Distribution-free triple EWMA control chart for monitoring the process location using the Wilcoxon rank-sum statistic with fast initial response feature

The exponentially weighted moving average (EWMA) control chart is a memory-type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small-to-moderate shifts. This paper proposes a new distribution-free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank-sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real-life illustration is provided to show the application and implementation of the new chart.     

Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes

In this work, both the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been reconfigured to monitor processes using a Bayesian approach. Our construction of these charts are informed by posterior and posterior predictive distributions found using three loss functions: the squared error, precautionary, and linex. We use these control charts on count data, performing a simulation study to assess chart performance. Our simulations consist of sensitivity analysis of the out-of-control shift size and choice of hyper-parameters of the given distributions. Practical use of theses charts are evaluated on real data.     

Run length quantiles of EWMA control charts monitoring normal mean or/and variance

Exponentially weighted moving average (EWMA) control charts are well-established devices for monitoring process stability. Typically, control charts are evaluated by considering their Average Run Length (ARL), that is the expected number of observations or samples until the chart signals. Because of the limitations of an average, various papers also dealt with the run length distribution and quantiles. Going beyond these papers, we develop algorithms for and evaluate the quantile performance of EWMA control charts with variance adjusted control limits and with fast initial response features, of EWMA charts based on the sample variance, and of EWMA charts simultaneously monitoring mean and variance. Additionally, for the mean charts we consider medium, late and very late process changes and their impact on appropriately conditioned run length quantiles. It is demonstrated that considering run length quantiles can protect from constructing distorted EWMA designs while optimising their zero-state ARL performance. The implementation of all the considered measures in the R package ‘spc’ allows any control chart user to consider EWMA schemes from the run length quantile prospective in an easy way.     

Directional control schemes for processes with mixed-type data

Mixed-type data consisting of both continuous observations and categorical observations are becoming prevalent in manufacturing processes and service management. The majority of existing statistical process control tools are designed to monitor either continuous data or categorical data but seldom both. In this article, we propose a directional exponentially weighted moving average control scheme composed of monitoring and diagnosis for mixed-type data. We assume that there is a latent unknown continuous distribution that determines the attribute levels of a categorical variable, and represent both continuous data and categorical data by standardised ranks. The proposed control chart also incorporates directional information to facilitate diagnosing the shift direction. Monte Carlo simulations demonstrate the efficiency of the proposed control scheme.     

New EWMA control charts for monitoring process dispersion using auxiliary information

The exponentially weighted moving average (EWMA) control chart is a well‐known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary‐information–based (AIB) EWMA (AIB‐EWMA) charts. These AIB‐EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB‐EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB‐Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB‐EWMA charts.     

A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

Multivariate EWMA control charts using individual observations for process mean and variance monitoring and diagnosis

Most multivariate control charts in the literature are designed to detect either mean or variation shifts rather than both. A simultaneous use of the Hotelling T ² and |S| control charts has been proposed but the Hotelling T ² reacts to mean shifts, dispersion changes, and changes of correlations among responses. The combination of two multivariate control charts into one chart sometimes loses the ability to provide detailed diagnostic information when a process is out-of-control. In this research a new multivariate control chart procedure based on exponentially weighted moving average (EWMA) statistics is proposed to monitor process mean and variance simultaneously to identify proper sources of variations. Two multivariate EWMA control charts using individual observations are proposed to achieve a quick detection of mean or variance shifts or both. Simulation studies show that the proposed charts are capable of identifying appropriate types of shifts in terms of correct detection percentages. A manufacturing example is used to demonstrate how the proposed charts can be properly set-up based on average run length values via simulations. In addition, correct detection rates of the proposed charts are explored.     

EWMA control chart limits for first‐ and second‐order autoregressive processes

Today's manufacturing environment has changed since the time when control chart methods were originally introduced. Sequentially observed data are much more common. Serial correlation can seriously affect the performance of the traditional control charts. In this article we derive explicit easy‐to‐use expressions of the variance of an EWMA statistic when the process observations are autoregressive of order 1 or 2. These variances can be used to modify the control limits of the corresponding EWMA control charts. The resulting control charts have the advantage that the data are plotted on the original scale making the charts easier to interpret for practitioners than charts based on residuals. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust proportional hazard-based monitoring schemes for reliability data

Reliability of products is a key factor for successful businesses. In general, the existing monitoring schemes have poor performance as reliability data are often censored. Also, the products are manufactured in multistage processes where the outgoing quality gets affected by the previous stage quality. Besides this cascade property, historical data with outliers make the analysis even more complicated. This paper discusses exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts for monitoring a two-stage dependent process. In particular, the proportional hazard (PH) model is assumed for modeling the relationship of quality characteristics. Furthermore, to remove the detrimental effects of outliers on the results, robust regression method known as the M-estimation is used. Besides a real case study, the performance of the proposed monitoring approach is assessed through a comprehensive simulation study. The results suggested that the EWMA chart outperforms the CUSUM chart.     

Adaptive CUSUM and EWMA charts with auxiliary information and variable sampling intervals for monitoring the process mean

The variable sampling interval (VSI) feature enhances the sensitivity of a control chart that is based on fixed sampling interval (FSI). In this paper, we enhance the sensitivities of the auxiliary information-based (AIB) adaptive Crosier cumulative sum (CUSUM) (AIB-ACC) and adaptive exponentially weighted moving average (EWMA) (AIB-AE) charts using the VSI feature when monitoring a mean shift which is expected to lie within a given interval. The Monte Carlo simulations are used to compute zero-state and steady-state run length properties of these control charts. It is found that the AIB-ACC and AIB-AE charts with VSI feature are uniformly more sensitive than those based on FSI feature. Real datasets are also considered to demonstrate the implementation of these control charts.     

Statistical monitoring performance for startup operations in a feedback control system

Previously, it has been held that statistical process control (SPC) and engineering process control (EPC) were two distinct domains for process improvement. However, we specifically consider the impact for integrating the two approaches on a first‐order dynamic system with ARIMA disturbances. We show how to model and analyze this system over a range of practical conditions. Our work results in a set of response surfaces that characterize the performance of the integrated design. We also compare these results to the case where the SPC and EPC policies are applied separately. In general, we find that the EPC approach performs best in terms of minimizing error, but that we can reduce the number and magnitude of adjustments using the integrated monitoring and control approach. This work also further supports our earlier findings that the integrated design is effective on complex dynamic systems during the initial transient or startup period. Copyright © 2001 John Wiley & Sons, Ltd.     

Shewhart and EWMA t control charts for short production runs

Short‐run productions are common in manufacturing environments like job shops, which are characterized by a high degree of flexibility and production variety. Owing to the limited number of possible inspections during a short run, often the Phase I control chart cannot be performed and correct estimates for the population mean and standard deviation are not available. Thus, the hypothesis of known in‐control population parameters cannot be assumed and the usual control chart statistics to monitor the sample mean are not applicable. t‐charts have been recently proposed in the literature to protect against errors in population standard deviation estimation due to the limitation of available sampling measures. In this paper the t‐charts are tested for implementation in short production runs to monitor the process mean and their statistical properties are evaluated. Statistical performance measures properly designed to test the chart sensitivity during short runs have been considered to compare the performance of Shewhart and EWMA t‐charts. Two initial setup conditions for the short run fixing the population mean exactly equal to the process target or, alternatively, introducing an initial setup error influencing the statistic distribution have been modelled. The numerical study considers several out‐of‐control process operating conditions including one‐step shifts for the population mean and/or standard deviation. The obtained results show that the t‐charts can be successfully implemented to monitor a short run. Finally, an illustrative example is presented to show the use of the investigated t charts. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic network monitoring and control of in situ image profiles from ultraprecision machining and biomanufacturing processes

In modern industries, advanced imaging technology has been more and more invested to cope with the ever‐increasing complexity of systems, to improve the visibility of information and enhance operational quality and integrity. As a result, large amounts of imaging data are readily available. This presents great challenges on the state‐of‐the‐art practices in process monitoring and quality control. Conventional statistical process control (SPC) focuses on key characteristics of the product or process and is rather limited to handle complex structures of high‐dimensional imaging data. New SPC methods and tools are urgently needed to extract useful information from in situ image profiles for process monitoring and quality control. In this study, we developed a novel dynamic network scheme to represent, model, and control time‐varying image profiles. Potts model Hamiltonian approach is introduced to characterize community patterns and organizational behaviors in the dynamic network. Further, new statistics are extracted from network communities to characterize and quantify dynamic structures of image profiles. Finally, we design and develop a new control chart, namely, network‐generalized likelihood ratio chart, to detect the change point of the underlying dynamics of complex processes. The proposed methodology is implemented and evaluated for real‐world applications in ultraprecision machining and biomanufacturing processes. Experimental results show that the proposed approach effectively characterize and monitor the variations in complex structures of time‐varying image data. The new dynamic network SPC method is shown to have strong potentials for general applications in a diverse set of domains with in situ imaging data.     

The use of fast initial response features on the homogeneously weighted moving average chart with estimated parameters under the effect of measurement errors

Fast initial response (FIR) features are generally used to improve the sensitivity of memory-type control charts by shrinking time-varying control limits in the earlier stage of the monitoring regime. This paper incorporates FIR features to increase the sensitivity of the homogeneously weighted moving average (HWMA) monitoring schemes with and without measurement errors under constant as well as linearly increasing variance scenarios. The robustness and the performance of the HWMA monitoring schemes are investigated in terms of numerous run-length properties assuming that the underlying process parameters are known and unknown. It is found that the FIR features improves the performance of the HWMA monitoring scheme as compared to the standard no FIR feature HWMA scheme, and at the same time, it is observed that the simultaneous use of a recently proposed FIR feature and multiple measurements significantly reduces the negative effect of measurement errors. An illustrative example on the volume of milk in bottles is used to demonstrate a real-life application.     

A control chart based on likelihood ratio test for monitoring process mean and variability

Recently, monitoring the process mean and variance simultaneously by using a single chart has drawn more and more attention. In this paper, we propose a new single chart that integrates the EWMA procedure with the generalized likelihood ratio (GLR) test statistics for jointly monitoring both the process mean and variance. It can be easily designed and constructed, and its average run length can be evaluated by a two‐dimensional Markov chain model. Owing to the good properties of the GLR test and EMWA, computation results show that it provides quite a robust and satisfactory performance in various cases, including the detection of the decrease in variability and the individual observation at the sampling point, which are very important in many practical applications but may not be well handled by the existing approaches in the literature. The application of our proposed method is illustrated by a real data example from chemical process control. Copyright © 2009 John Wiley & Sons, Ltd.     

Deviance residual-based control charts for monitoring the beta-distributed processes

Beta-distributed process outputs are common in manufacturing industry because they range from 0 to 1 based on inputs like yield. Under the normality assumption, Shewarts control charts and Hotelling's control charts based on the deviance residual have been applied to monitor the process mean of the beta-distributed process outputs. The normality assumption can be violated according to the shape of the beta distribution. Therefore, without the normality assumption, we propose antirank control charts, exponentially weighted moving average (EWMA) control charts and cumulative sum (CUSUM) control charts. The proposed control charts outperform the existing control charts in the experimental results. The previous research has been focused on monitoring the process mean only. For the first time, in order to monitor the process variance of the beta-distributed process outputs, we propose the multivariate exponentially weighted mean squared deviation (MEWMS) chart, the first norm distance of the MEWMS deviation from its expected value (MEWMSL₁) chart, the chart based on MEWMS deviation with the approximated distribution of trace (MEWMS_AT), the multivariate trace sum squared deviation (MTSSD) chart and the multivariate matrix sum squared deviation (MMSSD) chart based on the deviance residual. The proposed control charts are compared and recommended in terms of the experimental results. This research can be a guideline for practitioners who monitor the deviance residual.     

A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data

Exponentially distributed data are commonly encountered in high-quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero-state and steady-state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice.     

A simulation comparison of some distance-based EWMA control charts for monitoring the covariance matrix with individual observations

It is common in modern manufacturing to simultaneously monitor more than one process quality characteristic. In such a multivariate scenario, the monitoring of the covariance matrix, along with the mean vector, plays an important role in assessing whether a process stays in control or not. However, monitoring the covariance matrix is technically more difficult, especially when there is only one observation available in each subgroup, disabling the usual sample covariance matrix as an effective estimator. To monitor the covariance matrix with individual observations in Phase II stage, several exponentially weighted moving average (EWMA) control charts have been constructed based on the distance between the estimated process covariance matrix and its target value. In this paper, two new control charts are devised using the sum of the square roots of the absolute deviations and its combination with the sum of squared deviations. These distance-based control charts are compared via the simulation experiments on different simulated out-of-control covariance matrices with respect to the number of quality characteristics being monitored, the shift pattern, and the shift magnitude. The simulation results identify the control charts that perform relatively robust and show that these various control charts may have their respective merits on different out-of-control scenarios.     

On a class of mixed EWMA-CUSUM median control charts for process monitoring

Monitoring of any manufacturing, production, or industrial process can be controlled and improved by removing these special cause of variations using control charts. Shewhart-type control charts are effective to control a large amount of special variations, whereas, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts detect small and moderate variations efficiently in the process parameters. Monitoring of location parameter can be done with mean control charts under the assumption that the parameters are known or correctly estimated from in-control samples and data are free from outliers (but in practice data occasionally have outliers). In this study, we have proposed generalized mixed EWMA-CUSUM median control charts structures for known and unknown parameters based on auxiliary variables for detecting shifts in process location parameter. The proposed charts are compared with the corresponding charts for the mean, based on contaminated and uncontaminated data. Different performance measures are used to evaluate the performance of proposed control charts and revealed through results that the median-based charts are more sensitive to detect a shift in process location parameter in the presence of outliers. An illustrative example using real data is also shown for practical consideration.