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The synthetic chart principle proposed by Wu and Spedding (2000) initiated a stream of publications in the control charting literature. Originally, it was claimed that the new chart has superior average run length (ARL) properties. Davis and Woodall (2002) indicated that the synthetic chart is nothing else than a particular runs-rule chart. Moreover, they criticized the design of the performance evaluation and advocated use of the steady-state ARL. The latter measure was used then, e.g., in Wu et al. (2010). In most of the papers on synthetic charts that actually used the steady-state framework, it was not rigorously described. See Khoo et al. (2011) as an exception, where it was revealed that the cyclical steady-state design was considered. The aim of this paper is to carefully analyze the steady-state (cyclical and the more popular conditional) for the synthetic chart, the original \"2 of L + 1\" (L < 1) runs-rule chart, and competing EWMA charts with two types of control limits. It turns out that the EWMA chart has a uniformly (over a large range of potential shifts) better steady-state ARL performance than the synthetic chart. Furthermore, the synthetic control chart exhibits the poorest performance among all considered competitors. Thus, we advise not applying synthetic control charts.

In this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of processes with a low number of defects per inspected unit. Therefore, it is not possible to detect a decrease in the process mean level. A common solution to this problem is to apply a runs rule on the lower side of the chart. Motivated by this approach, we suggest a Shewhart-type chart, supplemented with two runs rules; one is used for detecting decreases in process mean level, and the other is used for improving the chart’s sensitivity in the detection of small and moderate increasing shifts in the process mean level. Using the Markov chain method, we examine the performance of various schemes in terms of the average run length and the expected average run length. Two illustrative examples for the use of the proposed schemes in practice are also discussed. The numerical results show that the considered schemes can detect efficiently various shifts in process parameters in either direction.

Process monitoring is a continuous process for improving the quality. Control chart is a process monitoring tool of SPC tool kit that plays an important role in providing widespread monitoring, to observe the changes in parameters. Mostly, the mean control charts are used for monitoring of process location. In a perfect situation, when there are no outliers, the mean charts are more efficient than median control charts. In reality, data is not always free from outliers, so the median charts are considered as the best for monitoring location parameters. The use of an auxiliary variable in a control chart may be the cause of efficiency gain. The current article considers EWMA median charts based on auxiliary variable(s). Different run length performance measures are considered to expedite the proposed charts in both contaminated and uncontaminated process environments under multivariate normal distributions. An illustrative example is provided to validate the performance of the proposed charts. From the results, we deduce that the performance of median control charts is much better than that of mean control charts in the presence of outliers; moreover, the performance of control charts can be enhanced by using more auxiliary variables.

An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean should be monitored. Castagliola et al. (2013a) proposed the two-sided run rules (RR) control charts for monitoring the CV and it is found that the RR CV charts revealed the problem of ARL-biased performances, especially when the monitored sample size is small, for detecting downward CV shifts. This paper alters the RR CV chart by suggesting the two one-sided run rules (ORR) CV charts achieve the unbiased ARL performances. Additionally, this paper also investigates the ORR CV charts in terms of the expected average run length (EARL) criterion, which is not discussed in Castagliola et al. (2013a). A Markov chain model is established for designing the proposed charts. The statistical performances of the ORR CV, RR CV and Shewhart CV (SH CV) charts are compared in terms of the average run length (ARL) and EARL criteria. The results show that the proposed charts surpass the RR CV and SH CV charts for detecting small and moderate upward and downward CV shifts. The implementation of the ORR CV charts is illustrated with an example using a real dataset.

Multivariate exponentially weighted moving average (MEWMA) charts are among the best control charts for detecting small changes in any direction. The well-known MEWMA is directed at changes in the mean vector. But changes can occur in either the location or the variability of the correlated multivariate quality characteristics, calling for parallel methodologies for detecting changes in the covariance matrix. This article discusses an exponentially weighted moving covariance matrix for monitoring the stability of the covariance matrix of a process. Used together with the location MEWMA, this chart provides a way to satisfy Shewhart's dictum that proper process control monitor both mean and variability. We show that the chart is competitive, generally outperforming current control charts for the covariance matrix.

We investigate the effects of non-normality on the statistical performance of the multivariate exponentially weighted moving average (MEWMA) control chart, and its special case, the Hotelling's chi-squared chart, when applied to individual observations to monitor the mean vector of a multivariate process variable. We show that the chi-squared chart is highly sensitive to non-normality. We argue that the performance is most sensitive to departures from multivariate normality with individual observations (subgroups of size one). We show that with individual observations, and therefore, by extension, with subgroups of any size, the MEWMA chart can be designed to be robust to non-normality and very effective at detecting process shifts of any size or direction, even for highly skewed and extremely heavy-tailed multivariate distributions.

Consider a large number of detectors each generating a data stream. The task is to detect online, distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts. We show how the (optimal) detection delay depends on the fraction of data streams undergoing distribution changes as the number of detectors goes to infinity. There are three detection domains. In the first domain for moderately large fractions, immediate detection is possible. In the second domain for smaller fractions, the detection delay grows logarithmically with the number of detectors, with an asymptotic constant extending those in sparse normal mixture detection. In the third domain for even smaller fractions, the detection delay lies in the framework of the classical detection delay formula of Lorden. We show that the optimal detection delay is achieved by the sum of detectability score transformations of either the partial scores or CUSUM scores of the data streams.

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.

When in-control process parameters are estimated, Phase II control chart performance will vary among practitioners due to the use of different Phase I data sets. The typical measure of Phase II control chart performance, the average run length (ARL), becomes a random variable due to the selection of a Phase I data set for estimation. Aspects of the ARL distribution, such as the standard deviation of the average run length (SDARL), can be used to quantify the between-practitioner variability in control chart performance. In this article, we assess the in-control performance of the exponentially weighted moving average (EWMA) control chart in terms of the SDARL and percentiles of the ARL distribution when the process parameters are estimated. Our results show that the EWMA chart requires a much larger amount of Phase I data than previously recommended in the literature in order to sufficiently reduce the variation in the chart performance. We show that larger values of the EWMA smoothing constant result in higher levels of variability in the in-control ARL distribution; thus, more Phase I data are required for charts with larger smoothing constants. Because it could be extremely difficult to lower the variation in the in-control ARL values sufficiently due to practical limitations on the amount of the Phase I data, we recommend an alternative design criterion and a procedure based on the bootstrap approach.

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.