Search Results (39)

This study investigates the impact of data distribution and bootstrap resampling on the anomaly detection performance of the Isolation Forest (iForest) algorithm in statistical process control. Although iForest has received attention for its multivariate and ensemble-based nature, its performance under non-normal data distributions and varying bootstrap settings remains underexplored. To address this gap, a comprehensive simulation was performed across 18 scenarios involving log-normal, gamma, and t-distributions with different mean shift levels and bootstrap configurations. The results show that iForest substantially outperforms the conventional Hotelling’s T² control chart, especially in non-Gaussian settings and under small-to-medium process shifts. Enabling bootstrap resampling led to marginal improvements across classification metrics, including accuracy, precision, recall, F1-score, and average run length (ARL)₁. However, a key limitation of iForest was its reduced sensitivity to subtle process changes, such as a 1σ mean shift, highlighting an area for future enhancement. Full article

In manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity, traditional MLE-based inverse Gaussian regression model (IGRM) control charts become unreliable. This study introduces novel Shewhart control charts using Pearson and deviance residuals based on the inverse Gaussian ridge regression (IGRR) model to address this issue. The proposed IGRR-based charts effectively handle multicollinearity, offering a robust alternative for process monitoring. Their performance is evaluated through Monte Carlo simulations using average run length (ARL) as the main criteria, demonstrating that Pearson residual-based IGRR charts outperform deviance residual-based charts and MLE-based methods, particularly under high multicollinearity. A real-world application to a Pakistan air quality dataset confirms their superior sensitivity in detecting pollution spikes, enabling timely environmental negotiations. These findings establish Pearson residual-based IGRR control charts as a practical and reliable tool for monitoring complex processes with correlated variables. Full article

Control charts are frequently used instruments for process quality monitoring. Another name for the NEEWMA control chart is the new extended exponentially weighted moving average (new extended EWMA) control chart. The lower control limit (LCL) and upper control limit (UCL) are equally spaced from the center line, giving it a symmetrical design. Because of its symmetry, the NEEWMA chart is very good at identifying even the tiniest changes in operation by detecting deviations from the target in both upward and downward directions. This study derives an explicit formula for the average run length (ARL) of the NEEWMA control chart based on the autoregressive (AR) model with exponential white noise. The focus is on the zero-state performance of the NEEWMA control chart, which is derived using explicit formulas. Banach’s fixed-point theorem was used to prove existence and uniqueness of this formula. The accuracy of this formula is validated by comparing it to the numerical integral equation (NIE) method using percentage accuracy (%Acc). The results show that the NEEWMA control chart is more efficient than the ARL evaluated by the NIE method, particularly regarding computation time. The performance of the NEEWMA control chart is compared with the EWMA and extended EWMA control charts by evaluating both the ARL and standard deviation run length (SDRL). The NEEWMA control chart outperforms the others in detection performance, followed by the extended EWMA and EWMA control charts. Further verification of its superior performance is provided through comparisons using the average extra quadratic loss (AEQL) and the performance comparison index (PCI), which confirm that it outperforms both the EWMA and extended EWMA control charts across various parameters and shift sizes. Finally, an illustrative example using real-life economic data demonstrates its efficiency. Full article

Background: Surgeries represent a mainstay of medical care globally. Patterns of complications are frequently recognized late and place a considerable burden on health care systems. The aim was to develop and test the first deep learning-adjusted CUSUM program (DL-CUSUM) to predict and monitor in-hospital mortality in real time after liver transplantation. Methods: Data from 1066 individuals with 66,092 preoperatively available data point variables from 2004 to 2019 were included. DL-CUSUM is an application to predict in-hospital mortality. The area under the curve for risk adjustment with Model of End-stage Liver Disease (D-MELD), Balance of Risk (BAR) score, and deep learning (DL), as well as the ARL (average run length) and control limit (CL) for an in-control process over 5 years, were calculated. Results: D-MELD AUC was 0.618, BAR AUC was 0.648 and DL model AUC was 0.857. CL with BAR adjustment was 2.3 with an ARL of 326.31. D-MELD reached an ARL of 303.29 with a CL of 2.4. DL prediction resulted in a CL of 1.8 to reach an ARL of 332.67. Conclusions: This work introduces the first use of an automated DL-CUSUM system to monitor postoperative in-hospital mortality after liver transplantation. It allows for the real-time risk-adjusted monitoring of process quality. Full article

This study investigates the extension of the c-chart control chart to Bayesian methodology, utilizing the gamma distribution to establish control limits. By comparing the performance of the Bayesian approach with that of two existing methods (the traditional frequentist method and the Bayesian with Jeffreys method), we assess its effectiveness in terms of the average run lengths (ARLs) and false alarm rates (FARs). Simulation results indicate that the proposed Bayesian method consistently outperforms the existing techniques, offering larger ARLs and smaller FARs that closely approximate the expected nominal values. While the Bayesian approach excels in most scenarios, challenges may arise with large values of the λ parameter, necessitating adjustments to the hyperparameters of the gamma prior. Specifically, smaller values of the rate parameter are recommended for optimal performance. Overall, our findings suggest that the Bayesian extension of the c-chart provides a promising alternative for enhanced process monitoring and control. Full article

In this article, we establish new distribution-free Shewhart-type control charts based on rank sum statistics with signaling multiple scans-type rules. More precisely, two Wilcoxon-type chart statistics are considered in order to formulate the decision rule of the proposed monitoring scheme. In order to enhance the performance of the new nonparametric control charts, multiple scans-type rules are activated, which make the proposed chart more sensitive in detecting possible shifts of the underlying distribution. The appraisal of the proposed monitoring scheme is accomplished with the aid of the corresponding run length distribution under both in- and out-of-control cases. Thereof, exact formulae for the variance of the run length distribution and the average run length (ARL) of the proposed monitoring schemes are derived. A numerical investigation is carried out and depicts that the proposed schemes acquire better performance towards their competitors. Full article

The time-between-events idea is commonly used for monitoring high-quality processes. This study aims to monitor the increase and/or decrease in the process mean rapidly using a one-sided exponentially weighted moving average (EWMA) chart for the detection of upward or downward mean shifts using a truncated gamma distribution. The use of the truncation method helps to enhance and improve the sensitivity of the proposed chart. The performance of the proposed chart with known and estimated parameters is analyzed by using the run length properties, including the average run length (ARL) and standard deviation run length (SDRL), through extensive Monte Carlo simulation. The numerical results show that the proposed scheme is more sensitive than the existing ones. Finally, the chart is implemented in real-world situations to highlight the significance of the proposed chart. Full article

Statistical process control (SPC) is used for monitoring and detecting anomalies in processes in the areas of manufacturing, environmental studies, economics, and healthcare, among others. Herein, we introduce an innovative SPC approach via mathematical modeling and report on its application via simulation studies to examine its suitability for monitoring processes involving correlated data running on advanced control charts. Specifically, an approach for detecting small to moderate shifts in the mean of a process running on a homogenously weighted moving average (HWMA) control chart, which is symmetric about the center line with upper and lower control limits, is of particular interest. A mathematical model for the average run length (ARL) of a moving average process with exogenous variables (MAX) focused only on the zero-state performance of the HWMA control chart is derived based on explicit formulas. The performance of our approach was investigated in terms of the ARL, the standard deviation of the run length (SDRL), and the median run length (MRL). Numerical examples are given to illustrate the efficacy of the proposed method. A detailed comparative analysis of our method for processes on HWMA and cumulative sum (CUSUM) control charts was conducted for process mean shifts in many situations. For several values of the design parameters, the performances of these two control charts are also compared in terms of the expected ARL (EARL), expected SDRL (ESDRL), and expected MRL (EMRL). It was found that the performance of the HWMA control chart was superior to that of the CUSUM control chart for several process mean shift sizes. Finally, the applicability of our method on a HWMA control chart is provided based on a real-world economic process. Full article

Statistical process control (SPC) is one of the most powerful techniques for improving quality, as it is able to detect special causes of problems in processes, products and services with a remarkable degree of accuracy. Among SPC tools, $\overline{\mathrm{X}}$ and R control charts are widely employed in process monitoring. However, scenarios involving vague, imprecise and even subjective data require a type-2 fuzzy set approach. Thus, $\overline{\mathrm{X}}$ and R control charts should be coupled with interval type-2 triangular fuzzy numbers (IT2TFN) in order to add further information to traditional control charts. This paper proposes a performance analysis of IT2TFN and $\overline{\mathrm{X}}$ and R control charts by means of average run length (ARL), standard deviation of the run length (SDRL) and RL percentile. Computer simulations were carried out considering 10,000 runs to obtain ARL, SDRL and the 5th, 25th, 50th, 75th and 95th RL percentiles. Simulation results reveal that the proposed control charts increased fault detection capability (speed of response) and slightly reduced the number of false alarms in processes under control. Moreover, it was observed that, in addition to superior performance, IT2TFN $\overline{\mathrm{X}}$-R control charts proved to be more robust and flexible when compared to traditional control charts. Full article

Poisson-Exponentially Weighted Moving Average (PEWMA) charts are one of the most frequently used control charts for monitoring count data. But as real-world data often shows overdispersion—prevalent in manufacturing, health care, economics, and marketing—the standard Poisson distribution falls short. One of the ways to tackle overdispersion is to use Poisson mixture distributions. Our study examines Average Run Length (ARL) performance in the presence of Poisson mixture distribution in the PEWMA control charts. Through meticulously designed experiments, we explore different control parameter combinations and employ simulation to evaluate the process. Our graphs illustrate the performance of the PEWMA control chart, offering desired in-control ARL across parameter combinations. Finally, the performance of the PEWMA control chart is presented for the real process data of fastener production. Full article

Exponentially weighted moving average (EWMA) and Shewhart control charts are commonly utilized to detect the small to moderate and large shifts in the process mean, respectively. This article introduces a novel Bayesian AEWMA control chart that employs various loss functions (LFs), including square error loss function (SELF) and LINEX loss function (LLF). The control chart incorporates an informative prior for posterior and posterior predictive distributions. Additionally, the control chart utilizes various paired ranked set sampling (PRSS) schemes to improve its accuracy and effectiveness. The average run length (ARL) and standard deviation of run length (SDRL) are used to evaluate the performance of the suggested control chart. Monte Carlo simulations are conducted to compare the performance of the proposed approach to other control charts. The results show that the proposed method outperforms in identifying out-of-control signals, particularly under PRSS schemes compared to simple random sampling (SRS). The proposed CCs effectiveness was validated using a real-life semiconductor manufacturing application, utilizing different PRSS schemes. The performance of the Bayesian AEWMA CC was evaluated, demonstrating its superiority in detecting out-of-control signs compared to existing CCs. This study introduces an innovative method incorporating various LFs and PRSS schemes, providing an enhanced and efficient approach for identifying shifts in the process mean. Full article

The Laney p′ control chart is a new type of attribute control chart that can be applied in situations where the process exhibits either overdispersion or underdispersion. While it has gained acceptance in the industry, there is still limited knowledge about its effectiveness in detecting process variation. It is well known that before applying a control chart, understanding its performance is crucial, especially when the parameters of the control chart need to be estimated from historical data. In this study, we used simulations to investigate the ability of the Laney p′ control chart to detect process variations when the parameters are estimated. We designed appropriate experiments to assess the impact of overdispersion on the average run length (ARL) performance. In this study, we assumed that the overdispersion comes from the variation in the mean fraction nonconforming of each sample. The mean value varies according to a uniform distribution. This study evaluated the performance of the Laney $p^{\prime }$ control chart using the average of the ARL (AARL) and the standard deviation of the ARL (SDARL). Additionally, real-world data were utilized to illustrate the practical applications of the Laney $p^{\prime }$ control chart in the PCB and IC substrate industries. The research findings can serve as valuable guidance for practical implementation. Full article

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length. Full article

The global navigation satellite system (GNSS), as a high-time resolution and high-precision measurement technology, has been widely used in the field of deformation monitoring. Owing to the influence of uncontrollable factors, there are inevitably some abnormal data in the GNSS monitoring series. Thus, it is necessary to detect and identify abnormal data in the GNSS monitoring series to improve the accuracy and reliability of the deformation disaster law analysis and warning. Many methods can be used to detect abnormal data, among which the statistical process control theory, represented by the cumulative sum (CUSUM), is widely used. CUSUM usually constructs statistics and determines control limits based on the threshold criteria of the average run length (ARL) and then uses the control limits to identify abnormal data in CUSUM statistics. However, different degrees of the ‘trailing’ phenomenon exist in the interval of abnormal data identified by the algorithm, leading to a higher false alarm rate. Therefore, we propose an improved CUSUM method that uses breaks for additive season and trend (BFAST) instead of ARL-based control limits to identify abnormal data in CUSUM statistics to improve the accuracy of identification. The improved CUSUM method is used to detect abnormal data in the GNSS coordinate series. The results show that compared with CUSUM, the improved CUSUM method shows stronger robustness, more accurate detection of abnormal data, and a significantly lower false alarm rate. Full article

In statistical process control, the control charts are an effective tool to monitor the process. When the process is examined based on an exponential family distributed response variable along with a single explanatory variable, the generalized linear model (GLM) provides better estimates and GLM-based charts are preferred. This study is designed to propose GLM-based control charts using different link functions (i.e., logit, probit, c-log-log, and cauchit) with the binary response variable. The Pearson residuals (PR)- and deviance residuals (DR)-based control charts for logistic regression are proposed under different link functions. For evaluation purposes, a simulation study is designed to evaluate the performance of the proposed control charts. The results are compared based on the average run length (ARL). Moreover, the proposed charts are implemented on a real application for COVID-19 death monitoring. The Monte Carlo simulation study and real applications show that the performance of the model-based control charts with the c-log-log link function gives a better performance as compared to model-based control charts with other link functions. Full article