ABSTRACT Traditional control charts usually fail to perform well in the case of outliers, or when the mean and variability of a process vary at the same time in quality control. In this paper, a very powerful exponentially weighted moving average (EWMA) control chart using the robust coefficient of variation (CV) has been proposed to overcome these hurdles. Unlike approaches that require data transformation or adaptive tuning, the scale‐invariance of the robust CV‐statistic can be used to stabilize the proposed RCV‐EWMA chart, keeping it sensitive in a polluted data setting. Through extensive Monte Carlo simulations, the capabilities of the chart are analyzed in different conditions of contamination levels and shift level. The total key performance indicators, such as Average Run Length (ARL), Standard Deviation of Run Length (SDRL), and Median Run Length (MRL) are given. The findings show that the suggested chart has good in‐control characteristics (ARL = 370) and is a worthwhile chart to detect small‐to‐still shifts despite up to 25% contamination. Its applicability in practice is also confirmed by a real data application that demonstrates how the chart can determine the abnormalities in the processes and be resistant to outliers. The results place the RCV‐EWMA control chart as an effective and dependable modern tool of monitoring processes especially those in very noisy or highly variable conditions.

This paper presents an analytical study of the double modified exponentially weighted moving average (DMEWMA) control chart for monitoring autoregressive integrated (ARI) and autoregressive fractionally integrated (ARFI) processes, with emphasis on its symmetry properties. The explicit formulas for the average run length (ARL) are derived using Fredholm integral equations of the second kind, with existence and uniqueness established via Banach’s fixed-point theorem. The numerical approximations are obtained through the numerical integral equation (NIE) method, and simulations confirm that explicit ARL formulas and the NIE approach yield identical results, validating the theoretical derivations. The results show that symmetry plays a dual role: it ensures performance symmetry in detection across short- and long-memory processes. Comparative studies indicate that for ARI processes, DMEWMA outperforms EWMA and MEWMA for small and moderate shifts, while for ARFI processes, it remains superior to EWMA but shows parity or slight inferiority to MEWMA under certain long-memory conditions. The applications to environmental and economic data illustrate the value of symmetrical control structures in providing robust, unbiased monitoring. With ARL computations completed in under 0.001 s, the DMEWMA chart demonstrates efficiency, balance, and versatility.

ABSTRACT The ratio of two normal random variables (RZ) is widely used to measure the quality characteristic in many fields or processes, including manufacturing, finance, medicine and so on. Monitoring changes in the RZ is of great importance for the timely detection of any problems and prevention of risks in processes. Due to the insensitivity of the Shewhart scheme to small shifts and the Exponentially Weighted Moving Average (EWMA) scheme to large shifts, some pioneer researchers have suggested the combined Shewhart-EWMA scheme for monitoring both small and large shifts. However, this method is gradually being replaced by another more effective and simple method, namely the Adaptive EWMA (AEWMA) scheme. To improve the detection efficiency of existing RZ charts for both small and large shifts, and at the same time without increasing the RZ charts’ complexity, this paper constructs an AEWMA-RZ scheme by introducing an adaptive method. The control limit h, average run length (ARL) and the standard deviation of the run length (SDRL) of the proposed AEWMA-RZ scheme are obtained by numerical Monte Carlo (MC) simulations, and the influence of different parameter combinations on the performance of the proposed AEWMA-RZ scheme is further investigated. A detailed comparison is made between the proposed AEWMA-RZ and two existing RZ monitoring schemes, namely the EWMA-RZ and the combined Shewhart-EWMA-RZ (CSEWMA-RZ) schemes. Simulation results show that the proposed AEWMA-RZ scheme is superior to the EWMA-RZ and CSEWMA-RZ schemes. Finally an example of the food industry ends the paper.

One well-known process detection tool that is sensitive to even little shift changes in the process is the Double Exponentially Weighted Moving Average (DEWMA) control chart. The present study aims to provide exact average run length (ARL) on the DEWMA chart under the data that is underlying the quadratic trend autoregressive (AR) model. At that point, the computed ARL via the numerical integral equation (NIE) technique was compared in terms of accuracy to the exact one that was developed by using the percentage accuracy (%Acc). And then, the computational times of both were also compared. The results revealed that the ARL results of exact ARL and ARL via the NIE method show hardly any difference in terms of accuracy, but exact ARL outperformed in terms of computational times that were computed instantly, whereas the other way spent approximately 2-3 seconds computing. Thereafter, the proposed ARL operating on the DEWMA chart was compared to the CUSUM and EEWMA charts. It was found to be more effective in terms of detection performance. Especially when there are little shift changes in the process. The run length formulas, which are the standard deviation run length (SDRL) and the median run length (MRL), were measures of sensitivity evaluation and were used to verify their capability. The sensitivity of detecting changes of exact ARL running on the DEWMA chart was illustrated by the real data utilized in fields of economics about natural gas importing in Thailand (Unit: 100 MMSCFD at heat value of natural gas 1,000 BTU/SCF). Apparently, the exact ARL of the DEWMA chart is an excellent choice to detect small shift changes under this scenario, which represents properties as a quadratic trend AR model.

This study introduces a novel Variable Sample Size Exponentially Weighted Moving Average (VSS-EWMA) control chart for monitoring the coefficient of variation, termed as Dynamic Adaptive CV (DACV) chart. Tailored for dynamic production settings where both the process mean and variability are subject to change, the proposed chart integrates an adaptive sampling strategy within the EWMA framework, allowing real-time adjustment of sample size in response to process conditions. Comparative analysis with the conventional Fixed Sample Size EWMA (FEWMA) chart reveals that DACV chart exhibits enhanced sensitivity in detecting small to moderate shifts in variability. Its performance is rigorously evaluated using Average Run Length (ARL), Standard Deviation of Run Length (SDRL), and run-length percentiles. Visualizations through heat maps further affirm its robustness across a wide range of shift magnitudes and smoothing parameters. A real-world application using semiconductor manufacturing data demonstrates the practical utility of DACV chart, underscoring its potential in contemporary quality monitoring systems.

Control charts with run rules improve the detection of small process shifts, helping identify assignable causes early. Run rules define data patterns that trigger alerts, making charts more responsive, especially where traditional Shewhart charts may miss minor changes. With advancements in automation and data collection, high-quality control tools have gained importance. One such tool is the charts, ideal for high-yield processes with rare defects. It counts conforming items before nonconforming ones, making it effective for low-defect environments. This study explores how different run rules affect the performance of the charts with Markov dependency, which models the correlation between products. Through simulations and average run length analysis, the study offers insights and recommendations to improve chart design and process monitoring.

In high-yield processes, the Shewhart type c-chart and u-chart are applicable for monitoring the rate of nonconformities. However, the effectiveness of these control charts diminishes significantly when the nonconformity rate is extremely low. To overcome the limitations of the c-chart, the cumulative quantity control chart is recommended for scenarios where the defect rate is very low. In this article, the m-of-m cumulative quantity control chart is proposed to improve the performance of the cumulative quantity control chart. The proposed control chart is designed to detect upward, downward, and both sided shifts in a process parameter. The Markov chain approach is used to compute the average run length of the proposed m-of-m control charts. A comparative analysis has been conducted to identify the most effective control chart. The performance of the proposed control charts is found to be superior to that of the cumulative quantity control chart in detecting upward shifts, while it is less effective for downward shifts. The practical application of the proposed control chart is demonstrated through an example.

The recently released third draft version of ICH E6(R3) has a great emphasis on Risk-Based Quality Management (RBQM) principles and includes the concept of Quality Tolerance Limits (QTLs) that are regarded as an example of predefined acceptable ranges that, if exceeded, might potentially effect participants safety or the reliability of trial results. This change allows for greater flexibility and adaptability in managing quality and risks in clinical trials, leading to more effective and efficient trials. In this paper, we conduct simulations to evaluate statistical methods, including statistical process control and Bayesian methods, for implementing QTLs in clinical trials. We evaluate the operating characteristics such as average run length, alarm rate, false alarm rate, and other performance metrics. Generally, all methods performed better with larger sample sizes and higher expected probabilities. There was greater variability in performance across methods early in the review cycle when sample sizes were small. Statistical process control methods performed better in most scenarios, while Bayesian methods were more effective at detecting an out-of-control process earlier for lower expected probabilities. Not all scenarios could be investigated; thus, method selection depends on factors like assumptions, statistical complexity, and feasibility.

Statistical process control may lead to false detection results in the presence of measurement error, so it is necessary to deal with the effect of measurement error. The Bayesian exponentially weighted moving average (EWMA) variability control chart, first proposed by Lin et al., is a distribution-free control chart, and it can effectively monitor process variance even if the process skewness varies with time. This paper investigates the influence of measurement error on the Bayesian EWMA variability control chart, and it proposes two designs for the Bayesian EWMA variability control chart in the presence of measurement error. One is to modify the control limits based on the biased error-prone monitoring statistics, called the error-embedded control chart. The other is to design the control limits based on the error-corrected monitoring statistics, called the error-corrected control chart. Simulation results prove that both of the proposed control charts are reliable and have good detection performance in the presence of measurement error. Moreover, the average run lengths of the proposed control charts are exactly the same, indicating that both of them are equivalent control charts. Comparison results show that the existing control chart in Lin et al. is not in-control robust and fails to detect a downward shift in process variance when measurement error is present. Thus, using the error-embedded control chart or the error-corrected control chart to monitor processes with measurement errors is reliable and effective. Moreover, the proposed control charts, where π11 = 1 and π10 = 0, can be applied to monitor processes without measurement errors since their detection performance is equal to that of the existing control chart in Lin et al. Finally, we demonstrate the application of the error-embedded control chart and the error-corrected control chart to analyze the data from the service time system of a bank branch and the data from a semiconductor manufacturing process, showing that the proposed control charts can indeed be applied to data with measurement errors.

ABSTRACTIn quality control, the resubmission‐based Shewhart control chart has been recognized for its approach of using fixed subgroup parameters to manage process monitoring. However, the rigidity of fixed values for m and n may limit its efficiency in terms of detection speed and sample economy. This study addresses this limitation by proposing an improved control chart that dynamically optimizes the subgroup parameters. Using an optimization tool to adjust m and n while ensuring a minimum in‐control average run length, the proposed method seeks to minimize both the out‐of‐control average run length and the average sample number. Comparative analyses against the resubmission‐based control chart reveal that the adaptive approach offers a more balanced tradeoff between timely detection and resource utilization. The findings suggest that revising the parameter selection framework can enhance process monitoring, making the improved chart a viable alternative for practitioners.

ABSTRACTMost existing control charts are designed for positively autocorrelated count data and seldom address the issue of overdispersion. The log‐linear Poisson autoregression model (LLPAM) can capture overdispersion in count data, accommodate both positive and negative autocorrelations, and incorporate real‐valued covariates. This makes it a more flexible alternative to the standard Poisson model. However, Shewhart‐type charts applied to LLPAM often exhibit inflated false alarm rates and reduced sensitivity to parameter shifts under moderate temporal dependence. To address these limitations, we propose two monitoring schemes based on Pearson residuals (PRs): a Shewhart‐type chart and an exponentially weighted moving average (EWMA) chart. Both methods allow simultaneous monitoring of LLPAM parameters under positive or negative autocorrelation. Simulation studies show that the proposed PR‐based charts consistently outperform the observation‐based Shewhart chart in terms of average run length (ARL), standard deviation of run length (SDRL), median run length (MDRL), and relative mean index (RMI), while maintaining false alarm rates close to nominal levels. An application to Escherichia coli infection data from North Rhine–Westphalia further demonstrates the practical utility of the proposed control charts.

The efficacy of control charts is evaluated using the primary indicator, Average Run Length (ARL), which assesses chart performance and process behavior. This research aims to determine the formula that can be utilized with the Fredholm integral method to compute the ARL base on exponentially weighted moving average (EWMA) chart for auto-regressive moving average process with factor variables (ARMAX (p,q,r)). The fixed-point principle confirmed the solution's being and irreproducibility, validating our proposed formula. Also, numerical methods for integral equations using Gauss-Legendre quadrature were used to estimate ARL so we could compare them with the output from the proposed explicit formula. The validity of the proposed formula was evaluated based on two criteria: accuracy and computational efficiency. We discover that ARL values obtained from the explicit formula are identical to those approximated via the numerical method, yielding an accuracy of 100%. Furthermore, the processing time required to calculate the ARL using the given formula is less than that of the numerical method. Hence, the proposed formula for the ARMAX(p,q,r) process can serve as a substitute for computing ARL values in EWMA chart. An alternative method for estimating ARL is the explicit formula provided for the ARMAX(p,q,r) process, as demonstrated using gasoline price data.

Control charts are essential tools for monitoring the stability of manufacturing processes. However, measurement error can reduce their effectiveness by weakening their ability to detect process shifts. This study introduces an improved version of the Generally Weighted Moving Average (GWMA) chart, called the Auxiliary Information Based GWMA with Measurement Error (AIB-GWMA-ME) chart. This new chart combines auxiliary information with a measurement error adjustment mechanism to improve monitoring accuracy. Three types of measurement error models are considered – namely, the covariate model, multiple measurements model, and linearly increasing variance model. For each model, the statistic of the AIB-GWMA-ME chart is developed, and the corresponding control limits are determined. Monte Carlo simulations are used to assess the chart’s performance based on Average Run Length (ARL). Results show that the AIB-GWMA-ME chart improves sensitivity to small shifts and performs better than existing GWMA and EWMA charts in the presence of measurement error.

This study introduces a novel control charting methodology based on the transmuted weighted exponential distribution (TWED) for monitoring time-between-events (TBE) data in industrial processes. Traditional Shewhart-type charts often rely on assumptions of normality and equal sampling probabilities, limiting their effectiveness in skewed or biased scenarios. The proposed TWED-TBE chart addresses these limitations by incorporating transmutation and weighting parameters, enhancing sensitivity to process shifts. Control limits for the TWED-TBE chart were derived analytically using the exact distribution of the monitoring statistic. Monte Carlo simulations were employed to evaluate chart performance under varying in-control average run lengths ( ). The parametric configuration (area-biased), and yielded superior results in detecting shifts. The chart consistently outperformed existing TBE-based -charts, achieving significantly lower values across a range of shift magnitudes ( to 1.0 ). Percentage reductions in exceeded in small shift scenarios, highlighting the chart's robustness. The proposed chart was further validated using simulated and real-world time-to-failure data. In both cases, TWED-TBE charts effectively identified shifts with greater accuracy and earlier detection compared to traditional methods. The findings confirm the utility of the TWED framework in enhancing the responsiveness of control charts under skewed lifetime data. This approach offers practical benefits for industries requiring reliable early detection of process deviations.

Statistical Process Control is essential for ensuring process stability and detecting variations in a production environment. This study introduces a control chart based on the Exponentially Weighted Moving Average (EWMA) that uses an adaptive sample size. The proposed approach enhances shift detection by dynamically adjusting the sample size in response to changes in process variation. Extensive Monte Carlo simulations were performed to assess the performance of the proposed control chart, focusing on metrics such as the Average Run Length (ARL) and the Standard Deviation of Run Length (SDRL). The findings show that the new chart surpasses both the Fixed Sample Size EWMA (FEWMA) and the Variable Sample Size EWMA charts, particularly in detecting small to moderate shifts in the process. This approach strikes a balance between detection sensitivity and computational efficiency, enabling prompt identification of process changes while maintaining robustness during in-control conditions. To illustrate its practical applicability, a real-world dataset was analyzed, demonstrating the effectiveness of the proposed method in actual process monitoring scenarios.

In the present study, an attempt has been made to develop the tables of constants for quantiles of Frechet distribution using mathematical equivalence with the largest extreme value distribution. The control charts are constructed and compared with traditional sample mean charts and weighted variance control charts using classical and Bayesian estimation techniques. Moreover, average run lengths are used for performance evaluation, which indicate that run lengths based on classical and Bayesian estimators are consistently smaller for the largest extreme value distribution, underscoring its efficacy. Further, robustness of proposed method is tested through sensitivity analysis. Comprehensive simulation study and analysis of real dataset validate the precision of the proposed control charts.

Quick-switch sampling (QSS) systems, which utilize process capability indices (PCIs) as benchmark measures, have garnered substantial attention in recent literature due to their effectiveness in assessing lot quality and cost-effectiveness. Nevertheless, current QSS models exhibit limited adaptability in rule-switching, diminishing their practical utility. In this paper, we introduce variables generalized QSS (GQSS) systems in two distinct forms with the aim of enhancing the rule-switching mechanism inherent in conventional QSS systems. By applying Markov chain theory and mean first passage time concepts, we determine the operational characteristics, average sample number, and average run length functions for GQSS systems based on unilateral PCIs. Furthermore, we develop non-linear optimization models to facilitate optimal system design. Through comprehensive analysis and comparative evaluation, our findings demonstrate that the proposed GQSS systems excel in detecting lot quality degradation while maintaining cost-effectiveness. To validate their feasibility, we present an industrial case study. In conclusion, the proposed GQSS systems offer a more adaptable and versatile rule-switching mechanism compared to existing QSS systems, thereby significantly broadening their practical applicability.

Quality has become crucial for consumers, prompting the need for strict control measures. Statistical Process Control (SPC) is widely used to monitor and improve performance, traditionally assuming independent, normally distributed data. However, real-world data often contains uncertainties from human, measurement, or environmental factors, challenging traditional control chart use such as control charts. To overcome this, fuzzy control limits based on fuzzy set theory are introduced. This study uses -cuts and fuzzy triangular numbers to develop fuzzy charts for monitoring solder paste thickness in integrated circuits. These fuzzy charts prove more effective than traditional ones, yielding lower average run length (ARL) values.

ABSTRACTThe generally weighted moving average (GWMA) control chart has been proposed as a generalization and alternative to the exponentially weighted moving average (EWMA) chart. Proponents of the GWMA claim that it is more efficient in detecting shifts in the process mean than the EWMA. Most research on the GWMA chart compares its out‐of‐control properties against an EWMA chart that is not appropriate for the given situation. Detractors of the GWMA chart point out that (1) the GWMA is usually compared against an EWMA chart that is not ideal for the given situation, (2) the GWMA has no recursive formula so all previous data values must be stored and used to compute the next GWMA chart, and (3) the GWMA can have weights that do not decrease as the age of the data increases. We compare this optimal GWMA chart against the EWMA chart that is optimal for the same shift. For a given shift, a GWMA chart can be constructed that has a shorter cyclic steady‐state average run length than the optimal EWMA chart. The optimal GWMA chart will usually have poor out‐of‐control performance for shifts other than those for which the GWMA was designed to be optimal. The GWMA chart is the preferred chart only in very specific circumstances.

The main objective of this study is to find an explicit formula for the average run length (ARL) of a Homogenously Weighted Moving Average control chart (HWMA) for an autoregressive process with a quadratic trend under zero state. The two-sided HWMA control chart construction procedure is proposed, and the performance of the control chart is measured using the average run length (ARL), standard deviation run length (SDRL), and mean run length (MRL). In addition, the accuracy of the explicit formula for ARL is compared with the accuracy of the numerical integral equation method. In this research, the performance of the HWMA and modified exponential weighted moving average control charts (MEWMA) for quadratic trend AR(1) and AR(3) models at different levels of process average change is compared. The efficacy of these control charts can additionally be assessed by the EARL, ESDRL, and EMRL metrics. The proposed control chart is applied to simulated and actual data, namely the finished goods inventory index of PCBA.