point and the size/location of the fault, which are important fault diagnostic metrics that are not typically provided in the image monitoring literature. Finally, we highlight some research opportunities and provide some advice to practitioners. Copyright © 2012 John Wiley & Sons, Ltd.     

A t‐chart for Monitoring Multi‐variety and Small Batch Production Run

Statistical process control is an important tool to monitor and control a process. It is used to ensure that the manufacturing process operates in the in‐control state. Multi‐variety and small batch production runs are common in manufacturing environments like flexible manufacturing systems and Just‐in‐Time systems, which are characterized by a wide variety of mixed products with small volume for each kind of production. It is difficult to apply traditional control charts efficiently and effectively in such environments. The method that control charts are plotted for each individual part is not proper, since the successive state of the manufacturing process cannot be reflected. In this paper, a proper t‐chart is proposed for implementation in multi‐variety and small batch production runs to monitor the process mean, and its statistical properties are evaluated. The run length distribution of the proposed t‐chart has been obtained by modelling the multi‐variety process. The ARL performance for various shifts, number of product types, and subgroup sizes has also been obtained. The results show that the t‐chart can be successfully implemented to monitor a multi‐variety production run. Finally, illustrative examples show that the proposed t‐chart is effective in multi‐variety and small batch manufacturing environment. Copyright © 2013 John Wiley & Sons, Ltd.     

A Comparison of Normal Approximation Rules for Attribute Control Charts

Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart (np‐chart or p‐chart) is one of the most popular methods to monitor the number of observed defects in products, such as semiconductor chips, automobile engines, and loan applications. The attribute control chart requires that the sample size n is sufficiently large and the defect rate p is not too small so that the normal approximation to the binomial works well. Some rules for the required values for n and p are available in the textbooks of quality control and mathematical statistics. However, these rules are considerably different, and hence, it is less clear which rule is most appropriate in practical applications. In this paper, we perform a comparison of five frequently used rules for n and p required for the normal approximation to the binomial. With this result, we also refine the existing rules to develop a new rule that has a reliable performance. Datasets are analyzed for illustration. Copyright © 2013 John Wiley & Sons, Ltd.     

Real-Time Monitoring of High-Dimensional Functional Data Streams via Spatio-Temporal Smooth Sparse Decomposition

High-dimensional data monitoring and diagnosis has recently attracted increasing attention among researchers as well as practitioners. However, existing process monitoring methods fail to fully use the information of high-dimensional data streams due to their complex characteristics including the large dimensionality, spatio-temporal correlation structure, and nonstationarity. In this article, we propose a novel process monitoring methodology for high-dimensional data streams including profiles and images that can effectively address foregoing challenges. We introduce spatio-temporal smooth sparse decomposition (ST-SSD), which serves as a dimension reduction and denoising technique by decomposing the original tensor into the functional mean, sparse anomalies, and random noises. ST-SSD is followed by a sequential likelihood ratio test on extracted anomalies for process monitoring. To enable real-time implementation of the proposed methodology, recursive estimation procedures for ST-SSD are developed. ST-SSD also provides useful diagnostics information about the location of change in the functional mean. The proposed methodology is validated through various simulations and real case studies. Supplementary materials for this article are available online.     

A Generalized Procedure for Monitoring Right‐censored Failure Time Data

Right‐censored failure time data is a common data type in manufacturing industry and healthcare applications. Some control charting procedures were previously proposed to monitor the right‐censored failure time data under some specific distributional assumptions for the observed failure times and censoring times. But these assumptions may not be always satisfied in the real‐world data. Therefore, a more generalized control chart technique, which can handle different types of distributions of the data, is highly needed. Considering the limitations of existing methodologies for detecting changes of hazard rate, this paper develops a generalized statistical procedure to monitor the failure time data in the presence of random right censoring when abundant historical failure times are available. The developed method makes use of the one‐sample nonparametric rank tests without any specific assumptions of the data distribution. The operating characteristic functions of the control chart are derived on the basis of the asymptotic properties of the rank statistics. Case studies are presented to show the effectiveness of the proposed control chart technique, and its performance is investigated and compared with some Shewhart‐type control charts based on the conditional expected value weight. Copyright © 2014 John Wiley & Sons, Ltd.     

Statistical Monitoring of a Sealing Process by Means of Multivariate Accelerometer Data

A multivariate control charting procedure is applied to on-line seal quality evaluation of a packaging process by means of an accelerometer. Based on physical insight it is elucidated in a first step which information in the raw accelerometer data are relevant with respect to the goal of detecting bad seals. Next, a principal component analysis (PCA) based processing of this multivariate information is performed and the related Hotelling's T² and Q test statistics are calculated for further data representation. In a last step proper control charts based on these statistics are used as a process monitoring tool for on-line distinction between good and bad seals. The obtained results show that a correct monitoring of accelerometer signals can be a useful tool for the on-line detection of 'bad seals' in a packaging process.     

Circle Chart for Monitoring of Periodic Measurements

Measurements with a periodicity are common in practice but there have been no specific monitoring control techniques for them. In this paper, we propose a type of control chart that plots measurements around a circle so that information from the same stage of different cycles can be readily compared. Some basic properties of such charts are investigated, and further developments are discussed. The basic circle chart can be applied under various kinds of control chart schemes, and there is potential for further development. Some application examples are also shown in this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

A Nonparametric Adaptive Sampling Strategy for Online Monitoring of Big Data Streams

With the rapid advancement of sensor technology, a huge amount of data is generated in various applications, which poses new and unique challenges for statistical process control (SPC). In this article, we propose a nonparametric adaptive sampling (NAS) strategy to online monitor nonnormal big data streams in the context of limited resources, where only a subset of observations are available at each acquisition time. In particular, this proposed method integrates a rank-based CUSUM scheme and an innovative idea that corrects the anti-rank statistics with partial observations, which can effectively detect a wide range of possible mean shifts when data streams are exchangeable and follow arbitrary distributions. Two theoretical properties on the sampling layout of the proposed NAS algorithm are investigated when the process is in control and out of control. Both simulations and case studies are conducted under different scenarios to illustrate and evaluate the performance of the proposed method. Supplementary materials for this article are available online.     

4G流媒体业务质量监测数据分析

4G是指第四代移动通信技术,是将无线通信和互联网等多媒体通信相结合的新一代移动通信系统.和第三代移动通信技术相比,4G提供了更快的通信速度、更好的业务质量(QoS)、更加丰富的移动通信增值服务、更强的技术融合和更加便捷的现实应用.4G的出现和媒体业务的多样化使得用户将更加注重对媒体业务的主观体验.本文根据用户对流媒体业务质量的需求分析,通过采集4G流媒体业务关键节点的数据,从理论数据上综合评价端到另一端的业务体验质量和网络性能.通过本文介绍的参数计算方法,客观地实现了用户对网络性能的评估.     

An Evaluation of Wheeler's Method for Monitoring the Rate of Rare Events

Its wide application in practice makes the monitoring of the rate of rare events a popular research topic. Recently a researcher proposed plotting the counts between events on an individuals X‐chart with an upper control limit to detect process improvement and plotting the reciprocals of the counts on an X‐chart to detect process deterioration. He also used the median as the center line and the median moving range to obtain control limits in both control charts to address the problem of the standard deviation estimate inflation caused by extreme values. In our paper, we investigated the statistical performance of the four proposed approaches using simulation. We find using the mean results in a high proportion of ineffective control limits, while using the median avoids the issue of ineffective control limits but produces an unacceptably high proportion of false alarms. Copyright © 2016 John Wiley & Sons, Ltd.     

A Hybrid Learning‐Based Model for Simultaneous Monitoring of Process Mean and Variance

Unnatural patterns exhibited on process mean and variance control charts can be associated separately with different assignable causes. Quick and accurate knowledge of the type of control chart patterns (CCPs), either because of process mean or variance, can greatly facilitate identification of assignable causes. Over the past few decades, however, process mean and variance CCPs are seldom studied simultaneously in the statistical process control literature. This study proposes a hybrid learning‐based model for simultaneous monitoring of process mean and variance CCPs. In this model, a self‐organization map neural network‐based quantization error control chart is responsible for detecting the out‐of‐control signals, a discrete particle swarm optimization‐based selective ensemble of back‐propagation networks is responsible for classifying the detected out‐of‐control signals into categories of mean and/or variance abnormality, and two discrete particle swarm optimization‐based selective ensembles of learning vector quantization networks are responsible for further identifying the detected mean and variance out‐of‐control signals as one of the specific CCP types, respectively. Extensive simulations indicate that the proposed hybrid learning‐based model outperforms other existing approaches in detecting mean and variance changes, while also capable of CCP recognition. In addition, a case study is conducted to demonstrate how the proposed hybrid learning‐based model can function as an effective tool for monitoring mean and variance simultaneously. Copyright © 2013 John Wiley & Sons, Ltd.     

Data transformation for geometrically distributed quality characteristics

Recently there has been an increasing interest in techniques of process monitoring involving geometrically distributed quality characteristics, as many types of attribute data are neither binomial nor Poisson distributed. The geometric distribution is particularly useful for monitoring high‐quality processes based on cumulative counts of conforming items. However, a geometrically distributed quantity can never be adequately approximated by a normal distribution that is typically used for setting 3‐sigma control limits. In this paper, some transformation techniques that are appropriate for geometrically distributed quantities are studied. Since the normal distribution assumption is used in run‐rules and advanced process‐monitoring techniques such as the cumulative sum or exponentially weighted moving average chart, data transformation is needed. In particular, a double square root transformation which can be performed using simple spreadsheet software can be applied to transform geometrically distributed quantities with satisfactory results. Simulated and actual data are used to illustrate the advantages of this procedure. Copyright © 2000 John Wiley & Sons, Ltd.     

A Semiparametric Mixed Model Approach to Phase I Profile Monitoring

Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric (P) modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. More recently, in the absence of an obvious P model, nonparametric (NP) methods have been employed in the profile monitoring context. For situations where a P model is adequate over part of the data but inadequate of other parts, we propose a semiparametric procedure that combines both P and NP profile fits. We refer to our semiparametric procedure as mixed model robust profile monitoring (MMRPM). These three methods (P, NP and MMRPM) can account for the autocorrelation within profiles and treat the collection of profiles as a random sample from a common population. For each approach, we propose a version of Hotelling's T² statistic for use in Phase I analysis to determine unusual profiles based on the estimated random effects and obtain the corresponding control limits. Simulation results show that our MMRPM method performs well in making decisions regarding outlying profiles when compared to methods based on a misspecified P model or based on NP regression. In addition, however, the MMRPM method is robust to model misspecification because it also performs well when compared to a correctly specified P model. The proposed chart is able to detect changes in Phase I data and has easily calculated control limits. We apply all three methods to the automobile engine data of Amiri et al.⁵ and find that the NP and the MMRPM methods indicate signals that did not occur in a P approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of Phase I Estimation on Phase II Control Chart Performance with Profile Data

This paper illustrates how phase I estimators in statistical process control (SPC) can affect the performance of phase II control charts. The deleterious impact of poor phase I estimators on the performance of phase II control charts is illustrated in the context of profile monitoring. Two types of phase I estimators are discussed. One approach uses functional cluster analysis to initially distinguish between estimated profiles from an in‐control process and those from an out‐of‐control process. The second approach does not use clustering to make the distinction. The phase II control charts are established based on the two resulting types of estimates and compared across varying sizes of sustained shifts in phase II. A simulated example and a Monte Carlo study show that the performance of the phase II control charts can be severely distorted when constructed with poor phase I estimators. The use of clustering leads to much better phase II performance. We also illustrate that the performance of phase II control charts based on the poor phase I estimators not only have more false alarms than expected but can also take much longer than expected to detect potential changes to the process. Copyright © 2014 John Wiley & Sons, Ltd.     

Design and Analysis of a Water Quality Monitoring Data Service Platform

Water is one of the basic resources for human survival. Water pollution monitoring and protection have been becoming a major problem for many countries all over the world. Most traditional water quality monitoring systems, however, generally focus only on water quality data collection, ignoring data analysis and data mining. In addition, some dirty data and data loss may occur due to power failures or transmission failures, further affecting data analysis and its application. In order to meet these needs, by using Internet of things, cloud computing, and big data technologies, we designed and implemented a water quality monitoring data intelligent service platform in C# and PHP language. The platform includes monitoring point addition, monitoring point map labeling, monitoring data uploading, monitoring data processing, early warning of exceeding the standard of monitoring indicators, and other functions modules. Using this platform, we can realize the automatic collection of water quality monitoring data, data cleaning, data analysis, intelligent early warning and early warning information push, and other functions. For better security and convenience, we deployed the system in the Tencent Cloud and tested it. The testing results showed that the data analysis platform could run well and will provide decision support for water resource protection.