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Statistical monitoring of warranty claims data using dynamic probability control limits has been shown to be effective in early detection of unforeseen reliability problems that emerge at the design and manufacturing phases. As the discrepancy between abnormal patterns and the normal pattern in aggregate warranty claims is usually small (especially at the early stage), we develop two new dynamic monitoring schemes that adopt CUSUM-type and EWMA-type statistics, named DyCUSUM and DyEWMA, respectively, to better address the warranty claims monitoring problem. Three effective algorithms – that is, the Monte Carlo simulation, Markov chain, and near-enumeration algorithms – are proposed to progressively determine control limits for the two schemes. In particular, comparison studies show that the near-enumeration algorithm can attain a higher approximation accuracy with a lower computational burden and is thus recommended. In-depth simulation experiments are then conducted to assess the performance of the schemes. We find that the DyEWMA scheme has superior and robust detection performance in various situations, whereas the DyCUSUM scheme is less effective and could even be ineffective in certain cases, compared with a Shewhart-type counterpart. Some specific suggestions are also provided to facilitate implementation of the proposed monitoring schemes. Improved schemes by combining the moving window approach to mitigate the 'inertia' problem is further discussed. Finally, a real case study is presented. [ABSTRACT FROM AUTHOR]

This paper investigates control charts for count data with a significant number of zeros. The proposed models are generalized to handle data exhibiting different types of dispersion, i.e. equidispersion, overdispersion, and underdispersion. To this effect, the zero-inflated Conway–Maxwell Poisson (ZICMP) distribution is employed. A Shewhart and an exponentially weighted moving average (EWMA) control chart are developed, referred to as ZICMP-Shewhart and ZICMP-EWMA charts, respectively. The ZICMP distribution incorporates various distributions, including the Conway–Maxwell–Poisson (COM-Poisson) and zero-inflated Poisson (ZIP), Geometric, and Bernoulli distributions, as special cases. Consequently, the flexibility and versatility of the ZICMP distribution enhance the applicability of the proposed control charts, thereby providing practitioners with an adaptable tool suitable for various scenarios.The control charts are examined for their ability to detect upward shifts in the process mean level, and their statistical performance is evaluated in terms of the average run-length (ARL). Through a simulation study, we demonstrate that the ZICMP-Shewhart chart is more effective for monitoring over-dispersed data, while the ZICMP-EWMA chart is more suitable for under-dispersed data. Finally, we provide two real-life examples to illustrate the applicability of the proposed charts. [ABSTRACT FROM AUTHOR]

The recent development of the omnibus sequential probability ratio test (OSPRT) chart marks a significant contribution to the advancement of joint monitoring schemes. As the OSPRT chart is a variable-sample-size control chart, practitioners often wish to understand its inspection efficiency, i.e. the number of observations it samples before producing a signal. In this article, we propose two enhanced optimization designs for the OSPRT chart based on the average number of observations of signal (ANOS) and expected value of the ANOS (EANOS) metrics under deterministic and unknown shift sizes, respectively. The ANOS metric is central to our design as it perfectly combines both the average run length (ARL) and the average sample number. A comparative analysis reveals that the OSPRT chart outperforms four benchmarking control charts in terms of the ANOS and EANOS metrics. Finally, an implementation of the OSPRT chart is presented with a ball shear test dataset. [ABSTRACT FROM AUTHOR]

This article aims to enhance the effectiveness of Phase I in statistical process monitoring by integrating the assessment of estimation uncertainty into control charts using the exceedance probability criterion. This criterion guarantees the desired in-control performance that a practitioner will achieve with a predefined high nominal coverage probability, which can help prevent high false alarm rates from occurring. In pursuit of this objective, we introduce two nonparametric approaches: one based on an analytical method and the other on a bootstrapping technique. Both approaches exhibit superior performance compared to the existing nonparametric method, particularly for Phase I, where small to moderate sample sizes are common. These proposed methodologies are especially advantageous for practitioners in real-world production environments. [ABSTRACT FROM AUTHOR]

In many modern industrial scenarios, measurements of the quality characteristics of interest are often required to be represented as functional data or profiles. This motivates the growing interest in extending traditional univariate statistical process monitoring (SPM) schemes to the functional data setting. This article proposes a new SPM scheme, which is referred to as adaptive multivariate functional EWMA (AMFEWMA), to extend the well-known exponentially weighted moving average (EWMA) control chart from the univariate scalar to the multivariate functional setting. The proposed method distinguishes itself by adaptively selecting the weighting parameter in the calculation of the EWMA statistic to enhance the sensitivity of the AMFEWMA control chart across a spectrum of potential out-of-control scenarios. Such adaptability is essential in industrial processes, where multivariate functional quality characteristics are also subject to varying degrees of change. The favorable performance of the AMFEWMA control chart over existing methods is assessed via an extensive Monte Carlo simulation. Its practical applicability is demonstrated through a case study in monitoring the quality of a resistance spot welding (RSW) process in the automotive industry through online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and are recognized as highly representative of the RSW process quality. The proposed method is implemented in the R package funcharts, available online on CRAN. [ABSTRACT FROM AUTHOR]

As a variable-sample-size control scheme, the sequential probability ratio test (SPRT) chart is favoured due to its sensitivity and high sampling efficiency. It is frequently documented that the SPRT chart inspects only a small number of observations at each sampling stage, making the said chart extremely appealing to quality engineers. In the current literature, most developments of the SPRT chart are established based on the average run length and average time to signal metrics. However, these metrics do not consider sampling efficiency. In this paper, we develop two optimal designs of the SPRT chart, based on (i) the average value of the average number of observations to signal (AANOS) and (ii) the expected value of the AANOS, with consideration of Phase-I process parameter estimation. We develop a model that integrates the concept of optimization and the guaranteed in-control performance (GICP) framework to neutralize the adverse effects of parameter estimation. Results show that the proposed optimal-GICP design preserves satisfactory out-of-control performances for moderate and large mean shifts, while keeping the false alarm rates at reasonably low levels. Finally, we illustrate an example of the SPRT chart with estimated process parameters for monitoring loop height measurements from a wire bonding dataset. [ABSTRACT FROM AUTHOR]

ABSTRACT Recently, considerable attention has been paid to the development of time between events and amplitude (TBEA) control charts. Almost all existing TBEA charts are of a parametric type. Parametric TBEA charts have the disadvantage of being very sensitive to deviations from the distributional assumptions and to the estimation of the process nominal parameters. This emphasizes the importance of developing nonparametric (or distribution‐free) TBEA control charts. In this paper, a new distribution‐free exponentially weighted moving average (EWMA) TBEA control chart based on the rank statistic, denoted as rank‐based EWMA TBEA chart, for simultaneously monitoring the time interval between successive occurrences of an event and its magnitude is proposed. This chart is an extension of the sign EWMA TBEA chart and uses a statistic close to the Wilcoxon Mann–Whitney statistic. The run length properties of the new TBEA chart are obtained by Markov‐chain techniques, and some numerical comparisons with other competing charts reveal its promising performance. An illustrative example is also provided to demonstrate the application and the implementation of the proposed TBEA control chart using real‐world data. [ABSTRACT FROM AUTHOR]

AbstractElectric 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 datasets. 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. [ABSTRACT FROM AUTHOR]

Given that an effective process monitoring implementation should take both the spatial and temporal variations into account, a novel online process monitoring scheme based on a newly formulated algorithm titled as spatial–temporal deviation analysis (STDA) is proposed. Different from the mainstream process monitoring methods that focus on characterizing the spatial and/or temporal variation in the historical normal samples, the proposed STDA algorithm is designed to adaptively and timely train a pair of projecting vectors to uncover potential deviation in the spatial–temporal variation of online monitored samples, so as to guarantee consistently enhanced monitoring performance. Instead of utilizing a fixed projecting framework trained offline, the STDA algorithm is repeatedly executed once a newly measured sample become available for online monitoring. Therefore, the proposed STDA‐based method could consistently ensure its effectiveness for online fault detection, because a projecting framework targeted to revealing deviation in spatial–temporal variation is dynamically determined for different online monitoring samples in a timely manner. Finally, the salient monitoring performance achieved by the proposed STDA‐based approach is evaluated through comparisons with other counterparts. [ABSTRACT FROM AUTHOR]

The two‐parameter exponential distribution (TPED) is often used to model time‐between‐events data. In this paper, we propose CUmulative SUM and exponentially weighted moving average charts for simultaneously monitoring the parameters (location and scale) of the TPED. A key feature of the proposed charts is their straightforward post‐signal diagnostics. Monte Carlo simulations are used to estimate the zero‐state and steady‐state average run‐length (ARL) profiles of the proposed charts. The ARL performances of existing and proposed charts are assessed in terms of expected weighted run‐length and relative mean index. It is found that the proposed charts outperform the existing charts. A real dataset is used to illustrate the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

Modern data collecting methods and computation tools have made it possible to monitor high‐dimensional processes. In this article, we investigate phase II monitoring of high‐dimensional processes when the available number of samples collected in phase I is limited in comparison to the number of variables. A new charting statistic for high‐dimensional multivariate processes based on the diagonal elements of the underlying covariance matrix is introduced and we propose a unified procedure for phases I and II by employing a self‐starting control chart. To remedy the effect of outliers, we adopt a robust procedure for parameter estimation in phase I and introduce the appropriate consistent estimators. The statistical performance of the proposed method is evaluated in phase II using the average run length (ARL) criterion in the absence and presence of outliers. Results show that the proposed control chart scheme effectively detects various kinds of shifts in the process mean vector. Finally, we illustrate the applicability of our proposed method via a manufacturing application. [ABSTRACT FROM AUTHOR]

Postoperative critical care management of congenital heart disease patients requires prompt intervention when the patient deviates significantly from clinician‐determined vital sign and hemodynamic goals. Current monitoring systems only allow for static thresholds to be set on individual variables, despite the expectations that these signals change as the patient recovers and that variables interact. To address this incongruency, we have employed statistical process monitoring (SPM) techniques originally developed to monitor batch industrial processes to monitor high‐frequency vital sign and hemodynamic data to establish multivariate trajectory maps for patients with d‐transposition of the great arteries following the arterial switch operation. In addition to providing multivariate trajectory maps, the multivariate control charts produced by the SPM framework allow for assessment of adherence to the desired trajectory at each time point as the data is collected. Control charts based on slow feature analysis were compared with those based on principal component analysis. Alarms generated by the multivariate control charts are discussed in the context of the available clinical documentation. [ABSTRACT FROM AUTHOR]

We show that an auxiliary information based (AIB) cumulative sum (CUSUM) chart is equivalent to a special case of the multivariate CUSUM control chart proposed by J. D. Healy. Due to this equivalence, the limitations and restrictions of the AIB-CUSUM chart also apply to Healy's multivariate CUSUM chart. [ABSTRACT FROM AUTHOR]

In this article, we propose a new adaptive exponentially weighted moving average (AEWMA) chart for monitoring the joint shifts in the location and scale parameters of the two‐parameter exponential distribution, namely the AEWMA‐II chart. A key feature of the proposed chart is its straightforward post‐signal diagnostics. The Monte Carlo simulation method is used to compute the steady‐state run‐length profiles of the proposed chart. The run‐length properties include the average run‐length and standard deviation of the run‐length. Through a comprehensive run‐length comparison, it is found that the AEWMA‐II chart performs better than the existing AEWMA chart. Moreover, with post‐signal diagnostics, the proposed chart also surpasses the existing chart. Finally, a real dataset is applied to illustrate the excellent performance and practical application of the proposed chart. [ABSTRACT FROM AUTHOR]

Monitoring the number of defects in constant‐size units is a well‐defined problem in the industrial domain and usually, the c$c$ control chart is used for monitoring the total number of defects in a product or a sample of products. The c‐chart tracks the total number of defects in each case by assuming that the underlying number of defects (single or several different types of defects) follows approximately the Poisson distribution. An interesting class of problems where the c$c$‐chart is used is when the number of defects in a surface is of interest. Although the number of defects on the surface of products characterizes the quality of the products, it is especially important how concentrated the defects are in specific parts of the product. In this paper, we introduce a scan‐based monitoring procedure, which simultaneously combines control charts for monitoring the evolvement of the number of defects (in general, events) through time and scan statistics for exploring the spatial distribution of defects. The numerical illustration showed that the new procedure has excellent performance under different scenarios. [ABSTRACT FROM AUTHOR]

This paper develops two novel process monitoring schemes for the mean of a Gaussian process: the Bayes factor (BF) and the improved Bayes factor (IBF) schemes. Conjugate priors are used to construct the plotting statistics. The performance of the proposed schemes is evaluated in terms of average run length (ARL), standard deviation of run length (SDRL), and several percentiles, and these performance metrics across different hyper‐parameters and various sample sizes are evaluated via Monte Carlo simulations. Both zero‐state and steady‐state out‐of‐control (OOC) performances are investigated comprehensively. The simulation results show that the IBF scheme outperforms the existing Bayesian exponentially weighted moving average (EWMA) schemes under different loss functions in zero‐state. In steady‐state conditions, the IBF scheme outperforms for small shifts. Finally, we present two examples to illustrate the practical application of the proposed schemes. [ABSTRACT FROM AUTHOR]

We introduce ChatSQC, an innovative chatbot system that combines the power of OpenAI's Large Language Models (LLM) with a specific knowledge base in Statistical Quality Control (SQC). Our research focuses on enhancing LLMs using specific SQC references, shedding light on how data preprocessing parameters and LLM selection impact the quality of generated responses. By illustrating this process, we hope to motivate wider community engagement to refine LLM design and output appraisal techniques. We also highlight potential research opportunities within the SQC domain that can be facilitated by leveraging ChatSQC, thereby broadening the application spectrum of SQC. A primary goal of our work is to provide a template and proof-of-concept on how LLMs can be utilized by our community. To continuously improve ChatSQC, we ask the SQC community to provide feedback, highlight potential issues, request additional features, and/or contribute via pull requests through our public GitHub repository. Additionally, the team will continue to explore adding supplementary reference material that would further improve the contextual understanding of the chatbot. Overall, ChatSQC serves as a testament to the transformative potential of AI within SQC, and we hope it will spur further advancements in the integration of AI in this field. [ABSTRACT FROM AUTHOR]

Nowadays advanced sensing technology enables high-resolution in-process data collection in various systems, known as profile data. These data facilitate in-process monitoring and anomaly detection, which have been extensively studied in recent years. This paper conducts a comprehensive survey on the recent literature for profile modeling and monitoring, including linear profiles, nonlinear profiles, spatial profiles, multi-stage profiles, profile network data, and partially observable profiles, covering techniques such as functional data analysis, tensor analysis, deep learning, etc. By summarizing the developments and challenges associated with the reviewed papers, this paper aims to provide researchers and practitioners with a valuable resource for understanding the latest research advances. [ABSTRACT FROM AUTHOR]

A great deal of research in statistical process control (SPC) involves the integration of different ideas to achieve the optimal detection of anomalies in the location parameter of a process. Likewise, the prime rationale of the combined (Shewhart-Memory-type) strategies is to promptly detect the shift of any size: small, moderate or large. An effort, along the same lines, is made to detect shifts in the mean of a normally distributed process. The usual difference estimator of the process mean instead of the sample mean is employed in the Mixed EWMA-Crosier CUSUM Combined Shewhart Mixed EWMA-CUSUM and Combined Shewhart Mixed EWMA-Crosier CUSUM charts to make their upgraded versions. This enhances the sensitivity of these charts against any shift size. The performance of the charts is appraised and compared with some notable charts of the same ilk, with reference to the average run length (ARL), relative average run length, extra quadratic loss and performance comparison index. An illustrative example is also provided. [ABSTRACT FROM AUTHOR]

The double EWMA (DEWMA) has been proposed as a more efficient control charting procedure for monitoring the mean of a process. Comparisons of the DEWMA and the EWMA charts, which often indicate the superiority of the DEWMA, are often flawed because the same smoothing constant is used in both charts. We take the approach of first selecting a shift that we would like to detect, and then compare the optimal DEWMA chart and the optimal EWMA chart for that particular shift. We consider the DEWMA chart whose smoothing constants are restricted to be the same and the general DEWMA. We find that there are situations where the optimal DEWMA outperforms, in the sense of a shorter out‐of‐control average run length (ARL) for a fixed in‐control ARL, but the improvement is slight. The optimal EWMA chart usually performs much better than the optimal DEWMA chart when the actual shift differs from the shift used to optimize the chart. The poor performance of the DEWMA chart away from the shift for which it was optimized, the nonmonotonicity of the DEWMA weights, and the additional computations required of the DEWMA chart indicate that the EWMA is a better overall choice than the DEWMA chart. [ABSTRACT FROM AUTHOR]

We provide an overview and discussion of some issues and guidelines related to monitoring univariate processes with control charts. We offer some advice to practitioners to help them set up control charts appropriately and use them most effectively. We propose a four-phase framework for control chart set-up, implementation, use, and maintenance. In addition, our recommendations may be useful for researchers in the field of statistical process monitoring. We identify some current best practices, some misconceptions, and some practical issues that rely on practitioner judgment. [ABSTRACT FROM AUTHOR]

Statistical process monitoring (SPM) offers an important toolkit used to monitor the stability of a process to improve the quality of outputs and/or services. More often, the design of control charts requires the estimation of the probability density function that involves selecting a common distribution that facilitates the estimation of the process parameters. The Bayesian approach is one of the most efficient techniques used in such instances. It incorporates informative and non-informative priors, i.e., uses information on past data and charting structures, to estimate parameters more efficiently than classical approaches. Bayesian approaches reduce the total expected cost over a finite horizon or the long-run expected average cost. This paper introduces a new Bayesian exponentially weighted moving average (EWMA) monitoring scheme for long runs based on an ARMA-GARCH model. The properties of the new monitoring scheme are investigated in terms of the run-length distribution. A case study on monitoring the USD to ZAR exchange rate is provided using the proposed Bayesian ARMA-GARCH EWMA monitoring scheme. [ABSTRACT FROM AUTHOR]

Fault detection plays a crucial role in ensuring the safety, availability, and reliability of modern industrial processes. This study focuses on data-driven fault detection methods, which have gained significant attention across various industrial sectors due to the rapid development of industrial automation technologies and the availability of extensive datasets. The objectives of this paper are to comprehensively review and present the theoretical foundations of widely used data-driven fault detection approaches. Specifically, these approaches are applied to fault detection in wind turbine systems, with performance evaluation conducted using multiple statistical measures. The data utilized in this study were collected from a simulated benchmark of a wind turbine system. The data-driven methods are tested under the assumption that the wind turbine operates in a steady-state region. Additionally, a comparative study is conducted to identify and discuss the primary challenges associated with the practical application of these methods in real-world scenarios. Simulation results show the effectiveness and efficacy of data-driven approaches concerning the sensitivity and robustness of wind turbine sensor faults as applied in practical industrial environments. [ABSTRACT FROM AUTHOR]

Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of various charting schemes. This paper comprehensively analyses the impacts of measurement errors on the detection ability of the cumulative sum (CUSUM) charting schemes for the ratio of two correlated normal variables. A thorough numerical assessment is performed using the Monte Carlo simulation, and the results indicate that the measurement errors negatively impact the performance of the CUSUM scheme for the ratio of two correlated normal variables. Increasing the number of measurements per set is not a lucrative approach for minimizing the negative impact of measurement errors on the performance of the CUSUM charting scheme when monitoring the ratio of two correlated normal variables. We consider a food formulation as an example that illustrates the quality control problems involving the ratio of two correlated normal variables in an industry with a measurement error. The results are presented, along with some suggestions for further study. [ABSTRACT FROM AUTHOR]

Monitoring the parameter of discrete distributions is common in industrial production. Also, it is often crucial to monitor the parameter of geometric distribution, which is often regarded as the nonconforming item rate. To enhance the detection of nonconforming item, we designed an exponentially weighted moving average (EWMA) scheme based on the weighted likelihood ratio test (WLRT) method, and this scheme is denoted as the EWLRT scheme, specifically designed for monitoring the increase of the parameter in geometric distribution. Moreover, the optimal statistical design of the EWLRT scheme is presented when the shift is known. Results from numerical comparisons through Monte Carlo simulations indicates that the EWLRT scheme performs better than the competing schemes in some scenarios. Additionally, the designed scheme is characterized by its simplicity and ease of use, making it ideally suited for scenarios involving single observation. An example is illustrated to demonstrate the effectiveness of the EWLRT scheme. [ABSTRACT FROM AUTHOR]

Exponential random graph models (ERGM) are known as one of the most flexible models for profile monitoring of the complex structure of dynamic social networks, especially for networks with a large number of nodes. Usually, only one realization of a network is available instead of a random sample and the correlations between nodes increase the computational cost. Parametrizing via ERGM, the parameters of the model corresponding to the features of the network (namely, edges, k -star, and triangles) are then monitored using Hotelling's T 2 and likelihood ratio test control charts in Phase I for two general scenarios in both the directed and undirected edges cases. The results show that the presented control charts efficiently characterize the profile consisting of a network at each sampling time. The power of each method at a constant nominal Type I error probability is numerically reported for different shifts in the parameters. The results are also employed in the analysis of Gnutella Internet Peer-to-Peer Networks. [ABSTRACT FROM AUTHOR]

In statistical process monitoring, control charts typically depend on a set of tuning parameters besides its control limit(s). Proper selection of these tuning parameters is crucial to their performance. In a specific application, a control chart is often designed for detecting a target process distributional shift. In such cases, the tuning parameters should be chosen such that some characteristic of the out-of-control (OC) run length of the chart, such as its average, is minimized for detecting the target shift, while the control limit is set to maintain a desired in-control (IC) performance. However, explicit solutions for such a design are unavailable for most control charts, and thus numerical optimization methods are needed. In such cases, Monte Carlo-based methods are often a viable alternative for finding suitable design constants. The computational cost associated with such scenarios is often substantial, and thus computational efficiency is a key requirement. To address this problem, a two-step design based on stochastic approximations is presented in this paper, which is shown to be much more computationally efficient than some representative existing methods. A detailed discussion about the new algorithm's implementation along with some examples are provided to demonstrate the broad applicability of the proposed methodology for the optimal design of univariate and multivariate control charts. Computer codes in the Julia programming language are also provided in the . [ABSTRACT FROM AUTHOR]

In many topical applications, the product's quality can be well described in terms of statistical regression relationships between one or more response and a set of explanatory variables. In the literature, various types of regression models have been proposed for profile monitoring applications, and each of those regression models can be implemented and applied in its standard frequentist's and its Bayesian variant. We formulate two popular Phase II multivariate cumulative sum control charts for monitoring multivariate linear profiles in terms of Bayesian regression models, and we show empirically that the resulting new Bayesian control charts perform better than the corresponding non-Bayesian control charts. For the comparative evaluation of the control charts we employ the average run length criterion. Moreover, we propose a new Bayesian approach, which we refer to as the informative prior generation method. The key idea of this method is to make use of historical datasets to generate informative prior distributions. The advantage of this method is that we do not ignore the historical data from Phase I. Instead we re-use it to construct informative prior distributions for Phase II monitoring. The applicability and the superiority of the proposed Bayesian control charts are illustrated through extensive simulation studies. [ABSTRACT FROM AUTHOR]

Stability in process parameters is required to ensure the quality of the finished item. Control charts, as one of the critical parts of statistical process monitoring (SPM), have seen widespread use across many disciplines for detecting and responding to shifts in process parameters. The adaptive EWMA (AEWMA) control chart is a well-known scheme that detects both small and large process shifts by integrating the features of the Shewhart and classical EWMA charts. In this study, we propose an enhanced AEWMA chart, termed the EAEWMA chart, that efficiently monitors small and large process mean shifts simultaneously. The proposed EAEWMA chart enhances the existing AEWMA chart using the shift estimator, based on the hybrid EWMA (HEWMA) statistic. The Monte Carlo simulation approach is employed as the computational method to obtain the numerical findings for the various performance metrics. The EAEWMA chart is compared with various existing charts, including AEWMA, HEWMA, EWMA, ACSUM, and IACCUSUM, in zero- and steady-state scenarios. Conclusively, two practical applications of the EAEWMA chart are presented, demonstrating its value for practitioners and engineers and illustrating its efficacy in real-world scenarios.

Control chart performance is often measured using average run length or median run length, which gives the expected or median number of samples to signal. It is often argued that on average, one chart will signal a process change quicker than another, and is therefore a better choice. Average and median run length do not, however, answer the question of which method will be more likely to signal first. We introduce the idea of "first to signal" and compare charts based on this criterion. [ABSTRACT FROM AUTHOR]

In statistical process monitoring, the CUSUM and EWMA control charts have received considerable attention because of their remarkable ability to detect small sustained shifts. In practice, small process variation and shifts are anticipated beforehand in many processes, so the focus should be on detecting a moderate to a large shift. The aforementioned charts identify minor changes in population parameters as out-of-control scenarios; thus, "small" and potentially practically insignificant shifts are producing signals. To counteract this, both charts are amended to accommodate an indifference region by optimizing the detection of a shift at the outer boundaries of the indifference region. The results show that the adapted CUSUM and EWMA monitoring schemes yield comparable results. On nearly all occasions, the CUSUM chart outperforms the EWMA chart, yet the EWMA chart seems more robust and is easier to interpret. Furthermore, we provide two practical examples to illustrate the use-case of optimized charts to mitigate small (unimportant) variations, such as seasonality and modest temporary shifts. Overall, this work provides a general approach tailored to practice in quality control, e.g., as prescribed by ISO standards. It also answers a recent call in statistical process monitoring literature to reconsider the design of control charts. [ABSTRACT FROM AUTHOR]

Nearly one hundred types of control charts have been proposed that incorporate ranked-set sampling (RSS) methods. The performance of these charts has been evaluated with comparisons to existing charts based on simple random sampling. The reduction of the standard error in estimating the parameter being monitored with RSS leads to uniformly better average run length performance. We show, however, that these performance comparisons can be very misleading once the sampling strategy over time is considered more carefully with the benefits of RSS being considerably overstated. We consider the most basic RSS method when monitoring the mean of the process, but the approach can be applied to evaluate other RSS monitoring methods. [ABSTRACT FROM AUTHOR]

In recent years, some statistical process monitoring (SPM) approaches have been used to control contingency table-based processes. The common assumption in this research is that the Neighborhood cells of the contingency table are temporally independent. This paper develops a new approach based on the Context-Tree method and Kullback-Leibler (KL) statistic to monitor the multi-way contingency tables by considering the dependence between Neighborhood cells in Phase II. The proposed approach is evaluated by using some simulation studies. In addition, the efficiency of the proposed approach has been approved using other sensitivity analyses in some numerical examples by contingency tables with more rows and columns and contingency tables with more categorical variables. Results show that proposed statistics have suitable performance in detecting the out-of-control condition under different shifts in a multi-way contingency table. [ABSTRACT FROM AUTHOR]

In recent years, researchers and practitioners have been exploring new methods for quality control, including image processing. The effective use of high‐volume image data can significantly improve the monitoring of production and service systems in terms of speed, accuracy, and cost. Adopting an image‐based approach is better than relying on operator‐based solutions, and it offers new perspectives for process monitoring. Image processing can involve extracting features to identify, classify, detect, and cluster. Although there are several transformations to extract features from images, the Fourier method cannot consider the concurrency of frequency and time data, and the wavelet method only considers two specific directions. In multidimensional transforms, the optimal method can provide more information using fewer coefficients. The contourlet transform has advantages such as multiresolution, localization, critical sampling, directionality, and anisotropy. This research investigates the advantages of applying the contourlet transform to images and using data in a generalized likelihood ratio control chart. The results show that this method is more accurate than others because it can examine various directions in images. The proposed methodology algorithm is also presented in this study. [ABSTRACT FROM AUTHOR]

Background: When the COVID-19 pandemic hit Saudi Arabia, decision-makers were confronted with the difficult task of implementing treatment and disease prevention measures. To make effective decisions, officials must monitor several pandemic attributes simultaneously. Such as spreading rate, which is the number of new cases of a disease compared to existing cases; infection rate refers to how many cases have been reported in the entire population, and the recovery rate, which is how effective treatment is and indicates how many people recover from an illness and the mortality rate is how many deaths there are for every 10,000 people. Methods: Based on a Susceptible, Exposed, Infected, Recovered Death (SEIRD) model, this study presents a method for monitoring changes in the dynamics of a pandemic. This approach uses a Bayesian paradigm for estimating the parameters at each time using a particle Markov chain Monte Carlo (MCMC) method. The MCMC samples are then analyzed using Multivariate Exponentially Weighted Average (MEWMA) profile monitoring technique, which will “signal” if a change in the SEIRD model parameters change. Results: The method is applied to the pre-vaccine COVID-19 data for Saudi Arabia and the MEWMA process shows changes in parameter profiles which correspond to real world events such as government interventions or changes in behaviour. Conclusions: The method presented here is a tool that researchers and policy makers can use to monitor pandemics in a real time manner.

Rising industrial pollution, exacerbated by climate change, underscores the need for effective environmental monitoring. Leveraging sensor advancements and Birnbaum-Saunders distribution, this study introduces a novel surveillance method for environmental data, crucial for shaping impactful industrial policies. Simulation studies demonstrate the method's performance, and a case study on nitrogen oxide levels in Italy validates its efficacy in the early detection of severe air pollution events.

AbstractSeveral versions of the exponentially weighted moving average (EWMA) control chart, such as the generally weighted moving average (GWMA), the double, triple, and quadruple EWMA (DEWMA, TEWMA, and QEWMA), and the homogeneously weighted moving average (HWMA) charts, have been developed to enhance its detection ability, especially for small and moderate shifts. These charts have been criticized as it is considered that an appropriately designed EWMA chart provides as good or better zero-state and steady-state average run-length (ARL) performance. In this article, we perform a careful comparison study of the above control charts under similar in-control (IC) run-length properties. We show that the “new” memory-type control charts have better out-of-control (OOC) run-length characteristics, especially for small to moderate shifts in the process mean for both the zero-state and steady-state cases, except for the HWMA chart where its steady-state OOC performance is very poor. We also present a comparison study based on the worst-case ARL measure. Finally, the extensions of the EWMA chart have better IC robustness ability than the EWMA and HWMA charts. [ABSTRACT FROM AUTHOR]

This research presents simultaneous design of production planning, maintenance strategy and control chart in which two issues are considered: (1) multiple assignable cause and (2) equipment failure. The first one means that various factors may shift the process to an out-of-control state; while the second one means that the equipment is not always available and may be suddenly failed. Also, to reduce the production costs, a rework process is performed on the nonconforming items right after the regular cycle. Furthermore, three types of maintenance activities are applied based on system conditions. The corrective maintenance is conducted when the equipment failure occurs. The preventive maintenance is accomplished when the process continues until the end of the cycle, and the predictive maintenance is performed whereas the chart issues a true alarm. To check the effectiveness of the model, three comparative studies are examined. The first one compares the suggested model with a similar model without the rework process; the second one demonstrates the importance of employing the statistical process monitoring; and the last one compares the model with a similar model without considering the equipment failure. The results show the superiority of the integrated model compared to the others in the cost-saving. [ABSTRACT FROM AUTHOR]

When the COVID-19 pandemic hit Saudi Arabia, decision-makers were confronted with the difficult task of implementing treatment and disease prevention measures. To make effective decisions, officials must monitor several pandemic attributes simultaneously. Such as spreading rate, which is the number of new cases of a disease compared to existing cases; infection rate refers to how many cases have been reported in the entire population, and the recovery rate, which is how effective treatment is and indicates how many people recover from an illness and the mortality rate is how many deaths there are for every 10,000 people. Based on a Susceptible, Exposed, Infected, Recovered Death (SEIRD) model, this study presents a method for monitoring changes in the dynamics of a pandemic. This approach uses a Bayesian paradigm for estimating the parameters at each time using a particle Markov chain Monte Carlo (MCMC) method. The MCMC samples are then analyzed using Multivariate Exponentially Weighted Average (MEWMA) profile monitoring technique, which will "signal" if a change in the SEIRD model parameters change. The method is applied to the pre-vaccine COVID-19 data for Saudi Arabia and the MEWMA process shows changes in parameter profiles which correspond to real world events such as government interventions or changes in behaviour. The method presented here is a tool that researchers and policy makers can use to monitor pandemics in a real time manner. [ABSTRACT FROM AUTHOR]

In this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of processes with a low number of defects per inspected unit. Therefore, it is not possible to detect a decrease in the process mean level. A common solution to this problem is to apply a runs rule on the lower side of the chart. Motivated by this approach, we suggest a Shewhart-type chart, supplemented with two runs rules; one is used for detecting decreases in process mean level, and the other is used for improving the chart's sensitivity in the detection of small and moderate increasing shifts in the process mean level. Using the Markov chain method, we examine the performance of various schemes in terms of the average run length and the expected average run length. Two illustrative examples for the use of the proposed schemes in practice are also discussed. The numerical results show that the considered schemes can detect efficiently various shifts in process parameters in either direction. [ABSTRACT FROM AUTHOR]

The increasing scale of modern chemical plants keeps popularizing investigation as well as application of distributed process monitoring approaches. With a goal of directly quantifying the normal relations between different blocks divided from the whole process, a novel multi‐block modeling strategy called block‐wise residual generator is proposed, which trains a residual generator for each block through using the partial least squares algorithm with single one output, so that the relation between the corresponding block and the others is quantified as a regression model in a block‐wise manner. The deviations caused by the abnormal samples to the normal relations quantified for different blocks could thus be efficiently captured by the residuals generated from the block regression models, which then provide sensitive information for fault detection and contribution‐based fault diagnosis. Moreover, the proposed method is applicable for both disjoint and overlapped block divisions, and the direct consideration of individually quantifying relations between different blocks can always guarantee its salient monitoring performance, as validated through comparisons with classical distributed process monitoring methods. A novel block‐wise residual generator (BWRG)‐based approach is proposed for distributed process monitoring. The training of BWRG is targeted to quantify the relation between different blocks in a block‐wise manner. The comparisons validated the salient superiority and consistent effectiveness of BWRG in distributed statistical process monitoring. [ABSTRACT FROM AUTHOR]

Due to the increased volume of data generated in the form of images, the role of various image processing and monitoring methods has become vital in improving quality. Monitoring image data requires development and implementation of effective data reduction methods. The extracted data from various image types are considered a rich and valuable source of information in statistical process monitoring (SPM). In this paper, we propose a new method to monitor extracted data from 2-dimensional (2D) grayscale images based using an integrated approach based on fuzzy transform (F-transform) and generalized likelihood ratio (GLR) test. F-transform is applied first to reduce the image dimension effectively and then the extracted data are used for statistical process monitoring utilizing a generalized likelihood ratio (GLR) control chart. The proposed approach can help practitioners to identify fault location and change point in the process. A case study based on real image data in tile industry along with numerical examples are also presented to evaluate the performance of the proposed method. Results indicate that the proposed approach has satisfactory performance from statistical point of view for detecting variations in processes. [ABSTRACT FROM AUTHOR]

Early detection of changes in the frequency of events is an important task in many fields, such as disease surveillance, monitoring of high‐quality processes, reliability monitoring, and public health. This article focuses on detecting changes in multivariate event data by monitoring the time‐between‐events (TBE). Existing multivariate TBE charts are limited because they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time‐to‐signal), especially when we are interested in detecting a change in one or a few processes with different rates. We propose a bivariate TBE chart, which can signal in real‐time. We derive analytical expressions for the control limits and average time‐to‐signal performance, conduct a performance evaluation and compare our chart to an existing method. Our findings showed that our method is an effective approach for monitoring bivariate TBE data and has better detection ability than the existing method under transient shifts and is more generally applicable. A significant benefit of our method is that it signals in real‐time and that the control limits are based on analytical expressions. The proposed method is implemented on two real‐life datasets from reliability and health surveillance. [ABSTRACT FROM AUTHOR]

Since all production processes are not perfect, all products produced by a company may not meet the quality standards desired by its customers. Moreover, equipment breakdowns and failures during the production cycle can delay the production process. Consequently, it is necessary to integrate statistical process monitoring and maintenance decisions in conjunction with inventory control. Additionally, to remain competitive and maintain market share, successful manufacturers should be able to offer warranty services for their products, which impose additional costs during the post-sale period of the product. The goal of this study is to minimize the total costs incurred in both the pre-sale and the post-sale periods. To that end, an integrated model of inventory control, maintenance scheduling, and statistical process monitoring is proposed for products sold under the free minimal repair warranty policy. Three comparative analyses are conducted to evaluate the impact of incorporating warranty, accounting for process failure and statistical process monitoring as part of the model. [ABSTRACT FROM AUTHOR]

Dynamic control limits can be useful in designing control charts, especially when sample sizes, risk scores, or other covariate values change over time. Computer simulation can be used to control the conditional false alarm rate and thus the in‐control run length properties. We show that this approach can be useful in designing adaptive exponentially weighted moving average (AEWMA) control charts for which the control chart smoothing parameter at a given time point depends on the observed value at that time point. We use AEWMA charts as examples, but the approach can be applied to the adaptive cumulative sum (CUSUM) chart and other types of adaptive charts. [ABSTRACT FROM AUTHOR]

Run length distributions are generally used to characterize the performance of a control chart in signaling alarms when a process is out‐of‐control. Since it is usually difficult to directly compare distributions, statistics of the run length distribution are commonly adopted as the performance criteria in practice. Particularly, the average run length (ARL) and its extended versions play a dominant role. However, due to the skewness of the run length distribution, the ARL cannot accurately reflect the central tendency and may be misleading in some cases. In order to comprehensively summarize the information of the run length distribution, a novel criterion is proposed based on the continuous ranked probability score (CRPS). The CRPS‐based criterion measures the difference between the run length distribution and the ideal constant value 0 for the run length. It has advantages of easy computation and good interpretability. Furthermore, theoretical properties and geometric representation guarantee that the CRPS‐based criterion is statistically consistent, informative of both first and second moments of the run length distribution, and robust to extreme values. Results of numerical experiments show that the proposed criterion favors control charts with higher probability to detect outliers earlier, and is a superior metric for characterizing the run length distribution. [ABSTRACT FROM AUTHOR]