Monitoring Process Variability for Stationary Process Data

Processes that arise naturally, for example, from manufacturing or the environment, often exhibit complicated autocorrelation structures. When monitoring such a process for changes in variance, accounting for that structure is critical. While charts for monitoring the variance of processes of independent observations and some specific autocorrelated processes have been proposed in the past, the chart presented in this article can handle a general stationary process. The performance of the proposed chart was examined through simulations for the first‐order autoregressive and first‐order autoregressive‐moving average processes and demonstrated with examples. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Nonparametric Control Chart for Monitoring Variability

Statistical process control is widely used in industrial processes, service fields, among others. While parametric control charts are useful in certain processes, there is often a lack of enough knowledge about the process distribution. So, nonparametric control charts are needed in such situations. This paper develops a new nonparametric control chart based on the Ansari–Bradley nonparametric test and the effective change point model. Simulation results show that our proposed control chart is superior to other nonparametric control charts in monitoring process variability for most cases. Our proposed control chart is easy in computation, and powerful for monitoring process variability. Copyright © 2016 John Wiley & Sons, Ltd.     

An AR‐Sieve Bootstrap Control Chart for Autocorrelated Process Data

There are two major approaches in dealing with autocorrelated process data in process control, that is, residual‐based approaches and methods that modify control limits to adjust for autocorrelation. We proposed a methodology for constructing control charts for autocorrelated process data using the AR‐sieve bootstrap. The simulation study illustrates the relative advantage of the AR‐sieve bootstrap control chart with respect to the in‐control and out‐of‐control run length and false alarm rate. The proposed methodology works even for small sample sizes and conditions of the near nonstationarity of the generating process. The proposed AR‐sieve bootstrap control chart presents the advantage of being distribution‐free for certain class of linear models as well as the tracking of actual process observations instead of model residuals, thus facilitating the implementation during actual plant operations. Copyright © 2011 John Wiley & Sons, Ltd.     

Distribution‐free mixed cumulative sum‐exponentially weighted moving average control charts for detecting mean shifts

In this paper, we propose distribution‐free mixed cumulative sum‐exponentially weighted moving average (CUSUM‐EWMA) and exponentially weighted moving average‐cumulative sum (EWMA‐CUSUM) control charts based on the Wilcoxon rank‐sum test for detecting process mean shifts without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured through the average run‐length, relative mean index, average extra quadratic loss, and average ratio of the average run‐length and performance comparison index. It is found that the proposed charts perform better than its counterparts considered in this paper under non‐normal distributions and outperform the classical mixed CUSUM‐EWMA and EWMA‐CUSUM charts in many cases under the normal distribution. The effect of the phase I sample size is also investigated on the phase II performance of the proposed charts. A numerical illustration is given to demonstrate the implementation and simplicity of the proposed charts.     

A t‐chart for Monitoring Multi‐variety and Small Batch Production Run

Statistical process control is an important tool to monitor and control a process. It is used to ensure that the manufacturing process operates in the in‐control state. Multi‐variety and small batch production runs are common in manufacturing environments like flexible manufacturing systems and Just‐in‐Time systems, which are characterized by a wide variety of mixed products with small volume for each kind of production. It is difficult to apply traditional control charts efficiently and effectively in such environments. The method that control charts are plotted for each individual part is not proper, since the successive state of the manufacturing process cannot be reflected. In this paper, a proper t‐chart is proposed for implementation in multi‐variety and small batch production runs to monitor the process mean, and its statistical properties are evaluated. The run length distribution of the proposed t‐chart has been obtained by modelling the multi‐variety process. The ARL performance for various shifts, number of product types, and subgroup sizes has also been obtained. The results show that the t‐chart can be successfully implemented to monitor a multi‐variety production run. Finally, illustrative examples show that the proposed t‐chart is effective in multi‐variety and small batch manufacturing environment. Copyright © 2013 John Wiley & Sons, Ltd.     

Distribution‐free Lepage Type Circular‐grid Charts for Joint Monitoring of Location and Scale Parameters of a Process

In the last 5 years, research works on distribution‐free (nonparametric) process monitoring have registered a phenomenal growth. A Google Scholar database search on early September 2015 reveals 246 articles on distribution‐free control charts during 2000–2009 and 466 articles in the following years. These figures are about 1400 and 2860 respectively if the word ‘nonparametric’ is used in place of ‘distribution‐free’. Distribution‐free charts do not require any prior knowledge about the process parameters. Consequently, they are very effective in monitoring various non‐normal and complex processes. Traditional process monitoring schemes use two separate charts, one for monitoring process location and the other for process scale. Recently, various schemes have been introduced to monitor the process location and process scale simultaneously using a single chart. Performance advantages of such charts have been clearly established. In this paper, we introduce a new graphical device, namely, circular‐grid charts, for simultaneous monitoring of process location and process scale based on Lepage‐type statistics. We also discuss general form of Lepage statistics and show that a new modified Lepage statistic is often better than the traditional of Lepage statistic. We offer a new and attractive post‐signal follow‐up analysis. A detailed numerical study based on Monte‐Carlo simulations is performed, and some illustrations are provided. A clear guideline for practitioners is offered to facilitate the best selection of charts among various alternatives for simultaneous monitoring of location‐scale. The practical application of the charts is illustrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Model‐based control chart for autoregressive and correlated data

In recent years, statistical process control for autocorrelated processes has received a great deal of attention. This is due in part to the improvements in measurement and data collection that allow processes to be sampled at higher frequency rates and, hence, data autocorrelation. A method for monitoring autocorrelated processes based on regression adjustment is presented in this paper. The performance of the residual‐based control chart in terms of the average run length is compared to observation‐based control charts via Monte Carlo simulations. In general, the observation‐based control charts perform very poorly when data are correlated over time. Under the assumption that the model is correct, the residual‐based control charts are superior for all cases considered here. This suggests using a residual‐based control chart to detect the mean shift. This is recommended particularly for chemical processes where there are often cascade processes with several inputs but only a few outputs, and where many of the variables are highly autocorrelated. Copyright © 2002 John Wiley & Sons, Ltd.     

A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale

Traditional statistical process control for variables data often involves the use of a separate mean and a standard deviation chart. Several proposals have been published recently, where a single (combination) chart that is simpler and may have performance advantages, is used. The assumption of normality is crucial for the validity of these charts. In this article, a single distribution‐free Shewhart‐type chart is proposed for monitoring the location and the scale parameters of a continuous distribution when both of these parameters are unknown. The plotting statistic combines two popular nonparametric test statistics: the Wilcoxon rank sum test for location and the Ansari–Bradley test for scale. Being nonparametric, all in‐control properties of the proposed chart remain the same and known for all continuous distributions. Control limits are tabulated for implementation in practice. The in‐control and the out‐of‐control performance properties of the chart are investigated in simulation studies in terms of the mean, the standard deviation, the median, and some percentiles of the run length distribution. The influence of the reference sample size is examined. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2011 John Wiley & Sons, Ltd.     

A Two‐Sided Cumulative Sum Chart for First‐Order Integer‐Valued Autoregressive Processes of Poisson Counts

Count data processes are often encountered in manufacturing and service industries. To describe the autocorrelation structure of such processes, a Poisson integer‐valued autoregressive model of order 1, namely, Poisson INAR(1) model, might be used. In this study, we propose a two‐sided cumulative sum control chart for monitoring Poisson INAR(1) processes with the aim of detecting changes in the process mean in both positive and negative directions. A trivariate Markov chain approach is developed for exact evaluation of the ARL performance of the chart in addition to a computationally efficient approximation based on bivariate Markov chains. The design of the chart for an ARL‐unbiased performance and the analyses of the out‐of‐control performances are discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Memory‐Type Control Charts for Monitoring the Process Dispersion

Control charts have been broadly used for monitoring the process mean and dispersion. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are memory control charts as they utilize the past information in setting up the control structure. This makes CUSUM and EWMA‐type charts good at detecting small disturbances in the process. This article proposes two new memory control charts for monitoring process dispersion, named as floating T ? S² and floating U ? S² control charts, respectively. The average run length (ARL) performance of the proposed charts is evaluated through a simulation study and is also compared with the CUSUM and EWMA charts for process dispersion. It is found that the proposed charts are better in detecting both positive as well as negative shifts. An additional comparison shows that the floating U ? S² chart has slightly smaller ARLs for larger shifts, while for smaller shifts, the floating T ? S² chart has better performance. An example is also provided which shows the application of the proposed charts on simulated datasets. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonparametric signed‐rank control charts with variable sampling intervals

Variable sampling interval (VSI) charts have been proposed in the literature for normal theory (parametric) control charts and are known to provide performance enhancements. In the VSI setting, the time between monitored samples is allowed to vary depending on what is observed in the current sample. Nonparametric (distribution‐free) control charts have recently come to play an important role in statistical process control and monitoring. In this paper a nonparametric Shewhart‐type VSI control chart is considered for detecting changes in a specified location parameter. The proposed chart is based on the Wilcoxon signed‐rank statistic and is called the VSI signed‐rank chart. The VSI signed‐rank chart is compared with an existing fixed sampling interval signed‐rank chart, the parametric VSI ‐chart, and the nonparametric VSI sign chart. Results show that the VSI signed‐rank chart often performs favourably and should be used.     

Single Variables Control Charts: an Overview

Control charts are widely used in industries to monitor a process for quality improvement. When dealing with variables data, we usually employ two control charts to monitor the process location and spread. We give an overview of the control charts proposed in the last decade or so in an effort to use only one chart to simultaneously monitor both process location and spread. Two approaches have been advocated for using one control chart for process monitoring. One approach plots two quality characteristics in the same chart while the other uses one plotting variable to represent the process location and spread. Copyright © 2006 John Wiley & Sons, Ltd.     

A New Nonparametric EWMA Control Chart for Monitoring Process Variability

The exponentially weighted moving average (EWMA) control chart is one of a potentially powerful process monitoring tool of the statistical process control. The EWMA chart has now been widely used because of its excellent ability to detect small to moderate shifts in the process parameter(s). In this study, we propose a new nonparametric/distribution‐free EWMA chart for efficiently monitoring the changes in the process variability. We use extensive Monte Carlo simulations to compute the run length profiles of the proposed EWMA chart. For a better performance comparison, the proposed EWMA chart is compared with a recent existing EWMA chart that has already shown to have better performance than the existing control charts. It turns out that the proposed EWMA chart performs substantially and uniformly better than the existing powerful EWMA chart. The working and implementation of the proposed and existing EWMA charts with the help of an illustrative example are also included in this study. Copyright © 2017 John Wiley & Sons, Ltd.     

A distribution-free tabular CUSUM chart for autocorrelated data

A distribution-free tabular CUSUM chart called DFTC is designed to detect shifts in the mean of an autocorrelated process. The chart's Average Run Length (ARL) is approximated by generalizing Siegmund's ARL approximation for the conventional tabular CUSUM chart based on independent and identically distributed normal observations. Control limits for DFTC are computed from the generalized ARL approximation. Also discussed are the choice of reference value and the use of batch means to handle highly correlated processes. The performance of DFTC compared favorably with that of other distribution-free procedures in stationary test processes having various types of autocorrelation functions as well as normal or nonnormal marginals.     

A New Distribution‐free Control Chart for Joint Monitoring of Unknown Location and Scale Parameters of Continuous Distributions

While the assumption of normality is required for the validity of most of the available control charts for joint monitoring of unknown location and scale parameters, we propose and study a distribution‐free Shewhart‐type chart based on the Cucconi 1 statistic, called the Shewhart‐Cucconi (SC) chart. We also propose a follow‐up diagnostic procedure useful to determine the type of shift the process may have undergone when the chart signals an out‐of‐control process. Control limits for the SC chart are tabulated for some typical nominal in‐control (IC) average run length (ARL) values; a large sample approximation to the control limit is provided which can be useful in practice. Performance of the SC chart is examined in a simulation study on the basis of the ARL, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparisons with a competing distribution‐free chart, known as the Shewhart‐Lepage chart (see Mukherjee and Chakraborti 2 ) show that the SC chart performs just as well or better. The effect of estimation of parameters on the IC performance of the SC chart is studied by examining the influence of the size of the reference (Phase‐I) sample. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2013 John Wiley & Sons, Ltd.     

A Hybrid Learning‐Based Model for Simultaneous Monitoring of Process Mean and Variance

Unnatural patterns exhibited on process mean and variance control charts can be associated separately with different assignable causes. Quick and accurate knowledge of the type of control chart patterns (CCPs), either because of process mean or variance, can greatly facilitate identification of assignable causes. Over the past few decades, however, process mean and variance CCPs are seldom studied simultaneously in the statistical process control literature. This study proposes a hybrid learning‐based model for simultaneous monitoring of process mean and variance CCPs. In this model, a self‐organization map neural network‐based quantization error control chart is responsible for detecting the out‐of‐control signals, a discrete particle swarm optimization‐based selective ensemble of back‐propagation networks is responsible for classifying the detected out‐of‐control signals into categories of mean and/or variance abnormality, and two discrete particle swarm optimization‐based selective ensembles of learning vector quantization networks are responsible for further identifying the detected mean and variance out‐of‐control signals as one of the specific CCP types, respectively. Extensive simulations indicate that the proposed hybrid learning‐based model outperforms other existing approaches in detecting mean and variance changes, while also capable of CCP recognition. In addition, a case study is conducted to demonstrate how the proposed hybrid learning‐based model can function as an effective tool for monitoring mean and variance simultaneously. Copyright © 2013 John Wiley & Sons, Ltd.     

A Spatiotemporal Method for the Monitoring of Image Data

Machine vision systems are increasingly being used in industrial applications because of their ability to quickly provide information on product geometry, surface defects, surface finish, and other product and process characteristics. Previous research for monitoring these visual characteristics using image data has focused on either detecting changes within an image or between images. Extending these methods to include both the spatial and the temporal aspects of image data would provide more detailed diagnostic information, which would be of great value to industrial practitioners. Therefore, in this article, we show how image data can be monitored using a spatiotemporal framework that is based on an extension of a generalized likelihood ratio control chart. The performance of the proposed method is evaluated through computer simulations and experimental studies. The results show that our proposed spatiotemporal method is capable of quickly detecting the emergence of a fault. The computer simulations also show that our proposed generalized likelihood ratio control charting method provides a good estimate of the change point and the size/location of the fault, which are important fault diagnostic metrics that are not typically provided in the image monitoring literature. Finally, we highlight some research opportunities and provide some advice to practitioners. Copyright © 2012 John Wiley & Sons, Ltd.     

CS‐EWMA Chart for Monitoring Process Dispersion

Control charts are the most extensively used technique to detect the presence of special cause variations in processes. They can be classified into memory and memoryless control charts. Cumulative sum and exponentially weighted moving average control charts are memory‐type control charts as their control structures are developed in such a way that the past information is not ignored as it is done in the case of memoryless control charts, like the Shewhart‐type control charts. The present study is based on the proposal of a new memory‐type control chart for process dispersion. This chart is named as CS‐EWMA chart as its plotting statistic is based on a cumulative sum of the exponentially weighted moving averages. Comparisons with other memory charts used to monitor the process dispersion are done by means of the average run length. An illustration of the proposed technique is done by applying the CS‐EWMA chart on a simulated dataset. Copyright © 2012 John Wiley & Sons, Ltd.     

A CCC‐r chart for high‐yield processes

The cumulative count of a conforming (CCC) chart is used to monitor high‐quality processes and is based on the number of items inspected until observing r non‐conforming ones. This charting technique is known as a CCC‐r chart. The function of the CCC‐r chart is the sensitive detection of an upward shift in the fraction defectives of the process, p. As r gets larger, the CCC‐r chart becomes more sensitive to small changes of upward shift in p. However, since many observations are required to obtain a plotting point on the chart, the cost is fairly high. For this trade‐off problem it is necessary to determine the optimal number of non‐conforming items observed before a point is plotted, the sampling (inspection) interval, and the lower control limit for the chart. In this paper a simplified optimal design method is proposed. For illustrative purposes, some numerical results for the optimal design parameter values are provided. The expected profits per cycle obtained using the proposed optimal design method are compared with those obtained using other misspecified parameter values. The effects of changing these parameters on the profit function are shown graphically. Copyright © 2001 John Wiley & Sons, Ltd.