Multivariate multinomial T2 control chart using fuzzy approach

Quality of a product is often measured through various quality characteristics generally correlated. Multivariate control charts are a response to the need for quality control in such situations. If quality characteristics are qualitative, it sometimes happens that the product quality is defined by linguistic variables – where quality levels are represented by some specific words – and product units are classified into several linguistic forms categories, depending on the degree of fulfilment of expectations, creating a situation of fuzzy classifications. This study first reviews the concepts found in the literature on the development of fuzzy multivariate control charts. We propose a method to control these fuzzy quality evaluations, with correlated multiple attributes quality characteristics, through the use of a Hotelling T² control chart.     

A clustering algorithm-based control chart for inhomogeneously distributed TFT-LCD processes

Statistical process control techniques have been widely used to improve processes by reducing variations and defects. In the present paper, we propose a multivariate control chart technique based on a clustering algorithm that can effectively handle a situation in which the distribution of in-control observations is inhomogeneous. A simulation study was conducted to examine the characteristics of the proposed control chart and to compare them with Hotelling’s T ² multivariate control charts that are widely used in real-world processes. Moreover, an experiment with real data from the thin film transistor liquid crystal display (TFT-LCD) manufacturing process demonstrated the effectiveness and accuracy of the proposed control chart.     

Optimum variable-dimension EWMA chart for multivariate statistical process control

The variable-dimension T² control chart (VDT² chart) was recently proposed for monitoring the mean of multivariate processes in which some of the quality variables are easy and inexpensive to measure while other variables require substantially more effort or expense. The chart requires most of the times that only the inexpensive variables be sampled, switching to sampling all the variables only when a warning is triggered. It has good ARL performance compared with the standard T² chart, while significantly reducing the sampling cost. However, like the T² chart, it has limited sensitivity to small and moderate mean shifts. To detect such shifts faster, we developed an exponentially weighted moving average (EWMA) version of the VDT² chart, along with Markov chain models for ARL calculation, and software (made available) for optimizing the chart design. The optimization software, which is based on genetic algorithms, runs in Windows^© and has a friendly user interface. The performance analysis shows the great gain in performance achieved by the incorporation of the EWMA procedure.     

Deep recurrent neural network‐based residual control chart for autocorrelated processes

With the growth of automation in process industries, there is correlation in the process variables. Deep learning has achieved many great successes in image and visual analysis. This paper concentrates on developing a deep recurrent neural network (RNN) model to characterize process variables at vary time lags, and then a residual chart is developed to detect mean shifts in autocorrelated processes. The experiment results indicate that the RNN‐based residual chart outperforms other typical methods (eg, autoregressive [AR]‐based control chart, back propagation network [BPN]‐based residual chart). This paper provides guideline for deep learning technique employed as an effective tool in autocorrelated process control.     

A mixed control chart to monitor the process

In this paper, we propose a mixed control chart to monitor the process quality using attribute data combined with variable data. The proposed control chart proceeds like an np control chart based on the number of nonconforming parts but requires variable data only when the decision is indeterminate. The control coefficients are determined by considering the in-control and the out-of-control average run lengths for various specified parameters. The extensive tables are provided for the industrial use. The advantages of the proposed control chart are discussed over the traditional np control chart.     

The variable sampling rate X̄ control charts for monitoring autocorrelated processes

Recent studies demonstrated that the adaptive X? control charts are more efficient than fixed parmeters (FP) X? control chart from statistical and economic criteria. The usual assumption for designing a control chart is that the observations from the process are independent. However, for many processes, such as chemical processes, consecutive measurements are often highly correlated, especially when the interval between samples is small. In the present paper, the observations are modeled as an AR(1) process plus a random error, and the properties of the variable sampling rate (VSR) X? charts are evaluated and studied under this model. Based on the study, the VSR X? chart is faster than the FP, variable sampling interval and variable sample size X? control charts in detecting mean shifts. However, when the level of autocorrelation is high or the process mean shift is large, the advantage of the VSR X? chart is reduced. Copyright © 2008 John Wiley & Sons, Ltd.     

A robust alternative to Hotelling's T2 control chart using trimmed estimators

A control chart is one of the primary techniques used in statistical process control. In phase I, historical observations are analysed in order to construct a control chart with which to determine whether the process has been in control over the period of time in which the data were collected. The presence of multiple outliers may go undetected by the usual control charts, such as Hotelling's T² due to the masking effect. In this paper we propose a robust alternative to Hotelling's T² control chart with estimators defined using trimming. Simulation studies show that the proposed control chart is more effective than T² in detecting outliers. Copyright © 2008 John Wiley & Sons, Ltd.     

New sampling strategies to reduce the effect of autocorrelation on the synthetic T2 chart to monitor bivariate process

In this paper, synthetic T² chart is developed to monitor bivariate process with correlated variables and autocorrelated observations. The proposed chart is a combination of the Hotelling's T² chart and the conforming run length chart. The operation and design of the chart are described when observations are autocorrelated and cross correlated. The first‐order vector autoregressive process VAR (1) is used to model the bivariate data from an autocorrelated process of interest. Using an average run length as performance measure criterion in the VAR (1) model, it is observed that autocorrelation seriously impact the performance of the synthetic T² chart. To reduce the effect of autocorrelation on the performance of the synthetic T² chart, the skip and mixed sampling strategies are implemented to form rational subgroups in the construction of synthetic T² chart. The average run length performance of the synthetic T² chart implementing these strategies is compared with that of the standard strategy of formation of rational subgroups. It is observed that implementing skip and mixed sampling strategies within rational subgroup improves the performance of the synthetic T² chart.     

On developing sensitive nonparametric mixed control charts with application to manufacturing industry

Control charts are designed under the normality assumption of the quality characteristic of the process. However, the normality assumption rarely holds in practice. In non-normal conditions, parametric charts tend to display more false alarm rates and invalid out-of-control comparisons. The exponentially weighted moving average chart is a frequently used memory-type control chart for monitoring the process target that only performs effectively under the smoothing parameter's small choices. This study proposes a nonparametric mixed exponentially weighted moving average-progressive mean chart based on sign statistic (NPMEP_SN) under simple and ranked set sampling schemes to address this said drawback. Normal and non-normal distributions are included in this study to observe the proposed chart's in-control behavior and out-of-control efficacy. The prominent feature of the proposed schemes is that it works efficiently in detecting small and persistent shifts in the process location corresponding to the given values of the smoothing parameter. The proposed scheme is also tested under the ranked set sampling scheme to enhance the NPMEP_SN chart's performance (hereafter named “NPMEP_RSN”). The performance of the proposed charts is investigated through simulations using run-length profiles. The proposed schemes were seen to outperform other alternatives, specifically under the ranked set sampling scheme. A real data-set related to the diameter of a piston ring is included as a demonstration of the proposal.     

On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

With the development of automation technologies, data can be collected in a high frequency, easily causing autocorrelation phenomena. Control charts of residuals have been used as a good way to monitor autocorrelated processes. The residuals have been often computed based on autoregressive (AR) models whose building needs much experience. Data have been assumed to be first-order autocorrelated, and first-order autoregressive (AR(1) ) models have been employed to obtain residuals. But for a p th-order autocorrelated process, how the AR(1) model affects the performance of the control chart of residuals remains unknown. In this paper, the control chart of exponentially weighted moving average of residuals (EWMA-R) is used to monitor the p th-order autocorrelated process. Taking the mean and standard deviation of run length as performance indicators, two types of EWMA-R control charts, with their residuals obtained from the p th-order autoregressive AR(p) and AR(1) models, respectively, are compared. The results of the numerical experiment show that for detecting small mean shifts, EWMA-R control charts based on AR(1) models outperform ones based on AR(p) models, whereas for detecting large shifts, they are sometimes slightly worse. A practical application is used to give a recommendation that a large number of samples are necessary for determining an EWMA-R control chart before using it.     

The economic and economic-statistical designs of the Hotelling's T2 chart based on the expected average run length

Existing economic and economic-statistical designs require practitioners to specify the Mahalanobis Distance Shift Size (MDSS) as an exact value. However, practitioners may find it difficult to specify this distance. This article proposes the economic and economic-statistical designs of the Hotelling's T² chart, where practitioners do not have to specify the MDSS. Adopting optimal design parameters based on the wrong MDSS results in a significant increase in cost. In comparison, adopting the optimal design parameters based on the proposed methodology results in a slight increase in cost. This article also studies the effects of different input parameters and statistical constraints.     

可变抽样区间不合格品数控制图

分析了休哈特控制图的不足,设计出具有两种抽样区间长度的可变抽样区间(VSI)np图,当点子接近控制限时,使用较短的抽样区间;当点子接近目标值时,使用较长的抽样区间.若点子超出控制限,则与固定抽样区间控制图(FSI)一样发出信号.同时还计算了在可变抽样区间下发信号前的平均时间,并与固定抽样区间np图进行比较,所设计的VSI控制图能缩短过程失控时间,从而可减少不合格品数.     

A mixed HWMA-CUSUM mean chart with an application to manufacturing process

Memory-type control charts play a significant role to identify slight changes in the parameters of the production process. In this article, we have proposed a new cumulative sum chart that utilizes the statistic of the homogeneously weighted moving average chart. The performance of the proposed chart is studied using Monte Carlo simulations. The proposed chart is compared with some existing charts under different run length profiles. The run length profile comparisons reveal that the proposed chart performs superior as compared to the existing control charts. A real-life application using a manufacturing process dataset is also part of this study.     

A mixed cumulative sum homogeneously weighted moving average control chart for monitoring process mean

The homogeneously weighted moving average (HWMA) control chart is famous to identify small deviations in the process mean. The plotting statistic of the HWMA chart assigns equal weight among the previous samples as compared to the plotting statistic of the exponentially weighted moving average chart. We propose a new HWMA chart that uses the plotting statistic of the cumulative sum chart. The run length performance of the proposed chart is measured in terms of the average, the standard deviation, some percentile points, and compared with some existing counterparts' charts. The comparison shows that the proposed chart performs superior to their existing counterparts. An application based on a real-life dataset is also presented.     

Economic statistical design of a T2 control chart with double warning lines

Recent studies have shown that enhancing the common T² control chart by using variable sample sizes (VSS) and variable sample intervals (VSI) sampling policies with a double warning line scheme (DWL) yields improvements in shift detection times over either pure VSI or VSS schemes in detecting almost all shifts in the process mean. In this paper, we look at this problem from an economical perspective, certainly at least as an important criterion as shift detection time if one considers what occurs in the industry today. Our method is to first construct a cost model to find the economic statistical design (ESD) of the DWL T² control chart using the general model of Lorenzen and Vance (Technometrics 1986; 28 :3–11). Subsequently, we find the values of the chart parameters which minimize the cost model using a genetic algorithm optimization method. Cost comparisons of Fixed ratio sampling, VSI, VSS, VSIVSS with DWL, and multivariate exponentially weighted moving average (MEWMA) charts are made, which indicate the economic efficacy of using either VSIVSS with DWL or MEWMA charts in practice if cost minimization is of interest to the control chart user. Copyright © 2010 John Wiley & Sons, Ltd.     

A wavelet‐based nonparametric CUSUM control chart for autocorrelated processes with applications to network surveillance

Statistical process control (SPC) has natural applications in data network surveillance. However, network data are commonly autocorrelated, which presents challenges to the basic SPC methods. Most existing SPC methods for correlated data assume parametric models to account for the correlation structure within the data. Those model assumptions can be difficult to justify in practice. In this paper, we propose a nonparametric cumulative sum (CUSUM) control chart for autocorrelated processes. In our proposed approach, we incorporate a wavelet decomposition and a nonparametric multivariate CUSUM control chart to obtain a robust procedure for autocorrelated processes without distribution assumptions. Extensive simulations show that the procedure appropriately controls the in‐control average run length and also has good sensitivity for detecting location shifts.     

Introducing randomness into univariate control chart sampling strategies for enhancing security against cyber-physical attacks in production systems

With recent technological advancements, production systems have become more susceptible to cyber-physical attacks. Such attacks can be intelligently designed to both alter product dimensions and avoid detection by current Quality Control (QC) tools. The objective of this work is to assess the performance of random sampling strategies for control charting in detecting cyber-physical attacks. More specifically, the methodology adopts traditional random sampling approaches used for inspection and applies them to univariate control charts. Different random sampling strategies are discussed and their performances under varying attack scenarios are evaluated. In addition, new control chart performance metrics were developed for a more in-depth analysis, to guide practitioners in assessing how well these control charts increase their robustness to cyber-physical attacks.     

Controlling autocorrelated data in multistage manufacturing processes with an application to textile industry

In recent years, much attention has been given to monitoring multistage processes in order to effectively improve the product reliability. To this end, the output of the process is investigated under special circumstances, and the values corresponding to reliability‐related quality characteristic are measured. However, analyzing reliability data is quite complicated because of their unique features such as being censored and obeying nonnormal distributions. A more sophisticated picture arises when the observations of the process are autocorrelated in some cases, which makes the application of previous control procedures futile. In this paper, the accelerated failure time (AFT) regression models have been modified in order to account for autocorrelated data. Then, a cumulative sum (CUSUM) control chart and an exponentially weighted moving average (EWMA) control chart based on conditional expected values have been proposed to monitor the quality variable with Weibull distribution while taking the effective covariates into consideration. Extensive simulation studies reveal that the CUSUM control chart outperforms its counterpart in detecting out‐of‐control conditions. Finally, a real case study in a textile industry has been provided to investigate the application of the CUSUM control scheme.     

The effects of constructed bivariate copulas on multivariate control charts effectiveness

The average control chart monitors the shifts in the process. The familiar multivariate control charts are used to detect the mean vector of the process such as multivariate cumulative sum (MCUSUM) and Hotelling's T² control charts. In this paper, the effects of constructing bivariate copulas on multivariate control charts, that is, MCUSUM and Hotelling's T² control charts are intensively investigated when observations are drawn from the exponential distribution. Moreover, the dependence levels of observations are classified to be weak, moderate, and strong in both positive and negative values by Kendall's tau. The numerical results were obtained by Monte Carlo simulation to explore the average run length (ARL). The simulation results show that the performance of Hotelling's T² control chart is superior to the MCUSUM control chart for all shifts in the mean vector of process. Furthermore, from applying the presented control chart to two sets of real data, data set of the strength of 1.5 cm glass fibers measured at the National Physical Laboratory, England and data set of the strength of glass of the aircraft window, it was found that for a small shift ($\delta \le 0.1$), the MCUSUM control chart is better than Hotelling's T² control chart.