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Surveillance of high-yield processes using deep learning models
Quality and Reliability Engineering International
Abstract
Quality testing and monitoring advancements have allowed modern production processes to achieve extremely low failure rates, especially in the era of Industry 4.0. Such processes are known as high-yield processes, and their data set consists of an excess number of zeros. Count models such as Poisson, Negative Binomial (NB), and Conway-Maxwell-Poisson (COM-Poisson) are usually considered good candidates to model such data, but the excess zeros are larger than the number of zeros, which these models fit inherently. Hence, the zero-inflated version of these count models provides better fitness of high-quality data. Usually , linearly/non-linearly related variables are also associated with failure rate data; hence, regression models based on zero-inflated count models are used for model fitting. This study is designed to propose deep learning (DL) based control charts when the failure rate variables follow the zero-inflated COM-Poisson (ZICOM-Poisson) distribution because DL models can detect complicated non-linear patterns and relationships in data. Further, the proposed methods are compared with existing control charts based on neural networks, principal component analysis designed based on Poisson, NB, and zero-inflated Poisson (ZIP) and non-linear principal component analysis designed based on Poisson, NB, and ZIP. Using run length properties, the simulation study evaluates monitoring approaches, and a flight delay application illustrates the implementation of the research. The findings revealed that the proposed methods have outperformed all existing control charts.
... Control charts effectively ensure that services and production processes run steadily and satisfactorily (Hyder et al. 2024;Ibrahim, Zhang, and Mahmood 2024). Numerous control charts for use in monitoring electric energy output have been suggested in the literature. ...
Electric energy production frequently uses combined cycle power plants (CCPPs) to handle peak loads. CCPPs must be continuously monitored for power performance to enhance the electrical output power. The electrical output datasets often show asymmetric behavior; therefore, the Birnbaum-Saunders (BS) distribution is one of the potential models for fitting such data-sets. In this study, novel exponentially weighted moving average (EWMA) control charts based on the Reparametrised Birnbaum-Saunders (RBS) regression model are developed. We perform a simulation study to evaluate the effectiveness of derived approaches in terms of run length characteristics. Moreover, a case study on the combined cycle power plant's (CCPP) electrical energy output is provided to demonstrate further the suitability of the recommended approach for early fault detection in electric power systems.
... A few of them are listed as follows: Kontokosta and Tull [31] implemented linear regression (OLS), random forest (RF), and support vector regression (SVR) models to fit New York City's energy data. Lim and Zhai [32] utilized OLS, SVR, artificial neural network (ANN) [33], multivariate adaptive regression spline (MARS), and Gaussian process emulator (GPE) models to predict the EUI of the simulated data generated through EnergyPlus. Deng et al. [34] adopted OLS, least absolute shrinkage and selection operator (LASSO) regression, SVR, ANN, RF, and extreme gradient boosted decision tree (XGBoost) models to forecast the energy efficiency reported in a survey (CBECS 2012) conducted for commercial buildings of the United States. ...
In the era of digitalization, the large availability of data and innovations in machine learning algorithms provide new potential to improve the prediction of energy efficiency in buildings. The building sector research in the Kingdom of Saudi Arabia (KSA) lacks actual/measured data-based studies as the existing studies are predominantly modeling-based. The results of simulation-based studies can deviate from the actual energy performance of buildings due to several factors. A clearer understanding of building energy performance can be better established through actual data-based analysis. This study aims to predict the energy efficiency of residential buildings in the KSA using supervised machine learning algorithms. It analyzes residential energy trends through data collected from an energy audit of 200 homes. It predicts energy efficiency using five supervised machine learning algorithms: ridge regression, least absolute shrinkage and selection operator (LASSO) regression, a least angle regression (LARS) model, a Lasso-LARS model, and an elastic net regression (ENR) model. It also explores the most significant explanatory energy efficiency variables. The results reveal that the ENR model outperforms other models in predicting energy consumption. This study offers a new and prolific avenue for the research community and other building sector stakeholders, especially regulators and policymakers.
Purpose
Monitoring attributes is crucial in industrial settings where quality features are not directly measurable. This study introduces a modified Cumulative Sum (CUSUM) scheme, named w CUSUM, to enhance the efficiency of monitoring attribute characteristics.
Design/methodology/approach
The w CUSUM scheme improves detection capability by elevating the difference between the actual and in-control numbers of nonconforming items to an exponent w . The charting parameters of the w CUSUM scheme are optimized to minimize the Average Number of Defectives ( AND ) across out-of-control scenarios while satisfying the constraint of the in-control Average Time to Signal ( ATS 0 ). A comparative analysis evaluates the w CUSUM scheme’s performance against the semi-optimal w CUSUM chart proposed by Wu et al . (2008). Sensitivity analysis is conducted to examine the impact of design parameters and inertia on the performance of the w CUSUM chart. A solar panel manufacturing case study demonstrates the proposed chart’s superiority.
Findings
The optimal w CUSUM outperforms the semi-optimal w CUSUM1 ( w = 1) by 13.21%, w CUSUM1.5 ( w = 1.5) by 10.58% and w CUSUM2 ( w = 2) by 20.93% in terms of AND under different settings. The w CUSUM enhances detection speed by 19% and 51%, assuming uniform and Rayleigh distributions of the shift, respectively, in comparison to its traditional counterpart. In addition, the w CUSUM outperforms the traditional scheme by 21% in terms of the Expected value of the out-of-control Average Number of Observations to Signal ( EANOS ). The case study shows a 65% detection efficacy improvement over the semi-optimal w CUSUM.
Research limitations/implications
The proposed w CUSUM chart offers practitioners a robust, economic and efficient tool for monitoring attribute processes. Although its current design aims to monitor a single attribute characteristic, future work could explore its application in multi-attribute scenarios.
Originality/value
This study introduces a novel w CUSUM scheme, tailoring the exponent w to achieve optimal performance. This approach supports customized control chart designs, enhancing adaptability to diverse process monitoring needs.
Simultaneous monitoring of the process parameters in a multivariate normal process has caught researchers’ attention during the last two decades. However, only statistical control charts have been developed so far for this purpose. On the other hand, machine-learning (ML) techniques have rarely been developed to be used in control charts. In this paper, three ML control charts are proposed using the concepts of artificial neural networks, support vector machines, and random forests techniques. These ML techniques are trained to obtain linear outputs, and then based on the concepts of memory-less control charts, the process is classified into in-control or out-of-control states. Two different input scenarios and two different training methods are used for the proposed ML structures. In addition, two different process control scenarios are utilized. In one, the goal is only the detection of the out-of-control situation. In the other one, the identification of the responsible variable (s)/process parameter (s) for the out-of-control signal is also an aim (detection–identification). After developing the ML control charts for each scenario, we compare them to one another, as well as to the most recently developed statistical control charts. The results show significantly better performance of the proposed ML control charts against the traditional memory-less statistical control charts in most compared cases. Finally, an illustrative example is presented to show how the proposed scheme can be implemented in a healthcare process.
The aim of this study is to investigate the overdispersion problem that is rampant in ecological count data. In order to explore this problem, we consider the most commonly used count regression models: the Poisson, the negative binomial, the zero-inflated Poisson and the zero-inflated negative binomial models. The performance of these count regression models is compared with the four proposed machine learning (ML) regression techniques: random forests, support vector machines, k-nearest neighbors and artificial neural networks. The mean absolute error was used to compare the performance of count regression models and ML regression models. The results suggest that ML regression models perform better compared to count regression models. The performance shown by ML regression techniques is a motivation for further research in improving methods and applications in ecological studies.
In statistical process control, the control charts are an effective tool to monitor the process. When the process is examined based on an exponential family distributed response variable along with a single explanatory variable, the generalized linear model (GLM) provides better estimates and GLM-based charts are preferred. This study is designed to propose GLM-based control charts using different link functions (i.e., logit, probit, c-log-log, and cauchit) with the binary response variable. The Pearson residuals (PR)- and deviance residuals (DR)-based control charts for logistic regression are proposed under different link functions. For evaluation purposes, a simulation study is designed to evaluate the performance of the proposed control charts. The results are compared based on the average run length (ARL). Moreover, the proposed charts are implemented on a real application for COVID-19 death monitoring. The Monte Carlo simulation study and real applications show that the performance of the model-based control charts with the c-log-log link function gives a better performance as compared to model-based control charts with other link functions.
Statistical process control for count data has difficulty overcoming multicollinearity. In this paper, we propose a new deep learning residual control chart based on the asymmetrical count response variable when there are highly correlated explanatory variables. We implement and compare different methods such as neural network, deep learning, principal component analysis based Poisson regression, principal component analysis based negative binomial regression, nonlinear principal component analysis based Poisson regression, and nonlinear principal component analysis based negative binomial regression in terms of the root mean squared error. Using two asymmetrical simulated datasets generated by the combined multivariate normal, binary and copula functions, the neural network and deep learning have a smaller mean, median, and interquartile range when compared to the principal component analysis based Poisson regression, principal component analysis based negative binomial regression, nonlinear principal component analysis based Poisson regression, and nonlinear principal component analysis based negative binomial regression. We also compare the deep learning and neural network based residual control charts in terms of the average run length with the copula based asymmetrical simulated data and real takeover bids data.
The application of wireless sensor networks is not limited to a particular domain. Technology advancements result in innovative solutions for simple communication to large applications via wireless sensor IoT networks. Besides the advancements, there is a serious issue in terms of threats or attacks on wireless sensor networks, which is common. Various intrusion detection methodologies have evolved so far to detect common network attacks. But it is essential to concentrate on other routing attacks like selective forwarding attack, black hole attack, Sybil attack, wormhole attack, identity replication attack, and hello flood attack. Existing research models concentrate on any one of the above-mentioned routing attacks and attain better detection performance. Detecting each attack through different detection mechanisms will increase the overall cost, and it is a tedious process. Considering this factor, in this research work, a novel intrusion detection system is introduced to detect routing attacks in wireless sensor networks using fuzzy and feed-forward neural networks. The experimental results demonstrate that the proposed model attains an average detection rate of 97.8% and a maximum detection accuracy of 98.8%, compared to existing techniques like support vector machine (SVM), decision tree (DT), and random forest (RF) models.
A residual (r) control chart of asymmetrical and non-normal binary response variable with highly correlated explanatory variables is proposed in this research. To avoid multicollinearity between multiple explanatory variables, we employ and compare a neural network regression model and deep learning regression model using Bayesian variable selection (BVS), principal component analysis (PCA), nonlinear PCA (NLPCA) or whole multiple explanatory variables. The advantage of our r control chart is able to process both non-normal and correlated multivariate explanatory variables by employing a neural network model and deep learning model. We prove that the deep learning r control chart is relatively efficient to monitor the simulated and real binary response asymmetric data compared with r control chart of the generalized linear model (GLM) with probit and logit link functions and neural network r control chart.
The control chart patterns are the most commonly used statistical process control (SPC) tools to monitor process changes. When a control chart produces an out-of-control signal, this means that the process has been changed. In this study, a new method based on optimized radial basis function neural network (RBFNN) is proposed for control chart patterns (CCPs) recognition. The proposed method consists of four main modules: feature extraction, feature selection, classification and learning algorithm. In the feature extraction module, shape and statistical features are used. Recently, various shape and statistical features have been presented for the CCPs recognition. In the feature selection module, the association rules (AR) method has been employed to select the best set of the shape and statistical features. In the classifier section, RBFNN is used and finally, in RBFNN, learning algorithm has a high impact on the network performance. Therefore, a new learning algorithm based on the bees algorithm has been used in the learning module. Most studies have considered only six patterns: Normal, Cyclic, Increasing Trend, Decreasing Trend, Upward Shift and Downward Shift. Since three patterns namely Normal, Stratification, and Systematic are very similar to each other and distinguishing them is very difficult, in most studies Stratification and Systematic have not been considered. Regarding to the continuous monitoring and control over the production process and the exact type detection of the problem encountered during the production process, eight patterns have been investigated in this study. The proposed method is tested on a dataset containing 1600 samples (200 samples from each pattern) and the results showed that the proposed method has a very good performance.
This study presents a relationship between two well‐known distributions, namely, geometric and binomial distributions. We will provide the statement of our result supported by its precise proof. In addition, we will give an illustrative example to explain the suggested relationship. We will indicate some industrial applications where the derived communicative property may be used. Moreover, the use of this linkage property will be shown in control charting setup.
To detect outbreaks of diseases in public health, several control charts have been proposed in the literature. In this context, the usual generalized linear model may be fitted for counts under a Negative Binomial distribution with a logarithm link function and the population size included as offset to model hospitalization rates. Different statistics are used to build CUSUM control charts to monitor daily hospitalizations and their performances are compared in simulation studies. The main contribution of the current paper is to consider different statistics based on transformations and the deviance residual to build control charts to monitor counts with seasonality effects and evaluate all the assumptions of the monitored statistics. The monitoring of daily number of hospital admissions due to respiratory diseases for people aged over 65 years in the city São Paulo-Brazil is considered as an illustration of the current proposal.
Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.
In this paper, a new procedure is developed to monitor a two-dependent process with second stage Poisson quality characteristic. In the proposed method, the log and the square-root link functions are first combined to introduce a new link function that establishes a relationship between the Poisson variable of the second stage and the quality characteristic of the first stage. Then, the standardized residual statistic, which is independent from the quality characteristic in the pervious stage and follows approximately standardized normal distribution, is computed based on the proposed link function. Then, Shewhart and EWMA cause-selecting charts are utilized to monitor standardized residuals. Finally, two examples and a case study with Poisson response variable are investigated and performance of the charts is evaluated by using average run length (ARL) criterion in comparison with the best literature method.
In multivariate quality control, the artificial neural networks (ANN)-based pattern recognition schemes generally performed better for monitoring bivariate process mean shifts and provided more efficient information for diagnosing the source variable(s) compared to the traditional multivariate statistical process control charting. However, these schemes revealed disadvantages in term of reference bivariate patterns in identifying the joint effect and excess false alarms in identifying stable process condition. In this study, feature-based ANN scheme was investigated for recognizing bivariate correlated patterns. Feature-based input representation was utilized into an ANN training and testing towards strengthening discrimination capability between bivariate normal and bivariate mean shift patterns. Besides indicating an effective diagnosis capability in dealing with low correlation bivariate patterns, the proposed scheme promotes a smaller network size and better monitoring capability as compared to the raw data-based ANN scheme.
When product quality follows the Gamma distribution and is related to one or more covariate(s), then Gamma regression model (GRM) profiling will be used. The Gamma profiling is generally based on a maximum likelihood estimator (MLE). In GRM profiling, when two or more covariates are linearly related, the MLE-based GRM profiling is unsuitable. In this situation, an alternative to MLE-based profiling is required. So, this study develops the Gamma ridge regression profiling based on Pearson and deviance residuals. The performance of the proposed profiling is evaluated with the help of a simulation study under different conditions, where average run length is considered as the performance evaluation criterion. The simulation findings show that the Pearson residual based profiling with ridge estimator is better than the deviance residuals-based profiling with MLE as well as ridge estimator. Furthermore, we consider an application to evaluate the performance of the proposed methods. ARTICLE HISTORY
Traditional monitoring techniques are frequently used for monitoring a response variable, while ignoring the other important variables. A simple linear regression model to introduce covariates-based charts has received a lot of attention in the recent publications. When the response variable belongs to the exponential family, the generalized linear model (GLM) is a flexible approach to model a phenomenon. This study uses gamma distribution to introduce GLM-based Shewhart-type control charts. The monitoring statistic is developed using the Pearson residuals (PRs) obtained from the gamma regression model. The suggested charts' performance is evaluated using the run-length properties and extensive Monte Carlo simulations. A comparison of Pearson-residual to the deviance-residual charts is also discussed in this article. Finally, to emphasize the significance of the study, the proposed control charts are implemented on a real-life data set.
In this paper, we propose a compound model based on the exponential distribution with its scale parameter randomized. Several mathematical properties of this new model are derived. By assuming that the quantitative characteristic of interest is distributed according to the proposed model, a new control chart is developed with the necessary measures for the control chart obtained using the belief estimator. We provide an application of the control chart to a real data set associated with health care system. In terms of the average run length, the proposed chart performs better than some existing charts. Furthermore, Monte Carlo simulations were performed to examine how the maximum likelihood estimators perform with regard to estimating parameters of the proposed model. The results indicate that the performance of the maximum likelihood estimators is reasonable.
Profile monitoring is a challenging issue in statistical process control (SPC). It aims to use a functional relationship between a response variable and one or more explanatory variable(s) to summarize the quality of a process/product. Most of the existing studies consider the same form of a functional relationship for both in-control (IC) and out-of-control (OC) situations or parametric approaches. However, non-parametric profiles with different relationships in OC conditions are very common. In this paper, we propose a novel ensemble framework to monitor changes in both regression relationship and variation of the profile for Phase II applications. This approach employs a pool of artificial neural networks (ANNs) as learners to enhance the efficiency of a base control chart, which is non-parametric exponentially weighted moving average (NEWMA) in this study. Then, a further ANN is used as a reasoning scheme (incorporator) to perform prediction by combining the outcomes of the learners. Experimental results demonstrate the effectiveness of the proposed framework, denoted by EANNN, in comparison with the base control chart, i.e., NEWMA, and other non-parametric methods. In addition, a practical example regarding a deep reactive ion-etching process from semiconductor device fabrication is provided to show the implementation of the proposed method.
During the evaluation and monitoring of a process, shifts are inherit parts of any statistical process control. In statistical process control, identifying the sources of such shifts is essential. Although there are many tools to identify the sources of such shifts, the control charts are most commonly used to identify these shifts. In this article, Shewhart, CUSUM, and EWMA control charts are proposed based on Liu deviance residuals for count data when there is a multicollinearity problem in Conway–Maxwell Poisson profiles to identify shifts. The comparisons of the proposed control charts are made with the deviance and ridge deviance-based Shewhart, CUSUM, and EWMA control charts. Thus, a numerical illustration through bike-sharing dataset and Monte Carlo simulation are considered. The simulation study is performed for the Poisson and
COM-Poisson distributions to see the effects of over- and underdispersion, the number of predictors as well as the shift size.
Control charts are widely used tool that provides quality inspectors with sensitive information for maintaining manufacturing process productivity. Numerous model‐based techniques have been presented in the literature to monitor industrial operations that focus on the normal response variable. However, non‐normal response results can occur as a result of quality control operations. In such cases, a new approach based on generalized linear model that provides multiple distribution options for response variables is required to achieve better results. Therefore, this study proposes GLM‐based moving average (MA) and double moving average (DMA) schemes formed on standardized residuals derived from a fitted Poisson regression model. The productivity of suggested methods and the existing exponentially weighted moving average (EWMA) scheme is explored in terms of run length attributes. The simulation outcomes revealed that moving average schemes based on standardized residuals (i.e., SR‐MA and SR‐DMA) outperform their predecessor (i.e., SR‐EWMA). Moreover, the SR‐DMA chart, with small values of span w, has proven to be more effective at detecting minor to moderate shifts in the process mean. Finally, a case study of a 3D manufacturing operation is shown to emphasize the importance of the proposed approaches.
The control charts are essential instruments that can impart crucial insights to quality controllers for maintaining the productivity of manufacturing processes. The conventional charting designs are based on a single study variable without exerting auxiliary information. Control charts derived from simple linear regression, generally with normality assumption, are one straightforward way of overcoming this difficulty. But, for a count distributed process, the generalized linear model (GLM) based strategy yields better outcomes. Hence, this study presents GLM-based progressive mean (PM) and double progressive mean (DPM) charting structures by employing the standardized residuals of the Poisson regression model. The functioning of the suggested and existing schemes (i.e., SR-EWMA) is investigated in the matter of run length distributions. The comparative analysis demonstrated that PM structures based on standardized residuals (i.e., SR-PM and SR-DPM) outperform the existing counterpart (i.e., SR-EWMA). Specifically, the SR-DPM chart is found to be more productive in identifying increasing alterations in the process mean. Finally, a case study about a 3D manufacturing procedure is presented to accentuate the significance of the suggested methods.
Advancement in technology brings a revolutionary change in the quality of the final product or items. Most of the manufacturing processes produce a large number of conforming items along with a few non-conforming items. For real-time monitoring of these highly efficient processes , monitoring of time-between-events is a well-known approach adopted in the literature of statistical process control. Usually, it is assumed that the time-between-events follows an exponential or gamma distribution. However, the generalized gamma distribution is the most popular choice for modelling skewed data. In this article, we consider a two-sided monitoring scheme based on the generalized gamma distribution. Two-sided monitoring schemes for skewed distributions often encounter bias in its run length properties. Therefore, we address this problem with modified control limits in a more general distributional setup. A Monte Carlo simulation-based study is designed, and results showed encouraging performance properties. A couple of practical applications in connection to monitoring renewable energy and coal mine explosions have been discussed.
In recent years, advancement in technology brought a revolutionary change in the manufacturing processes. Therefore, manufacturing systems produce a large number of conforming items with a small amount of non-conforming items. The resulting dataset usually contains a large number of zeros with a small number of count observations. It is claimed that the excess number of zeros may cause over-dispersion in the data (i.e., when variance exceeds mean), which is not entirely correct. Actually, an excess amount of zeros reduce the mean of a dataset which causes inflation in the dispersion. Hence, modeling and monitoring of the products from high-yield processes have become a challenging task for quality inspectors. From these highly efficient processes, produced items are mostly zero-defect and modeled based on zero-inflated distributions like zero-inflated Poisson (ZIP) and zero-inflated Negative Binomial (ZINB) distributions. A control chart based on the ZIP distribution is used to monitor the zero-defect process. However, when additional over-dispersion exists in the zero-defect dataset, a control chart based on the ZINB distribution is a better alternative. Usually, it is difficult to ensure that data is over-dispersed or under-dispersed. Hence, a flexible distribution named zero-inflated Conway–Maxwell–Poisson (ZICOM-Poisson) distribution is used to model over or under-dispersed zero-defect dataset. In this study, CUSUM charts are designed based on the ZICOM-Poisson distribution. These provide a flexible monitoring method for quality practitioners. A simulation study is designed to access the performance of the proposed monitoring methods and their comparison. Moreover, a real application is presented to highlight the importance of the stated proposal.
Deep learning has achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks have a long history, recent advances have greatly improved their performance in computer vision, natural language processing, etc. From the statistical and scientific perspective, it is natural to ask: What is deep learning? What are the new characteristics of deep learning, compared with classical methods? What are the theoretical foundations of deep learning? To answer these questions, we introduce common neural network models (e.g., convolutional neural nets, recurrent neural nets, generative adversarial nets) and training techniques (e.g., stochastic gradient descent, dropout, batch normalization) from a statistical point of view. Along the way, we highlight new characteristics of deep learning (including depth and over-parametrization) and explain their practical and theoretical benefits. We also sample recent results on theories of deep learning, many of which are only suggestive. While a complete understanding of deep learning remains elusive, we hope that our perspectives and discussions serve as a stimulus for new statistical research.
In this industry 4.0 revolution, most of the manufacturing processes are equipped with the digital devices which are continuously recording the data. To monitor the quality of a manufacturing system, variable about number of conforming or nonconforming items is usually used and statistical analysis based on it is further utilized for developing the policies. In this era of sophisticated and modern technology, most of the manufacturing systems are producing near zero‐defect items. Such processes are known as high‐quality processes, and their dataset consists of excess number of zeros. Generally, the zero excess or near zero‐defect dataset is well fitted by the zero‐inflated distributions, and the zero‐inflated Poisson (ZIP) and zero‐inflated Negative Binomial (ZINB) distributions are the most common models. Most of the time, in high‐quality processes, few covariates are also measured along with defect counts. Hence, to model such processes, generalized linear model (GLM) based on ZIP and ZINB distributions are used to fit the data. In monitoring perspective, data‐based control charts are designed to monitor high‐quality datasets while the GLM‐based control charts based on the residuals of the GLM models are used to monitor a change in the mean of the zero excess datasets. In this study, we have developed memory‐type data‐based and GLM‐based control charts (i.e., exponentially weighted moving average and cumulative sum) to monitor the increasing average defect counts in a high‐quality process. Further, the proposed methods are evaluated using run‐length properties and compared with its competitive charts. Furthermore, to highlight the importance of the study, the proposed methods are implemented on a dataset concerning the number of flight delays between Atlanta and Orlando airports.
We study deep neural networks and their use in semiparametric inference. We establish novel nonasymptotic high probability bounds for deep feedforward neural nets. These deliver rates of convergence that are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second‐step inference after first‐step estimation with deep learning, a result also new to the literature. Our nonasymptotic high probability bounds, and the subsequent semiparametric inference, treat the current standard architecture: fully connected feedforward neural networks (multilayer perceptrons), with the now‐common rectified linear unit activation function, unbounded weights, and a depth explicitly diverging with the sample size. We discuss other architectures as well, including fixed‐width, very deep networks. We establish the nonasymptotic bounds for these deep nets for a general class of nonparametric regression‐type loss functions, which includes as special cases least squares, logistic regression, and other generalized linear models. We then apply our theory to develop semiparametric inference, focusing on causal parameters for concreteness, and demonstrate the effectiveness of deep learning with an empirical application to direct mail marketing.
In this paper, we propose new process control charts for monitoring Poisson and Conway-Maxwell-Poisson (COM-Poisson) profiles with highly correlated variables. We first propose an iterative ridge estimator for Poisson regression under multicollinearity and then modify it to COM-Poisson regression. After we define ridge deviance residuals which are approximately normal distributed, we construct Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) type control charts based on the ridge deviance residuals for monitoring both Poisson and COM-Poisson profiles. The performances of the proposed control charts are evaluated by using average run length criterion and the proposed control chart are compared to the existing method for monitoring the Poisson profiles through simulation study based on real historical data and COM-Poisson profile through a hypothetical data set.
Control charts are commonly applied for monitoring and controlling the performance of the manufacturing process. Usually, control charts are designed based on the main quality characteristics variable. However, there exist numerous other variables which are highly associated with the main variable. Therefore, generalized linear model (GLM)-based control charts were used, which are capable of maintaining the relationship between variables and of monitoring an abrupt change in the process mean. This study is an effort to develop the Phase II GLM-based memory type control charts using the deviance residuals (DR) and Pearson residuals (PR) of inverse Gaussian (IG) regression model. For evaluation, a simulation study is designed, and the performance of the proposed control charts is compared with the counterpart memory less control charts and data-based control charts (excluding the effect of covariate) in terms of the run length properties. Based on the simulation study, it is concluded that the exponential weighted moving average (EWMA) type control charts have better detection ability as compared with Shewhart and cumulative sum (CUSUM) type control charts under the small or/and moderate shift sizes. Moreover, it is shown that utilizing covariate may lead to useful conclusions. Finally, the proposed monitoring methods is implemented on the dataset related to the yarn manufacturing industry to highlight the importance of the proposed control chart.
In practice, quality characteristics do not always follow a normal distribution, and quality control processes sometimes generate non‐normal response outcomes, including continuous non‐normal data and discrete count data. Thus, achieving better results in such situations requires a new control chart derived from various types of response variables. This study proposes a procedure for monitoring response variables that uses control charts based on randomized quantile residuals obtained from a fitted regression model. Simulation studies demonstrate the performance of the proposed control charts under various situations. We illustrate the procedure using two real‐data examples, based on normal and negative binomial regression models, respectively. The simulation and real‐data results support our proposed procedure.
Emerge in technology brought well‐organized manufacturing systems to produce high‐quality items. Therefore, monitoring and control of products have become a challenging task for quality inspectors. From these highly efficient processes, produced items are mostly zero‐defect and modeled based on zero‐inflated distributions. The zero‐inflated Poisson (ZIP) and zero‐inflated Negative Binomial (ZINB) distributions are the most common distributions, used to model the high‐yield and rare health‐related processes. Therefore, data‐based control charts under ZIP and ZINB distributions (i.e., Y‐ZIP and Y‐ZINB) are proposed for the monitoring of high‐quality processes. Usually, with the defect counts, few covariates are also measured in the process, and the generalized linear model based on the ZIP and ZINB distributions are used to estimate their parameters. In this study, we have designed monitoring structures (i.e., PR‐ZIP and PR‐ZINB) based on the ZIP and ZINB regression models which will provide the monitoring of defect counts by accounting the single covariate. Further, proposed model‐based charts are compared with the existing data‐based charts. The simulation study is designed to access the performance of monitoring methods in terms of run length properties and a case study on the number of flight delays between Atlanta and Orlando during 2012–2014 is also provided to highlight the importance of the stated research.
In the modern era of digitalization, manufacturing industries needed monitoring methods to timely detect an abrupt change in the process. Control charts are widely used online monitoring method and used in several sectors for the surveillance of the process. Usually, control charts are developed for a single study variable, but there exists auxiliary information along with the study variable. Because of the linear relation between the study variable and auxiliary variable, several control chart studies are designed based on the simple linear regression model, but they are restricted to the normally distributed response variable. When the response variable follows an exponential family distribution, then the generalized linear modeling (GLM) approach provides better estimates. Hence, this study is designed to propose GLM‐based control charts when the response variable follows the inverse Gaussian (IG) distribution. In GLM‐based control charts, deviance and Pearson residuals of the IG regression are considered as plotting statistics. For the evaluation purpose, a simulation study is designed, and the performance of the proposed methods is compared with existing counterparts in terms of the run length properties. Moreover, run‐rules are also implemented to gain the efficiency of the Shewhart type GLM‐based control charts under small‐to‐moderate shifts. Finally, an example related to the yarn manufacturing industry is also used to highlight the importance of the stated proposal.
This paper presents a new method for recognition of nine control chart patterns (CCPs) based on the intelligent use of shape and statistical features and optimized fuzzy system. The proposed technique contains three levels of separation. In each level of separation, an effective set of shape and statistical features are utilized as the input of classifier for recognizing a part of patterns. Due to the good performance of the adaptive neuro-fuzzy inference system (ANFIS) in pattern recognition problems, in the proposed method an ANFIS is used as a classifier at each level of separation which is trained by chaotic whale optimization algorithm (CWOA). Intelligent utilization of new extracted features, improving robustness of ANFIS and considering nine patterns in CCP recognition problem are the main contribution of the proposed method. The simulation results showed that the proposed method performs better than other similar methods and can recognize the type of pattern with 99.77% accuracy.
With the growth of automation in process industries, there is correlation in the process variables. Deep learning has achieved many great successes in image and visual analysis. This paper concentrates on developing a deep recurrent neural network (RNN) model to characterize process variables at vary time lags, and then a residual chart is developed to detect mean shifts in autocorrelated processes. The experiment results indicate that the RNN‐based residual chart outperforms other typical methods (eg, autoregressive [AR]‐based control chart, back propagation network [BPN]‐based residual chart). This paper provides guideline for deep learning technique employed as an effective tool in autocorrelated process control.
As product quality has increased rapidly in recent years, monitoring and control of products have become more and more difficult. The items were produced with zero defects, and zero‐inflated distributions are used to fit the defect count data. Recently, many studies were designed for the estimation and monitoring methods based on the zero‐inflated distributions. As zero‐inflated models are useful in the modeling of high‐yield and rare health‐related processes, so, the stated study is designed to provide a summary of past and current trends of monitoring methods under the zero‐inflated models. Moreover, a review is done on the several zero‐inflated models and their applications in different industries. Finally, some future directions are also highlighted to overcome existing unsolved issues.
Sometimes the quality of a process is best expressed by a relationship between response variables and explanatory variables. Checking over the time the stability of such functional relationships using statistical methods is called “profile monitoring”. Since 2007, when a detailed review paper in the field of profile monitoring was presented, an increasing number of papers have been published in this area. In this paper, we present a conceptual classification scheme and classify the papers in this area since 2008 up to 2018. The relevant papers are categorized and analyzed under different metrics and directions for future studies are recommended.
Copula functions also known as copulas, which connect the marginal distributions to their joint distributions, are useful in simulating the linear or nonlinear relationships among multivariate data in the scientific and engineering studies. Copula is a multivariate distribution function with marginally uniform random variables on [0, 1]. Copula functions have some appealing properties such as they allow scale-free measures of dependence and are useful in constructing families of joint distributions. As seen recently, copulas have been applied in statistics, insurance, finance, economics, survival analysis, image processing, and engineering applications. In this paper, we aim to briefly describe the copula functions, their properties, copula families, simulations, and examples of copula applications.
The Poisson distribution is commonly used to describe count data for a control chart. However, it may not be appropriate for overdispersion or underdispersion. Thus, it is necessary to generalize the control chart to work well in such situations. This paper proposes a strategy for monitoring dispersed count data with multicollinearity between input variables by combining generalized linear model and principal component analysis. In the strategy, the generalized linear model using flexible distributions is performed on principal component scores from principal component analysis. The deviance residuals from the fitted model are then used to monitor the process. Simulation is conducted for performance under various situations. Also, a real dataset that is not suitable for a classical control chart is used in our example. The results from the simulated data and real data example support our proposed method.
A major tool for quality control and management, statistical process control (SPC) monitors sequential processes, such as production lines and Internet traffic, to ensure that they work stably and satisfactorily. Along with covering traditional methods, Introduction to Statistical Process Control describes many recent SPC methods that improve upon the more established techniques. The author—a leading researcher on SPC—shows how these methods can handle new applications.
After exploring the role of SPC and other statistical methods in quality control and management, the book covers basic statistical concepts and methods useful in SPC. It then systematically describes traditional SPC charts, including the Shewhart, CUSUM, and EWMA charts, as well as recent control charts based on change-point detection and fundamental multivariate SPC charts under the normality assumption. The text also introduces novel univariate and multivariate control charts for cases when the normality assumption is invalid and discusses control charts for profile monitoring. All computations in the examples are solved using R, with R functions and datasets available for download on the author’s website.
Offering a systematic description of both traditional and newer SPC methods, this book is ideal as a primary textbook for a one-semester course in disciplines concerned with process quality control, such as statistics, industrial and systems engineering, and management sciences. It can also be used as a supplemental textbook for courses on quality improvement and system management. In addition, the book provides researchers with many useful, recent research results on SPC and gives quality control practitioners helpful guidelines on implementing up-to-date SPC techniques.
The effect of parameters estimation on profile monitoring methods has only been studied by a few researchers and only the assumption of a normal response variable has been tackled. However, in some practical situation, the normality assumption is violated and the response variable follows a discrete distribution such as Poisson. In this paper, we evaluate the effect of parameters estimation on the Phase II monitoring of Poisson regression profiles by considering two control charts, namely the Hotelling’s T² and the multivariate exponentially weighted moving average (MEWMA) charts. Simulation studies in terms of the average run length (ARL) and the standard deviation of the run length (SDRL) are carried out to assess the effect of estimated parameters on the performance of Phase II monitoring approaches. The results reveal that both in-control and out-of-control performances of these charts are adversely affected when the regression parameters are estimated.
Nowadays, multi-source image acquisition attracts an increasing interest in many fields such as multi-modal medical image segmentation. Such acquisition aims at considering complementary information to perform image segmentation since the same scene has been observed by various types of images. However, strong dependency often exists between multi-source images. This dependency should be taken into account when we try to extract joint information for precisely making a decision. In order to statistically model this dependency between multiple sources, we propose a novel multi-source fusion method based on the Gaussian copula. The proposed fusion model is integrated in a statistical framework with the hidden Markov field inference in order to delineate a target volume from multi-source images. Estimation of parameters of the models and segmentation of the images are jointly performed by an iterative algorithm based on Gibbs sampling. Experiments are performed on multi-sequence MRI to segment tumors. The results show that the proposed method based on the Gaussian copula is effective to accomplish multi-source image segmentation.
Major difficulties in the study of high-quality processes with traditional process monitoring techniques are a high false alarm rate and a negative lower control limit. The purpose of time-between-events control charts is to overcome existing problems in the high-quality process monitoring setup. Time-between-events charts detect an out-of-control situation without great loss of sensitivity as compared with existing charts. High-quality control charts gained much attention over the last decade because of the technological revolution. This article is dedicated to providing an overview of recent research and presenting it in a unifying framework. To summarize results and draw a precise conclusion from the statistical point of view, cross-tabulations are also given in this article. Copyright
Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment.
Control charts based on the Poisson distribution are commonly used to monitor count data in attributes. However, the Poisson distribution is based on the underlying equidispersion assumption that is limiting as discussed by different researchers in the literature. Therefore, a generalized control chart is required that can be used to monitor both overdispersed and underdispersed count data. This article reviews the methods to implement for dispersed count data and present ideas for future work in this area. A comprehensive literature review for researchers and practitioners is presented in this article. Copyright © 2014 John Wiley & Sons, Ltd.
A procedure for monitoring multiple discrete counts is proposed. This procedure is based on the likelihood ratio statistic for Poisson counts when input variables are measurable. This statistic is the deviance residual resulting from a generalized linear model. The likelihood ratio statistic is derived and shown to be more effective than using a C chart on the raw counts.
In many production processes, measures of quality of a product cannot be conveniently represented numerically, it is necessary or more convenient to use counts of defective or nonconforming products out of a random sample of n products as indications whether a production process is in control or out of control. The count of nonconforming products is usually assumed to be a binomial random variable with parameters n and p, where p is the actual fraction of nonconforming products produced. The Shewhart fraction nonconforming or p control chart is perhaps the simplest type of control charts commonly used for monitoring binomial counts. A modified exponentially weighted moving average (EWMA) control chart is developed in this paper for monitoring binomial counts. The average run length (ARL) and the probability function of the run length of the modified EWMA control chart can be computed exactly using results from the Markov chain theory. The modified EWMA control chart is demonstrated to be generally superior than the Shewhart control chart based on ARL consideration. The use of the modified EWMA control chart is illustrated with an example.