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In this article, we develop a new control chart based on the Exponentially Weighted Moving Average (EWMA) statistic, termed the New Extended Exponentially Weighted Moving Average (NEEWMA) statistic, designed to recognize slight changes in the process mean. We derive expressions for the mean and variance of the NEEWMA statistic, ensuring an unbiased estimation of the mean, with simulation results showing lower variance compared to traditional EWMA charts. Evaluating its performance using Average Run Length (ARL), our analysis reveals that the NEEWMA control chart outperforms EWMA and Extended EWMA (EEWMA) charts in swiftly recognizing shifts in the process mean. Illustrating its operational methodology through Monte Carlo simulations, an illustrative example using practical data is also provided to showcase its effectiveness.

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In various practical situations, the information about the process distribution is sometimes partially or completely unavailable. In these instances, practitioners prefer to use nonparametric charts as they don't restrict the assumption of normality or specific distribution. In this current article, a nonparametric double homogeneously weighted moving average control chart based on the Wilcoxon signed-rank statistic is developed for monitoring the location parameter of the process. The run-length profiles of the newly developed chart are obtained by using Monte Carlo simulations. Comparisons are made based on various performance metrics of run-length distribution among proposed and existing nonparametric counterparts charts. The extra quadratic loss is used to evaluate the overall performance of the proposed and existing charts. The newly developed scheme showed comparatively better results than its existing counterparts. For practical implementation of the suggested scheme, the real-world dataset related to the inside diameter of the automobile piston rings is also used.

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This research presents a new adaptive exponentially weighted moving average control chart, known as the coefficient of variation (CV) EWMA statistic to study the relative process variability. The production process CV monitoring is a long-term process observation with an unstable mean. Therefore, a new modified adaptive exponentially weighted moving average (AAEWMA) CV monitoring chart using a novel function hereafter referred to as the "AAEWMA CV" monitoring control chart. the novelty of the suggested AAEWMA CV chart statistic is to identify the infrequent process CV changes. A continuous function is suggested to be used to adapt the plotting statistic smoothing constant value as per the process estimated shift size that arises in the CV parametric values. The Monte Carlo simulation method is used to compute the run-length values, which are used to analyze efficiency. The existing AEWMA CV chart is less effective than the proposed AAEWMA CV chart. An industrial data example is used to examine the strength of the proposed AAEWMA CV chart and to clarify the implementation specifics which is provided in the example section. The results strongly recommend the implementation of the proposed AAEWMA CV control chart.

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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-S2 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.

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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.

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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.

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Control charts are a statistical approach for monitoring cancer data that can assist discover patterns, trends, and unusual deviations in cancer-related data across time. To detect deviations from predicted patterns, control charts are extensively used in quality control and process management. Control charts may be used to track numerous parameters in cancer data, such as incidence rates, death rates, survival time, recovery time, and other related indicators. In this study, CDEC chart is proposed to monitor the cancer patients recovery time censored data. This paper presents a composite dual exponentially weighted moving average Cumulative sum (CDEC) control chart for monitoring cancer patients recovery time censored data. This approach seeks to detect changes in the mean recovery time of cancer patients which usually follows Weibull lifetimes. The results are calculated using type I censored data under known and estimated parameter conditions. We combine the conditional expected value (CEV) and conditional median (CM) approaches, which are extensively used in statistical analysis to determine the central tendency of a dataset, to create an efficient control chart. The suggested chart's performance is assessed using the average run length (ARL), which evaluates how efficiently the chart can detect a change in the process mean. The CDEC chart is compared to existing control charts. A simulation study and a real-world data set related to cancer patients recovery time censored data is used for results illustration. The proposed CDEC control chart is developed for the data monitoring when complete information about the patients are not available. So, instead of doping the patients information we can used the proposed chart to monitor the patients information even if it is censored. The authors conclude that the suggested CDEC chart is more efficient than competitor control charts for monitoring cancer patients recovery time censored data. Overall, this study introduces an efficient new approach for cancer patients recovery time censored data, which might have significant effect on quality control and process improvement across a wide range of healthcare and medical studies.

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In recent years, with the increasing number and complexity of infectious diseases, the idea of using control charts to monitor public health and disease has been proposed. In this paper, we study multivariate control charts for monitoring a bivariate integer-valued autocorrelation process with bivariate Poisson distribution and select the optimal control scheme by comparing the performance of control charts. Furthermore, the meningococcal patient event in two states in Australia serves as an example to illustrate the application of these methods. The results show that the D exponentially weighted moving average control scheme can detect the changes in the mean value faster, which is a significant advantage.

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In the present article, a double generally weighted moving average (DGWMA) control chart based on a three-parameter logarithmic transformation is proposed for monitoring the process variability, namely the S2-DGWMA chart. Monte-Carlo simulations are utilized in order to evaluate the run-length performance of the S2-DGWMA chart. In addition, a detailed comparative study is conducted to compare the performance of the S2-DGWMA chart with several well-known memory-type control charts in the literature. The comparisons indicate that the proposed one is more efficient in detecting small shifts, while it is more sensitive in identifying upward shifts in the process variability. A real data example is given to present the implementation of the new S2-DGWMA chart.

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In competitive business, such as insurance and telecommunications, customers can easily replace one provider for another, which leads to customer attrition. Keeping customer attrition rate low is crucial for companies, since retaining a customer is more profitable than recruiting a new one. As a main statistical process control (SPC) method, the CUSUM scheme is able to detect small and persistent shifts in customer attrition. However, customer attrition summaries are typically available on an uneven time scale (e.g. 4-week and 5-week 'business month'), which may not satisfy the assumptions of traditional CUSUM designs. This paper mainly develops a latent CUSUM chart based on an exponential model for monitoring 'monthly' customer attrition, under varying time scales. Both maximum likelihood and least squares methods are studied, where the former mostly performs better and the latter is advantageous for quite small shifts. We apply a Markov chain algorithm to obtain the average run length (ARL), make calibrations for different combinations of parameters, and present reference tables of cutoffs. Three more complicated models are considered to test the robustness of deviations from the initial model. Furthermore, a real example of monitoring monthly customer attrition from a Chinese insurance company is used to illustrate the scheme.

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A useful tool that has gained popularity in the Quality Control area is the control chart which monitors a process over time, identifies potential changes, understands variations, and eventually improves the quality and performance of the process. This article introduces a new class of multivariate semiparametric control charts for monitoring multivariate mixed-type data, which comprise both continuous and discrete random variables (rvs). Our methodology leverages ideas from clustering and Statistical Process Control to develop control charts for MIxed-type data. We propose four control chart schemes based on modified versions of the KAy-means for MIxed LArge KAMILA data clustering algorithm, where we assume that the two existing clusters represent the reference and the test sample. The charts are semiparametric, the continuous rvs follow a distribution that belongs in the class of elliptical distributions. Categorical scale rvs follow a multinomial distribution. We present the algorithmic procedures and study the characteristics of the new control charts. The performance of the proposed schemes is evaluated on the basis of the False Alarm Rate and in-control Average Run Length. Finally, we demonstrate the effectiveness and applicability of our proposed methods utilizing real-world data.

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Control charts are widely known quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum double generally weighted moving average chart (referred as Max-DGWMA), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed Max-DGWMA chart is compared with that of the Max-EWMA, Max-DEWMA, Max-GWMA and SS-DGWMA charts, using time-varying control limits, through Monte-Carlo simulations. The comparisons reveal that the proposed chart is more efficient than the Max-EWMA, Max-DEWMA and Max-GWMA charts, while it is comparable with the SS-DGWMA chart. An automotive industry application is presented in order to implement the Max-DGWMA chart. The goal is to establish statistical control of the manufacturing process of the automobile engine piston rings. The source of the out-of-control signals is interpreted and the efficiency of the proposed chart in detecting shifts faster is evident.

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In this work, we develop and study upper and lower one-sided EWMA control charts for monitoring correlated counts with finite range. Often in practice, data of that kind can be adequately described by a first-order binomial or beta-binomial autoregressive model. Especially, when there is evidence that data demonstrate extra-binomial variation, the latter model is preferable than the former. The proposed charts can be used for detecting upward or downward shifts in process mean level. Practical guidelines concerning the statistical design of the proposed charts are given, while the effect of the extra-binomial variation is investigated as well. Comparisons with existing control charting procedures are also provided. Finally, an illustrative real-data example is also given.

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A generalization of moving average (MA) control chart for the exponential distribution under classical statistics is presented in this article. The designing of the MA control chart for the exponential distribution under neutrosophic statistics is also presented. A Monte Carlo simulation under neutrosophic is introduced and applied to determine the neutrosophic control limits coefficients and neutrosophic average run length and neutrosophic standard deviation for various shifts. The application of the proposed chart is given using Betaine data. The comparison and real example studies show the efficiency of the proposed chart over the existing charts.

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In the context of public health surveillance, the aim is to monitor the occurrence of health-related events. Among them, statistical process monitoring focuses very often on the monitoring of rates and proportions (i.e. values in (0,1)) such as the proportion of patients with a specific disease. A popular control chart that is able to detect quickly small to moderate shifts in process parameters is the exponentially weighed moving average control chart. There are various models that are used to describe values in (0,1). However, especially in the case of rare health events, zero values occur very frequently which, for example, denote the absence of the disease. In this paper, we study the performance and the statistical design of exponentially weighed moving average control charts for monitoring proportions that arise in a health-related framework. The proposed chart is based on the zero-inflated Beta distribution, a mixed (discrete-continuous) distribution, suitable for modelling data in [0,1). We use a Markov chain method to study the run length distribution of the exponentially weighed moving average chart. Also, we investigate the statistical design as well as the performance of the proposed charts. Comparisons with a Shewhart-type chart are also given. Finally, we provide an example for the practical implementation of the proposed charts.

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The improvement of surgical quality and the corresponding early detection of its changes is of increasing importance. To this end, sequential monitoring procedures such as the risk-adjusted CUmulative SUM chart are frequently applied. The patient risk score population (patient mix), which considers the patients' perioperative risk, is a core component for this type of quality control chart. Consequently, it is important to be able to adapt different shapes of patient mixes and determine their impact on the monitoring scheme. This article proposes a framework for modeling the patient mix by a discrete beta-binomial and a continuous beta distribution for risk-adjusted CUSUM charts. Since the model-based approach is not limited by data availability, any patient mix can be analyzed. We examine the effects on the control chart's false alarm behavior for more than 100,000 different scenarios for a cardiac surgery data set. Our study finds a negative relationship between the average risk score and the number of false alarms. The results indicate that a changing patient mix has a considerable impact and, in some cases, almost doubles the number of expected false alarms.

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The uncertainty/indeterminate in control chart parameter/observations affects the performance of the control chart. This paper addresses the indeterminacy and its effect on the Shewhart X-bar control using multiple dependent state repetitive sampling. The probabilities and neutrosophic average run length for in-control and out-of-control processes are derived. The tables and figures of the proposed chart are presented when uncertainty/indeterminate is present in sample size and proceeding subgroups. The efficiency of the proposed chart is compared with the existing charts and the proposed chart is found to be efficient in terms of neutrosophic average run length.

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BACKGROUND: The influenza surveillance has been received much attention in public health area. For the cases with excessive zeroes, the zero-inflated Poisson process is widely used. However, the traditional control charts based on zero-inflated Poisson model, ignore the association between influenza cases and risk factors, and thus may lead to unexpected mistakes when implementing monitoring charts. METHOD: In this paper, we proposed risk-adjusted zero-inflated Poisson cumulative sum control charts, in which the risk factors were put to adjust the risk of influenza and the adjustment was made by zero-inflated Poisson regression. We respectively proposed the control chart monitoring the parameters individually and simultaneously. RESULTS: The performance of our proposed risk-adjusted zero-inflated Poisson cumulative sum control chart was evaluated and compared with the unadjusted standard cumulative sum control charts in simulation studies. The results show that for different distribution of impact factors and different coefficients, the risk-adjusted cumulative sum charts can generate much less false alarm than the standard ones. Finally, the influenza surveillance data from Hong Kong is used to illustrate the application of the proposed chart. CONCLUSIONS: Our results suggest that the adjusted cumulative sum control chart we proposed is more accurate and credible than the unadjusted standard control charts because of the lower false alarm rate of the adjusted ones. Even the unadjusted control charts may signal a little faster than the adjusted ones, the alarm they raise may have low credibility since they also raise alarm frequently even the processes are in control. Thus we suggest using the risk-adjusted cumulative sum control charts to monitor the influenza surveillance data to alert accurately, credibly and relatively quickly.

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A statistically robust set of rules is proposed for trending excursions in environmental monitoring data. These rules were designed to minimize false alarms when the process is in control, but signal quickly when the process goes out of control. An adverse trend is an early warning that the system is drifting from normal operating conditions. Prompt action may prevent further deterioration and avoid costly out-of-specification events. Adverse trends are defined as an alert level excursion rate of >2.5% and an action level excursion rate of >0.15%. These definitions were derived from setting action levels at the 99.85th percentile and alert levels at the 97.5th percentile. These percentiles were chosen because they are functional equivalents of control limits and warning limits used in statistical process control charting, which are set at three and two standard deviations above the mean, respectively. In addition, the U.S. Pharmacopeial recommended microbial recovery rates should also be implemented as trend metrics for microbial environmental monitoring of aseptic processing facilities. Occasional isolated alert level excursions may occur even if the process remains in a state of control. However, repeated alert level excursions occurring at a rate >2.5% indicate the process is changing and the system is drifting from normal operating conditions. An adverse trend of alert level excursions should be investigated for root cause. It is critical to determine if an alert level excursion, at its onset, indicates an adverse trend. A total of 24 rules at various sample sizes were tested for their ability to detect an adverse trend at the onset of an excursion using data obtained over a period of 1 year. The rationale for choosing these rules is described.

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Profile data emerges when the quality of a product or process is characterized by a functional relationship among (input and output) variables. In this paper, we focus on the case where each profile has one response variable Y, one explanatory variable x, and the functional relationship between these two variables can be rather arbitrary. The basic concept can be applied to a much wider case, however. We propose a general method based on the Generalized Likelihood Ratio Test (GLRT) for monitoring of profile data. The proposed method uses nonparametric regression to estimate the on-line profiles and thus does not require any functional form for the profiles. Both Shewhart-type and EWMA-type control charts are considered. The average run length (ARL) performance of the proposed method is studied. It is shown that the proposed GLRT-based control chart can efficiently detect both location and dispersion shifts of the on-line profiles from the baseline profile. An upper control limit (UCL) corresponding to a desired in-control ARL value is constructed.