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The study presents a new parameter free adaptive exponentially weighted moving average (AEWMA) control chart tailored for monitoring process dispersion, utilizing an adaptive approach for determining the smoothing constant. This chart is crafted to adeptly detect shifts within anticipated ranges in process dispersion by dynamically computing the smoothing constant. To assess its effectiveness, the chart's performance is measured through concise run-length profiles generated from Monte Carlo simulations. A notable aspect is the incorporation of an unbiased estimator in computing the smoothing constant through the suggested function, thereby improving the chart's capability to identify different levels of increasing and decreasing shifts in process dispersion. The comparison with an established adaptive EWMA-S 2 dispersion chart highlights the considerable efficiency of the proposed chart in addressing diverse magnitudes of process dispersion shifts. Additionally, the study includes an application to a real-life dataset, showcasing the practicality and user-friendly nature of the proposed chart in real-world situations., (© 2024. The Author(s).)

The Max-Mixed EWMA Exponentially Weighted Moving Average (MM EWMA) control chart is a statistical process control technique used for joint monitoring of the mean and variance of a process. This control chart is designed to detect small and moderate shifts in the mean and variance of a process by comparing the maximum of two statistics, one based on the mean and the other on the variance. In this paper, we propose a new MM EWMA control chart. The proposed chart is compared with existing control charts using simulation studies, and the results show that the chart performs better in detecting small and moderate shifts in both the mean and variance. The proposed chart can be helpful in quality control applications, where joint monitoring of mean and variance is necessary to ensure a product's or process's quality. The real-life application of the proposed control chart on yogurt packing in a cup data set shows the outperformance of the MM EWMA control chart. Both simulations & real-life application results demonstrate the better performance of the proposed chart in detecting smaller shifts during the production process., (© 2024. The Author(s).)

This article introduces an adaptive approach within the Bayesian Max-EWMA control chart framework. Various Bayesian loss functions were used to jointly monitor process deviations from the mean and variance of normally distributed processes. Our study proposes the mechanism of using a function-based adaptive method that picks self-adjusting weights incorporated in Bayesian Max-EWMA for the estimation of mean and variance. This adaptive mechanism significantly enhances the effectiveness and sensitivity of the Max-EWMA chart in detecting process shifts in both the mean and dispersion. The Monte Carlo simulation technique was used to calculate the run-length profiles of different combinations. A comparative performance analysis with an existing chart demonstrates its effectiveness. A practical example from the hard-bake process in semiconductor manufacturing is presented for practical context and illustration of the chart settings and performance. The empirical results showcase the superior performance of the Adaptive Bayesian Max-EWMA control chart in identifying out-of-control signals. The chart's ability to jointly monitor the mean and variance of a process, its adaptive nature, and its Bayesian framework make it a useful and effective control chart., (© 2024. The Author(s).)

In the current study, we demonstrate the use of a quality framework to review the process for improving the quality and safety of the patient in the health care department. The researchers paid attention to assessing the performance of the health care service, where the data is usually heterogeneous to patient's health conditions. In our study, the support vector machine (SVM) regression model is used to handle the challenge of adjusting the risk factors attached to the patients. Further, the design of exponentially weighted moving average (EWMA) control charts is proposed based on the residuals obtained through SVM regression model. Analyzing real cardiac surgery patient data, we employed the SVM method to gauge patient condition. The resulting SVM-EWMA chart, fashioned via SVM modeling, revealed superior shift detection capabilities and demonstrated enhanced efficacy compared to the risk-adjusted EWMA control chart., (© 2024. The Author(s).)

The simultaneous monitoring of both the process mean and dispersion has gained considerable attention in statistical process control, especially when the process follows the normal distribution. This paper introduces a novel Bayesian adaptive maximum exponentially weighted moving average (Max-EWMA) control chart, designed to jointly monitor the mean and dispersion of a non-normal process. This is achieved through the utilization of the inverse response function, particularly suitable for processes conforming to a Weibull distribution. To assess the effectiveness of the proposed control chart, we employed the average run length (ARL) and the standard deviation of run length (SDRL). Subsequently, we compared the performance of our proposed control chart with that of an existing Max-EWMA control chart. Our findings suggest that the proposed control chart demonstrates a higher level of sensitivity in detecting out-of-control signals. Finally, to illustrate the effectiveness of our Bayesian Max-EWMA control chart under various Loss Functions (LFs) for a Weibull process, we present a practical case study focusing on the hard-bake process in the semiconductor manufacturing industry. This case study highlights the adaptability of the chart to different scenarios. Our results provide compelling evidence of the exceptional performance of the suggested control chart in rapidly detecting out-of-control signals during the hard-bake process, thereby significantly contributing to the improvement of process monitoring and quality control., (© 2024. The Author(s).)

This paper aims to introduce a novel family of probability distributions by the well-known method of the T-X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan-Quinn information criterion (HQINC), the Cramer-von-Misses (CRMI), and the ANDA (Anderson-Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study., (© 2024. The Author(s).)

The simultaneous monitoring of both process mean and dispersion, particularly in normal processes, has garnered significant attention within the field. In this article, we present a new Bayesian Max-EWMA control chart that is intended to track a non-normal process mean and dispersion simultaneously. This is accomplished through the utilization of the inverse response function, especially in cases where the procedure follows a Weibull distribution. We used the average run length (ARL) and the standard deviation of run length (SDRL) to assess the efficacy of our suggested control chart. Next, we contrast our suggested control chart's performance with an already-existing Max-EWMA control chart. Our results show that compared to the control chart under consideration, the proposed control chart exhibits a higher degree of sensitivity. Finally, we present a useful case study centered around the hard-bake process in the semiconductor manufacturing sector to demonstrate the performance of our Bayesian Max-EWMA control chart under different Loss Functions (LFs) for a Weibull process. The case study highlights how flexible the chart is to various situations. Our results offer strong proof of the outstanding ability of the Bayesian Max-EWMA control chart to quickly identify out-of-control signals during the hard-bake procedure. This in turn significantly contributes to the enhancement of process monitoring and quality control., (© 2024. The Author(s).)

Quality control often employs memory-type control charts, including the exponentially weighted moving average (EWMA) and Shewhart control charts, to identify shifts in the location parameter of a process. This article pioneers a new Bayesian Adaptive EWMA (AEWMA) control chart, built on diverse loss functions (LFs) such as the square error loss function (SELF) and the Linex loss function (LLF). The proposed chart aims to enhance the process of identifying small to moderate as well as significant shifts in the mean, signifying a notable advancement in the field of quality control. These are implemented utilizing an informative prior for both posterior and posterior predictive distributions, employing various paired ranked set sampling (PRSS) schemes. The effectiveness of the suggested chart is appraised using average run length (ARL) and the standard deviation of run length (SDRL). Monte Carlo simulations are employed to contrast the recommended approach against other control charts. The outcomes demonstrate the dignitary performance of the recommended chart in identifying out-of-control signals, especially applying PRSS designs, in comparison to simple random sampling (SRS). Finally, a practical application was conducted in the semiconductor manufacturing context to appraise the efficacy of the offered chart using various paired ranked set sampling strategies. The results reveal that the suggested control chart performed well in capturing the out-of-control signals far better than the already in use control charts. Overall, this study interposes a new technique with diverse LFs and PRSS designs, improving the precision and effectiveness in detecting process mean shifts, thereby contributing to advancements in quality control and process monitoring., (© 2023. The Author(s).)

In this article, we introduce a novel Bayesian Max-EWMA control chart under various loss functions to concurrently monitor the mean and variance of a normally distributed process. The Bayesian Max-EWMA control chart exhibit strong overall performance in detecting shifts in both mean and dispersion across various magnitudes. To evaluate the performance of the proposed control chart, we employ Monte Carlo simulation methods to compute their run length characteristics. We conduct an extensive comparative analysis, contrasting the run length performance of our proposed charts with that of existing ones. Our findings highlight the heightened sensitivity of Bayesian Max-EWMA control chart to shifts of diverse magnitudes. Finally, to illustrate the efficacy of our Bayesian Max-EWMA control chart using various loss functions, we present a practical case study involving the hard-bake process in semiconductor manufacturing. Our results underscore the superior performance of the Bayesian Max-EWMA control chart in detecting out-of-control signals., (© 2023. The Author(s).)

This study introduces the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart within the framework of measurement error, examining two separate loss functions: the squared error loss function and the linex loss function. We conduct an analysis of the posterior and posterior predictive distributions utilizing a conjugate prior. In the presence of measurement error (ME), we employ a linear covariate model to assess the control chart's effectiveness. Additionally, we explore the impacts of measurement error by investigating multiple measurements and a method involving linearly increasing variance. We conduct a Monte Carlo simulation study to assess the control chart's performance under ME, examining its run length profile. Subsequently, we offer a specific numerical instance related to the hard-bake process in semiconductor manufacturing, serving to verify the functionality and practical application of the suggested Bayesian AEWMA control chart when confronted with ME., (© 2023. The Author(s).)

The article introduces a novel Bayesian AEWMA Control Chart that integrates different loss functions (LFs) like the square error loss function and Linex loss function under an informative prior for posterior and posterior predictive distributions, implemented across diverse ranked set sampling (RSS) designs. The main objective is to detect small to moderate shifts in the process mean, with the average run length and standard deviation of run length serving as performance measures. The study employs a hard bake process in semiconductor production to demonstrate the effectiveness of the proposed chart, comparing it with existing control charts through Monte Carlo simulations. The results underscore the superiority of the proposed approach, particularly under RSS designs compared to simple random sampling (SRS), in identifying out-of-control signals. Overall, this study contributes a comprehensive method integrating various LFs and RSS schemes, offering a more precise and efficient approach for detecting shifts in the process mean. Real-world applications highlight the heightened sensitivity of the suggested chart in identifying out-of-control signals compared to existing Bayesian charts using SRS., (© 2023. The Author(s).)

In recent times, there has been a growing focus among researchers on memory-based control charts. The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts and the adaptive control charting approaches got the attention. Control charts are commonly employed to oversee processes, assuming the monitored variable follows a normal distribution. However, it's worth noting that this assumption does not hold true in many real-world situations. The use of the algebraic expression for normalization, which can be used for all kinds of skewed distributions with a closed-form distribution function, using the proposed continuous function to adapt a smoothing constant, motivates this study. In the present manuscript, we design an EWMA statistic-based adaptive control chart to monitor the irregular variations in the mean of two parametric Weibull distribution and use Hasting approximation for normalization. The adaptive control charts are used to update the smoothing constant according to the estimated shift. Here we use the proposed continuous function to adapt the smoothing constant. The average run length and standard deviation of run length are calculated under different parameter settings. The effectiveness of the proposed chart is argued in terms of ARLs over the considered EWMA chart through Monte-Carlo (MC) simulation method. The proposed chart is examined, followed by a real data set to demonstrate the design and application procedures., (© 2023. The Author(s).)

Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production., (© 2023. Springer Nature Limited.)

The objective of this study is to investigate the behavior of the Bayesian exponentially weighted moving average (EWMA) control chart in the presence of measurement error (ME). It explores the impact of different ranked set sampling designs and loss functions on the performance of the control chart when ME is present. The analysis incorporates a covariate model, multiple measurement methods, and a conjugate prior to account for ME. The performance evaluation of the proposed Bayesian EWMA control chart with ME includes metrics such as average run length and standard deviation of run lengths. The findings, obtained through Monte Carlo simulation and real data application, indicated that ME significantly affects the performance of the Bayesian EWMA control chart when RSS schemes are employed. Particularly noteworthy is the superior performance of the median RSS scheme compared to the other two schemes in the presence of ME., (© 2023. Springer Nature Limited.)

The extended exponential weighted moving average (EEWMA) statistic is a memory type statistic that uses past observations along with the current information for the estimation of a population parameter to improve the efficiency of the estimators. This study utilized the EEWMA statistic to estimate the population mean with a suitable auxiliary variable. The ratio and product estimators are proposed for the surveys that are time-based by using current information along with that information. The approximate mean square errors are computed for the proposed memory type estimators and mathematical comparison is discussed to demonstrate the efficiency of the estimator. The simulation study was carried out to evaluate the performance of the proposed memory type estimators. It can be seen from the results that the efficiency of the estimator enhances by utilizing the current sample as well as past information. A real-life example is presented to illustrate the usage of proposed estimators., (© 2023. Springer Nature Limited.)

The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals., (© 2023. The Author(s).)