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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]

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]

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]

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]

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]

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]

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, 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]

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]

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]

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]

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]

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent sample sizes, Shewhart type attribute control charts are known to be less efficient than their measurement counterparts (like the X ¯ chart) and, for this reason, practitioners often compensate it by supplementing them with an EWMA (Exponentially Weighted Moving Average) scheme. However, because of the discrete nature of count data, it is unfortunately impossible to compute exactly and accurately (by means of Markov chain of integral equation methods) the run length (RL) properties, such as its mean (ARL) and its standard deviation (SDRL) of these EWMA attribute control charts and, consequently, it is impossible to efficiently design them in order to minimize some out-of-control characteristics. For this reason, we propose in this paper a dedicated approach called "continuousify" method which, coupled with a classical Markov chain technique, allows to compute the RL properties of any EWMA attribute control chart in a reliable way. A numerical comparison shows that the RL properties obtained by using the proposed "continuousify" approach are very much alike to the ones calculated via simulation and without the "continuousify" approach. Illustrative examples are also provided to show how the proposed method can be implemented in practice. [ABSTRACT FROM AUTHOR]

In profile monitoring, it is usually assumed that the observations between or within each profile are independent of each other. However, this assumption is often violated in manufacturing practice, and it is of utmost importance to carefully consider autocorrelation effects in the underlying models for profile monitoring. For this reason, various statistical control charts have been proposed to monitor profiles when between- or within-data is correlated in Phase II, in which the main aim is to develop control charts with quicker detection ability. As a novel approach, this study aims to employ machine learning techniques as control charts instead of statistical approaches in monitoring profiles with between-profile autocorrelations. Specifically, new input features based on conventional statistical control chart statistics and normalized estimated parameters are defined that are capable of adequately accounting for the between-autocorrelation effect of profiles. In addition, six machine learning techniques are extended and compared by means of Monte Carlo simulations. The simulation results indicate that machine learning techniques can obtain more accurate results compared with statistical control charts. Moreover, adaptive neuro-fuzzy inference systems outperform other machine learning techniques and the conventional statistical control charts. [ABSTRACT FROM AUTHOR]

One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I. This assessment is carried out in the absence and presence of outliers. We show that, in both cases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method. [ABSTRACT FROM AUTHOR]

Phase I or retrospective process monitoring plays a key part in an overall statistical process monitoring (SPM) regime and is increasingly emphasized in the recent literature. At present, a lot of the data in a variety of settings (public and private sector organizations) are collected individually and sequentially and thus are serially correlated (or autocorrelated). Though a reasonable amount of work is available in the control charting literature for prospective (Phase II) autocorrelated data monitoring, very little work exists for the retrospective phase (Phase I). In this article, we present a Shewhart-type control chart for Phase I monitoring of individual autocorrelated data, assuming normality, with estimated parameters. The methodology, while developed and presented for the first-order autoregressive (AR(1)) model for simplicity, may be adapted to more general time series models. The correct charting constants, adjusted for autocorrelation and parameter estimation, are derived, and tabulated for a nominal in-control (IC) false alarm probability (FAP). Simulation results show that the proposed chart is favorably IC FAP robust and effective for reasonably small sample sizes, moderate autocorrelation, and some model miss-specifications, compared to other approaches. An illustration using some public health data involving prescription fentanyl transactions is provided to show the potential for broader areas of applications of the proposed methodology. Along with a summary and recommendations, some future research areas are indicated. An R package is developed and made available for implementing the proposed methodology on demand. [ABSTRACT FROM AUTHOR]

We show that the so‐called modified exponentially weighted moving average (EWMA) control chart is very closely related to a moving average‐based EWMA chart. These charts have ill‐advised weighting functions that assign more weight to some past data values than to the most recent data values. We show that these weighting functions adversely affect their run length properties and that one can obtain better overall performance with an ordinary EWMA chart. [ABSTRACT FROM AUTHOR]

In recent years, adaptive control charts in which the design parameters depend on the observed samples have been successfully used as efficient alternatives for traditional control charts with constant parameters. In crisp run control rules, the process state may change very sharply from in-control to out-of-control conditions which increase the rate of false alarms. To overcome this drawback, this paper presents an adaptive Shewhart-type control chart, where the design parameters (sample size (n), sampling interval (h), and control limit coefficients (k and k r , s )) are defined with linguistic variables. To accomplish that, the chart parameters are determined based on the location of eight previous chart statistics using a set of fuzzy rules in a continuous environment. In order to improve the sensitivity of the proposed control chart in detecting small shifts in both location and scale parameters, the adaptive procedure is designed by integration of fuzzy Western Electric rules and fuzzy adaptive sampling rules. After designing the control charts using a fuzzy inference system (FIS), in order to provide an economic design of the proposed control chart, a tuned Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal values corresponding to membership functions of the control chart parameters. Finally, using simulation studies, the capability of the proposed control chart is analyzed and compared with common charts in the literature. The results confirm that under different shifts in location and scale parameters, the proposed control chart outperforms other charts in terms of both economic and statistical criteria. [ABSTRACT FROM AUTHOR]

In industrial production, the exponentially weighted moving average scheme is widely used to monitor shifts in product quality, especially small-to-moderate shifts. In this paper, we propose a modified one-sided EWMA scheme for Type I right-censored Weibull lifetime data for detecting shifts in the scale parameter with the shape parameter fixed. A comparative analysis with existing cumulative sum and exponentially weighted moving average results from the literature is provided. The zero-state and steady-state behaviour of the new scheme are considered with regard to the average run length, the standard deviation of the run length, and other performance measures. Our simulation shows stronger power in detecting changes in the censored lifetime data using the modified scheme than that using the traditional exponentially weighted moving average scheme, and the new scheme is superior to the cumulative sum scheme in most situations. A real-data example further demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we show that a recently proposed auxiliary information‐based (AIB) adaptive EWMA (AE) chart is sensitive (not robust) to the changes in the mean of an auxiliary variable when monitoring the changes in the mean of a quality variable, called the AIB‐AE chart. To circumvent the weakness of the AIB‐AE chart, we develop a new AIB estimator for the mean of a quality variable that is slightly robust to the changes in the mean of an auxiliary variable. Based on this newly developed estimator, a new AIB EWMA (AIB‐E) chart is proposed for monitoring the mean of a quality variable. The zero‐state and steady‐state average run‐length profiles of the AIB‐AE and AIB‐E charts are estimated with Monte Carlo simulations. It is found that the AIB‐E chart is not only slightly robust to the changes in the mean of an auxiliary variable, but it also outperforms the AIB‐AE chart when detecting small shifts in the mean of a quality variable. Illustrative examples are also included in this study to demonstrate the implementation of the existing and proposed AIB charts. [ABSTRACT FROM AUTHOR]

Distribution-free control charts are an efficient quality monitoring tool to inspect lots of parts manufactured within a finite production horizon. In this work, the performance of the Exponentially Weighted Moving Average chart based on the Wilcoxon signed rank statistic is investigated for on-line monitoring of finite production runs. The chart's on-target performance is evaluated through a specific non-homogeneous Markov chain model under different process scenarios. A numerical analysis is conducted for determining its optimal design and a performance comparison with other available schemes is presented for different symmetric distributions of observations. Finally, an illustrative example is presented to show a practical implementation of the investigated chart. [ABSTRACT FROM AUTHOR]

It was recently demonstrated that homogeneously weighted moving average (HWMA) control charts are improper devices for an online detection of changes within a series of random variables. However, another attempt was made to bail out the concept underlying these charts. Here we want to re‐emphasize that HWMA charts are dispensable by rebutting the arguments of the latter contribution. [ABSTRACT FROM AUTHOR]

Multiple dependent state sampling (MDSS) is a feature that was recently proposed for acceptance sampling plans. In addition, it is increasingly recommended to use this technique, and its generalization, with quality control charts. In our paper, we show that the MDSS feature is an extension of chain sampling in acceptance sampling applications. In addition, we show that use of the MDSS feature with control charts is equivalent to the use of standard supplementary runs rules. Analytical methods based on Markov chains for determining the performance of control charts with runs rules can also be applied to MDSS acceptance sampling applications. Additionally, we provide a derivation approach for some of the formulas for the performance measures for the MDSS charts and point out some incorrect derivations. [ABSTRACT FROM AUTHOR]

Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based on alternative weighting of past data, usually to put greater emphasis on past data and less weight on current and recent data. In other cases, the output of one process monitoring method, such as the EWMA statistic, is used as the input to another method, such as the CUSUM chart. Often the recursive formula for a control chart statistic is itself used recursively to form a new control chart statistic. We find the use of these ad hoc methods to be unjustified. Statistical performance comparisons justifying the use of these methods have been either flawed by focusing only on zero-state run length metrics or by making comparisons to an unnecessarily weak competitor. [ABSTRACT FROM AUTHOR]

We review the rapidly growing literature on auxiliary information-based (AIB) process monitoring methods. Under this approach, there is an assumption that the auxiliary variable, which is correlated with the quality variable of interest, has a known mean, or some other parameter, which cannot change over time. We demonstrate that violations of this assumption can have serious adverse effects both when the process is stable and when there has been a process shift. Some process shifts in the quality variable of interest can become undetectable. We also show that the basic AIB approach is a special case of simple linear regression profile monitoring. The AIB charting techniques require strong assumptions. Based on our results, we warn against the uncritical use of the AIB approach in quality control applications. [ABSTRACT FROM AUTHOR]

This paper presents an integrated model of three interrelated topics including the statistical process monitoring, maintenance scheduling, and production cycle length for imperfect manufacturing systems. The novelty of this paper is to take five features into consideration, including: (1) The produced items deteriorate over time, hence, the inventory is depleted in two ways i.e. responding to demand and gradually deteriorating products; (2) The non-conforming products can be reworked to increase the cost-saving by eliminating the waste items; (3) A non-uniform sampling scheme is employed such that the hazard rate does not exceed its threshold value; (4) The economic-statistical design of a control chart is used to accelerate the detection of process faults as well as reduce the risk of false alarms; and (5) The time value of money is taken into account to obtain more precise financial flow estimations. Finally, four comparative studies along with a sensitivity analysis on the most important parameters are conducted. The results confirm that considering the product deterioration and time value of money improves the model adaptability in real-world applications. Besides, employing the variable sampling scheme and the rework operations reduces the production rate of non-conforming items. The results also show that the total cost in economic-statistical model is slightly higher than that of the economic one. However, the economic-statistical model performs severely better than the economic one in terms of both in-control and out-of-control average run length metrics. [ABSTRACT FROM AUTHOR]

In the last decade numerous papers have appeared in the statistical process monitoring literature where the in‐control and out‐of‐control average run length (ARL) profiles of the exponentially weighted moving average chart, and some of its variants, have been approximated under the assumption that the signal event can be represented by a sequence of independent Bernoulli random variables. In this short note we show that these approximations, presented in the literature as being exact, can be very inaccurate when compared with the true ARL values. Moreover, the use of these poor ARL approximations has led to many flawed articles, which should be either corrected or retracted. [ABSTRACT FROM AUTHOR]

For monitoring processes, exponentially weighted moving average (EWMA) control charts have been found to be very powerful and reliable tools. Meanwhile, some processes require great attention at the startup to ascertain that the processes are free from any disturbances. In this article, we propose a generalized time‐varying fast initial response for EWMA control charts. This chart is a special case of the previously proposed time‐varying EWMA control chart. The proposed scheme is highly sensitive in detecting small shifts in a given process, particularly at the process startup. The proposed chart is compared with its counterparts using the zero state average run length. We also show an application of the proposed EWMA chart to a real‐life situation. [ABSTRACT FROM AUTHOR]

A measurement system fit for use is an essential resource to perform quality control activities: its assessment must be carried out periodically to quantify its bias(location) and precision(width) error to qualify it for the purpose it is used. In particular, the measurement system capability must be determined to evaluate how much of the observed variability originates from the gauge's precision error. Gauge Repeatability and Reproducibility (R&R$R{\&}R$) studies are aimed at getting a reliable estimate of the precision error σM$\sigma _M$ of the measurement system. The outcome of a Gauge R&R$R{\&}R$ study are point estimates and confidence intervals of the precision error components and related measurement capability metrics. Here, a general bootstrap‐based procedure is proposed to get confidence interval estimations of the measurement error and its components from a Gauge (R&R$R{\&}R$) study for continuous observations carried out with either the Average and Range (ARGG) control chart or the experimental design method. An application of the proposed bootstrap‐method is presented for a dataset of observations. [ABSTRACT FROM AUTHOR]

An integral part of the design of control charts, including the multivariate exponentially weighted moving average (MEWMA) control chart, is the determination of the appropriate control limits for prospective monitoring. Methods using Markov chain analyses, integral equations, and simulation have been proposed to determine the MEWMA chart limits when the limits are based on a specified in-control average run length (ARL) value. A drawback of the usual approach is that the conditional false alarm rate (CFAR) for these charts varies over time in what might be in an unexpected and undesirable way. We define the CFAR as the probability of a false alarm given no previous false alarm. We do not condition on the results of a Phase I sample, as done by others, in studies of the effect of estimation error on control chart performance. We propose the use of dynamic probability control limits (DPCLs) to keep the CFAR constant over time at a specified value. The CFAR at any time, however, could be controlled to be any specified value using our approach. Using simulation, we determine the DPCLs for the MEWMA control chart being used to monitor the mean vector with an assumed known variance-covariance matrix. We consider cases where the sample size is both fixed and time-varying. For varying sample sizes, the DPCLs adapt automatically to any change in the sample size distribution. In all cases, the CFAR is held closely to a fixed value and the resulting in-control run length performance follows closely to that of the geometric distribution. [ABSTRACT FROM AUTHOR]

In modern industries, statistical process monitoring (SPM) and maintenance management are extensively employed to increase the production rate of conforming items. Aiming at minimizing the expected total cost per time unit subject to some statistical constraints, this study proposes a hybrid quality-maintenance model for imperfect short-run process. To bring the proposed model closer to real short-run systems, it is considered that the process mean may shift to an out-of-control condition due to occurrence of several types of assignable causes. Furthermore, it is supposed that the time-to-failure follows a non-homogenous Poisson process implying that the system may suddenly fail with an increasing failure rate function. Moreover, a non-uniform sampling scheme is developed in order to improve the system reliability. Finally, the main advantages of the proposed model are highlighted by conducting two comparative studies. The first one illustrates the efficiency of the non-uniform sampling scheme in increasing the in-control time interval and decreasing the expected total cost. The second one confirms the importance of considering the system failure on both the expected total cost and in-control time interval. [ABSTRACT FROM AUTHOR]

During the last two decades, many new methods have appeared in statistical process monitoring with synthetic-type control charts being a prominent constituent. These charts became popular due to their simplicity and proclaimed excellent change point detection performance. Synthetic charts are nothing more than the application of well-known and long established runs rules. We show that better performance can be obtained by using exponentially weighted moving average (EWMA) charts. Expanding on some previous questioning articles, we critically reflect upon recently developed variants of synthetic-type charts in order to emphasize that there is no reason to apply this special class of control charts. This paper renews and extends criticism in order to respond to newly developed synthetic charts, called “revised” and “modified” by incorporation of further restrictions on the observations leading to an out-of-control signal. Furthermore, we demonstrate that “improved synthetic charts” (synthetic charts augmented with an outer Shewhart limit) perform weaker than EWMA–Shewhart chart combinations. [ABSTRACT FROM AUTHOR]

In healthcare monitoring, the quality of medical services and patient outcomes are significantly influenced by the unnatural variations emphasizing the importance of effective control and monitoring strategies. In such scenarios the quality is compromised when a shift in the medical process is not detected timely. In this study, we commenced a comprehensive analysis of the variability present in the patient's hematocrit levels. We introduced a novel approach using fuzzy control charts for individual measurements to detect shift within hematocrit levels effectively. For the initial forecasting of hematocrit level variability, we employed the exponential smoothing method by using R software. Following this, we proposed a set of fuzzy control charts intended for individual measurements, including the fuzzy moving average control chart, fuzzy weighted moving control chart, and fuzzy moving range control chart. These control charts are defined with fuzzy control rules, allowing them to analyze and interpret the small shifts in the process precisely. Also, to measure the process's capability for providing a deeper understanding of the processes, fuzzy process capability indices are introduced. A Monte Carlo simulation approach is employed to obtain the performance metrics. Finally, a case study sourced from Kaggle was conducted to evaluate the performance of the proposed fuzzy control charts for assessing hematocrit levels. • Innovative fuzzy control charts, including FMACC, FWMACC, and FMRCC, are proposed for individual measurements in health monitoring. • The proposed control charts use fuzzy control rules to detect small shifts in complex medical data. • Fuzzy Process Capability Indices are proposed for assessing process capability and improving the precision of healthcare decision-making. • The study aims to enhance patient care and treatment results by connecting healthcare practices with fuzzy control chart methods. • The research aims to improve patient care and treatment outcomes by enhancing data analysis and monitoring techniques. [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 E A E W M A 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 E A E W M A chart is compared with various existing charts, including A E W M A , H E W M A , E W M A , A C S U M , and I A C C U S U M , 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. [ABSTRACT FROM AUTHOR]