Exponentially weighted moving average chart using zero-inflated negative binomial distribution

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are used to detect smaller shifts in process parameters. The usual EWMA and CUSUM charts depend on the normality assumption for a better detection ability. This study proposes an efficient EWMA control chart based on the spirit of Tukey control chart, especially designed for skewed distributions. The performance of the proposed and the competing charts is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). We have observed that the proposed chart is quite efficient at detecting process shifts of smaller magnitude, especially for skewed distributions. For practical considerations, the proposed chart is implemented at aerospace manufacturing data on industrial production index.

Exponentially weighted moving average (EWMA) control charts are consistently used for the detection of small shifts contrary to Shewhart charts, which are commonly used for the detection of large shifts in the process. There are many interesting features of EWMA charts that have been studied for complete data in the literature. The aim of present study is to introduce and compare the double exponentially weighted moving average (DEWMA) and EWMA control charts under type-I censoring for Poisson-exponential distribution. The monitoring of mean level shifts using censored data is of a great interest in many applied problems. Moreover, a new idea of conditional median is introduced and further compared with the existing conditional expected values approach for monitoring the small mean level shifts. The performance of the DEWMA and EWMA charts is evaluated using the average run length, expected quadratic loss, and performance comparison index measures. The optimum sample size comparisons for the specified and unspecified parameters are also part of this study. Two applications for practical considerations are also discussed. It is observed that different censoring rates and the size of shifts significantly affect the performance of the EWMA and DEWMA charts. Copyright © 2016 John Wiley & Sons, Ltd.

Exponentially weighted moving average (EWMA) control chart can be designed to quickly detect small shifts in the mean of a sequence of independent normal observations. But this chart cannot perform well for skewed distribution. The main goal of this article is to suggest an EWMA control chart method that can be used to monitoring small shifts in a skewed distribution. Weighted variance method is introduced to construct a kind of EWMA chart for skewed distribution and the optimization design of this chart is given by using average run length as a performance assessment criteria. Pair of asymmetry control limits could be evaluated by sample dates in skewed distribution. The advantage of this method in detecting little drift for skewed distribution was illustrated by comparing with others control charts.

ABSTRACTRuns rules are usually used with Shewhart-type charts to enhance the charts' sensitivities toward small and moderate shifts. Abbas et al. in 2011 took it a step further by proposing two runs rules schemes, applied to the exponentially weighted moving average (EWMA) chart and evaluated their average run length (ARL) performances using simulation. They showed that the proposed schemes are superior to the classical EWMA chart and other schemes being investigated. Besides pointing out some erroneous ARL and standard deviation of the run length (SDRL) computations in Abbas et al., this paper presents a Markov chain approach for computing the ARL, percentiles of the run length (RL) distribution and SDRL, for the two runs rules schemes of Abbas et al. Using Markov chain, we also propose two combined runs rules EWMA schemes to quicken the two schemes of Abbas et al. in responding to large shifts. The runs rules (basic and combined rules) EWMA schemes will be compared with some existing control charting methods, where the former charts are shown to prevail.

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

Rational subgroups of size n = 1 are frequently encountered in process monitoring and control. The Shewhart control chart for individuals is often used in these situations. It is well-known that the in-control average run length (ARL) of this chart is 370.4 under the assumption that the observations are selected at random from a normal population. When the assumption of normality is violated, the ARL of the individuals control chart is adversely affected. We show that an exponentially weighted moving average (EWMA) control chart can be designed so that it is robust to the normality assumption, that is, so that the in-control ARL is reasonably close to the normal-theory value for both skewed and heavy-tailed symmetric non-normal distributions. The EWMA chart also performs quite well in detecting shifts in the process mean.

The average run length (ARL), the average number of in-control signals before an out-of-control signal occurs, is a critical measure of the performance of a control chart. Various methods have been explored for estimating the ARL, including Markov chain-based approximation, integration method, and the Monte Carlo method, especially for time-dependent charting statistics. Although computationally expensive, the Monte Carlo method is generic and applicable to all control charts. Typically, it involves choosing the maximum run length in advance and discarding iterations that fail to produce out-of-control signals to accommodate some unusually lengthy runs. However, these discarded runs provide information for estimating the run length. This paper introduces a new Monte Carlo approximation that retains failed iterations as Type I censored observations for ARL estimation. Our approach relies on the memoryless expectation of the run length distribution to have a simple and efficient ARL estimator. This assumption is necessary for mean estimation in Type I censored data and aligns with existing ARL approximations used in popular control charts like Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts. Numerical simulations demonstrate our method’s computational and statistical efficiency across the mean, median, EWMA, and CUSUM charts.

Statistical process control (SPC) is the method that monitors process quality characteristics. Through control charts, one can detect whether the present process malfunction. However, some annoyances may arise while the engineers need to choose appropriately control chart under different levels of process variation. The Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely used for monitoring semiconductor manufacturing processes. Generally weighted moving average (GWMA) control chart is a new method of SPC, which was proposed by Sheu and Lin (2003). The main objective of this research is using step-by-step procedures to present a comparative study of the monitoring performance for Shewhart, CUSUM, EWMA and GWMA control charts. According to a specified in-control average run length (ARL), we determine the parameters of each control chart based on the Monte Carlo numerical simulation. The setting parameters in each control chart sre displayed and tabulated. While the process means or the process standard deviations are changing in different levels, the performance of each weighted control chart can be then compared by using the ARL. A rule of thumb for selecting better control schemes is provided as a truthfully reference to help engineers in choosing the more appropriate control charts immediately when the assignable causes occurred.

This study aimed to design an exponentially weighted moving average (EWMA) chart for the quality review of nuchal translucency (NT) and to assess its performance compared with the methods currently in use: retrospective distribution-based methods and the cumulative sum (CUSUM) chart. The EWMA model was designed for NT quality review using simulation. The NT measurements obtained during routine first-trimester screening in our centre over a two-and-a-half-year period were retrieved from the database. The NT distribution parameters, EWMA and CUSUM chart were established, and the methods were compared. On the basis of the results from the simulation, the optimal EWMA settings were established. A set of 9338 NT measurements obtained from nine sonographers was used to construct the EWMA and CUSUM charts and to calculate the distribution parameters. Distribution-based methods were unable to reveal the temporal periods of poor performance. The EWMA model agreed closely with the CUSUM but had the advantage promptly indicating when the process returned to an in-control state, thus extending its use to long-term prospective and retrospective quality assessments. The EWMA provides a universal, easy and efficient tool for NT quality review when the prompt and effective detection of suboptimal performance is desired.

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.

New extended exponentially weighted moving average control chart for monitoring process mean

This article introduces Bayesian predictive monitoring of time-between-events using Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charts with predictive control limits. It is shown that the proposed methodology not only overcomes the requirement of a large Phase-I data set to establish control limits, but also feasible for online process monitoring. In addition to Bayesian memory-type charts with dynamic control limits, a comparison of the frequentist sequential charts, designed by using the unbiased and biased estimator of the process parameter, is also given in this article. For the performance evaluation of the predictive TBE chart in the presence of practitioner-to-practitioner variability, we use the average of the in-control average run length (AARL) and the standard deviation of the in-control run length (SDARL).

PM2.5 air pollution poses significant health risks, particularly in urban areas such as Jakarta, where concentrations frequently surpass acceptable levels due to rapid urbanization. This study addresses autocorrelation in air quality data and evaluates the monitoring performance of XGBoost and Support Vector Regression (SVR) models using Individual and Exponentially Weighted Moving Average (EWMA) Charts. PM2.5 levels were obtained from Jakarta's Air Quality Index. The findings reveal that the SVR model effectively manages autocorrelation, while the combination of XGBoost and the EWMA chart yielded superior monitoring performance. Specifically, this approach detected only one out-of-control (OOC) point in Phase II and none in Phase I, with identified shifts ranging from moderate to large. Overall, the XGBoost and EWMA chart integration offers a robust solution for precise air quality monitoring and minimizes false alarms. The identification of OOC points provides actionable insights by highlighting significant deviations in air quality data that may require immediate intervention. Key points:•SVR and XGBoost model regression was introduced to enhance forecasting accuracy.•EWMA chart based on XGBoost residuals has better monitoring results.

The exponentially weighted moving average (EWMA) control charts with variable sampling intervals (VSIs) have been shown to be substantially quicker than the fixed sampling intervals (FSI) EWMA control charts in detecting process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the performances of the EWMA and combined X¯–EWMA control charts with VSIs are evaluated under non-normality. It is shown that adding the VSI feature to the EWMA control charts results in very substantial decreases in the expected time to detect shifts in process mean under both normality and non-normality. However, the combined X¯–EWMA chart has its false alarm rate and its detection ability is affected if the process data are not normally distributed.

The exponentially weighted moving average (EWMA) control chart is very effective in detecting small shifts in process mean or variance, but so far has not been well presented in the field of analytical chemistry. The main difference from the Shewhart chart is that the EWMA chart combines current data with historical observations by essentially taking a weighted average with weighting factor w of the most current sample observations and historical observations. We show that the EWMA chart with 0.05 < w < 0.20 is more effective in detecting small shifts in mean and variance than the Shewhart chart. In addition, the EWMA chart can also be used to forecast the observation in the next period, which can help analysts take preventive actions before process departures to the out-of-control state. Another advantage of using the EWMA chart is its good performance for observations that are not normally distributed or are autocorrelated.