Monitoring Process Variance Using an ARL‐unbiased EWMA‐p Control Chart

Control charts are effective tools for signal detection in manufacturing processes. As much of the data in industries come from processes having non‐normal or unknown distributions, the commonly used Shewhart variable control charts cannot be appropriately used, because they depend heavily on the normality assumption. The average run length (ARL) is generally used to measure the detection performance of a process when using a control chart, but it is biased for the monitoring statistic with an asymmetric distribution. That is, the ARL‐biased control chart leads to take longer to detect the shifts in parameter than to trigger a false alarm. To overcome this problem, we herein propose an ARL‐unbiased exponentially weighted moving average proportion (EWMA‐p) chart to monitor the process variance for process data with non‐normal or unknown distributions. We further explore the procedure to determine the control limits and to investigate the out‐of‐control variance detection performance of the ARL‐unbiased EWMA‐p chart. With a numerical example involving non‐normal service times from a bank branch in Taiwan, we illustrate the applications of the proposed ARL‐unbiased EWMA‐p chart and also compare the out‐of‐control detection performance of the ARL‐unbiased EWMA‐p chart, the arcsin transformed symmetric EWMA variance, and other existing variance charts. The proposed ARL‐unbiased EWMA‐p chart shows superior detection performance. Thus, we recommend the ARL‐unbiased EWMA‐p chart for process data with non‐normal or unknown distributions. Copyright © 2015 John Wiley & Sons, Ltd.     

A double sampling scheme for process variability monitoring

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries come from processes exhibiting nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. This paper thus proposes a standardized asymmetric exponentially weighted moving average (EWMA) variance chart with a double sampling scheme (SDS EWMA‐AV chart) for monitoring process variability. We further explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using the proposed SDS EWMA‐AV chart. The performance of the SDS EWMA‐AV chart and that of the single sampling EWMA variance (SS EWMA‐V) chart are then compared, with the former showing superior out‐of‐control detection performance versus the latter. We also compare the out‐of‐control variance detection performance of the proposed chart with those of nonparametric variance charts, the nonparametric Mood variance chart (NP‐M chart) with runs rules, and the nonparametric likelihood ratio‐based distribution‐free EWMA (NLE) chart and the combination of traditional EWMA (CEW) and the SS EWMA‐V control charts by considering cases in which the critical quality characteristic presents normal, double exponential, uniform, chi‐square, and exponential distributions. Comparison results show that the proposed chart always outperforms the NP‐M with runs rules, the NLE, CEW, and the SS EWMA‐V control charts. We hence recommend employing the SDS EWMA‐AV chart. Finally, a numerical example of a service system for a bank branch in Taiwan is used to illustrate the application of the proposed variability control chart.     

A Distribution‐freeCUSUMChart for Monitoring Variability of AutocorrelatedProcesses

We present a distribution‐free tabular cumulative sum chart for monitoring the variability of an autocorrelated process. A quantity known as the asymptotic variance parameter is employed as a measure of the variability, and a distribution‐free tabular cumulative sum chart is applied to variance estimates calculated from batches of nonoverlapping samples. The proposed chart is applicable to a stationary process with a general marginal distribution and a general autocorrelation structure. It also determines control limits analytically without trial‐and‐error simulations. The performance of the proposed chart is tested on stationary processes with both normal and nonnormal marginals with various autocorrelation structures. Copyright © 2014 John Wiley & Sons, Ltd.     

Improved CUSUM monitoring of Markov counting process with frequent zeros

There has been a growing interest in monitoring processes featuring serial dependence and zero inflation. The phenomenon of excessive zeros often occurs in count time series because of the advancement of quality in manufacturing process. In this study, we propose three control charts, such as the cumulative sum chart with delay rule (CUSUM‐DR), conforming run length (CRL)‐CUSUM chart, and combined Shewhart CRL‐CUSUM chart, to enhance the performance of monitoring Markov counting processes with excessive zeros. Numerical experiments are conducted based on integer‐valued autoregressive time series models, for example, zero‐inflated Poisson INAR and INARCH, to evaluate the performance of the proposed charts designed for the detection of mean increase. A real example is also illustrated to demonstrate the usability of our proposed charts.     

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 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.     

Phase II monitoring of covariance stationary autocorrelated processes

Statistical process control charts are intended to assist operators in detecting process changes. If a process change does occur, the control chart should detect the change quickly. Owing to the recent advancements in data retrieval and storage technologies, today's industrial processes are becoming increasingly autocorrelated. As a result, in this paper we investigate a process‐monitoring tool for autocorrelated processes that quickly responds to process mean shifts regardless of the magnitude of the change, while supplying useful diagnostic information upon signaling. A likelihood ratio approach was used to develop a phase II control chart for a permanent step change in the mean of an ARMA (p, q) (autoregressive‐moving average) process. Monte Carlo simulation was used to evaluate the average run length (ARL) performance of this chart relative to that of the more recently proposed ARMA chart. Results indicate that the proposed chart responds more quickly to process mean shifts, relative to the ARMA chart, while supplying useful diagnostic information, including the maximum likelihood estimates of the time and the magnitude of the process shift. These crucial change point diagnostics can greatly enhance the special cause investigation. Copyright © 2010 John Wiley & Sons, Ltd.     

Model‐based Multivariate Monitoring Charts for Autocorrelated Processes

Autocorrelation or nonstationarity may seriously impact the performance of conventional Hotelling's T² charts. We suggest modeling processes with multivariate autoregressive integrated moving average time series models and propose two model‐based monitoring charts. One monitors the predicted value and provides information about the need for mean adjustments. The other is a Hotelling's T² control chart applied to the residuals. The average run length performance of the residual‐based Hotelling's T² chart is compared with the observed data‐based Hotelling's T² chart for a group of first‐order vector autoregressive models. We show that the new chart in most cases performs well. Copyright © 2013 John Wiley & Sons, Ltd.     

MEWMA Control Chart and Process Capability Indices for Simple Linear Profiles with Within‐profile Autocorrelation

A multivariate exponentially weighted moving average (MEWMA) control chart is proposed for detecting process shifts during the phase II monitoring of simple linear profiles (SLPs) in the presence of within‐profile autocorrelation. The proposed control chart is called MEWMA‐SLP. Furthermore, two process capability indices are proposed for evaluating the capability of in‐control SLP processes, and their utilization is demonstrated through examples. Intensive simulations reveal that the MEWMA‐SLP chart is more sensitive than existing control charts in detecting profile shifts. Copyright © 2016 John Wiley & Sons, Ltd.     

Effective Control Charts for Monitoring Multivariate Process Dispersion

When monitoring process dispersion, it is common to pay more attention to dispersion increases than to decreases for practical reasons. Nonetheless, it is also important to detect dispersion decreases for two reasons: (i) it deserves further investigations as to why the process has improved; and (ii) if the process has changed, the settings of the control chart would need to be adjusted for effective future monitoring. In this paper, we first propose an effective control chart for detecting multivariate dispersion decreases in phase II process monitoring, which is constructed using the same approach as that of the one‐sided likelihood‐ratio‐test‐based multivariate chart proposed recently in the literature for detecting dispersion increases. We then discuss a combined charting scheme by combining these two one‐sided charts for detecting either dispersion increases or decreases. Comparative simulation studies show that the proposed combined control charting scheme outperforms several existing two‐sided control charts in terms of the average run length when the process dispersion indeed increases or decreases. Two real‐life examples are presented to demonstrate the applicability of the proposed charts. Copyright © 2011 John Wiley & Sons, Ltd.     

Process monitoring with ICA‐based signal extraction technique and CART approach

In order to reduce the variation in a manufacturing process, traditional statistical process control (SPC) techniques are the most frequently used tools in monitoring engineering process control (EPC)‐controlled processes for detecting assignable cause process variation. Even though application of SPC with EPC can successfully detect time points when abnormalities occur during process, their combination can also cause an increased occurrence of false alarms when autocorrelation is present in the process. In this paper, we propose an independent component analysis‐based signal extraction technique with classification and regression tree approach to identify disturbance levels in the correlated process parameters. For comparison, traditional cumulative sum (CUSUM) chart was constructed to evaluate the identifying capability of the proposed approach. The experimental results show that the proposed method outperforms CUSUM control chart in most instances. Copyright © 2008 John Wiley & Sons, Ltd.     

A New Cumulative Sum Quality Control Scheme for Monitoring the Process Mean

A control chart is a powerful statistical process monitoring tool that is frequently used in many industrial and service organizations to monitor in‐control and out‐of‐control performances of the manufacturing processes. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recognized as potentially powerful tool in quality and management control. These control charts are sensitive to both small and moderate changes in the process. In this paper, we propose a new CUSUM (NCUSUM) quality control scheme for efficiently monitoring the process mean. It is shown that the classical CUSUM control chart is a special case of the proposed controlling scheme. The NCUSUM control chart is compared with some of the recently proposed control charts by using characteristics of the distribution of run length, i.e. average run length, median run length and standard deviation of run length. It is worth mentioning that the NCUSUM control chart detects the random shifts in the process mean substantially quicker than the classical CUSUM, fast initial response‐based CUSUM, adaptive CUSUM with EWMA‐based shift, adaptive EWMA and Shewhart–CUSUM control charts. An illustrative example is given to exemplify the implementation of the proposed quality control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

New Exponentially Weighted Moving Average Control Charts for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have received considerable attention for detecting small changes in the process mean or the process variability. Several EWMA control charts are constructed using logarithmic and normalizing transformations on unbiased sample variance for monitoring changes in the process dispersion. In this paper, we propose new EWMA control charts for monitoring process dispersion based on the best linear unbiased absolute estimators obtained under simple random sampling (SRS) and ranked set sampling (RSS) schemes, named EWMA‐SRS and EWMA‐RSS control charts. The performance of the proposed EWMA control charts is evaluated in terms of the average run length and standard deviation of run length, estimated by using Monte Carlo simulations. The proposed EWMA control charts are then compared with their existing counterparts for detecting increases and decreases in the process dispersion. It turns out that the EWMA‐RSS control chart performs uniformly better than its analogues for detecting overall changes in process dispersion. Moreover, the EWMA‐SRS chart significantly outperforms the existing EWMA charts for detecting increases in process variability. A real data set is also used to explain the construction and operations of the proposed EWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponentially weighted moving average chart with a likelihood ratio test for monitoring autocorrelated processes

In this article, an exponential weighted moving average chart based on a likelihood ratio test is developed to monitor the mean and variance shifts simultaneously for autocorrelated processes. A simple method is used to transform the positively autocorrelated data to the negatively autocorrelated data. The average run length of the proposed chart is derived from a simulation approach. The performance of our proposed chart is compared with some existing charts. The results show that the proposed chart provides better performance for detecting a wide range of shifts in the process mean and variance simultaneously. Additionally, the economic performance of different charts under the first-order autoregressive model is provided. A real example of a stepper motor in the heating, ventilation, and air conditioning module is used to demonstrate the application of the proposed method.     

New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion

A statistical quality control chart is widely recognized as a potentially powerful tool that is frequently used in many manufacturing and service industries to monitor the quality of the product or manufacturing processes. In this paper, we propose new synthetic control charts for monitoring the process mean and the process dispersion. The proposed synthetic charts are based on ranked set sampling (RSS), median RSS (MRSS), and ordered RSS (ORSS) schemes, named synthetic‐RSS, synthetic‐MRSS, and synthetic‐ORSS charts, respectively. Average run lengths are used to evaluate the performances of the control charts. It is found that the synthetic‐RSS and synthetic‐MRSS mean charts perform uniformly better than the Shewhart mean chart based on simple random sampling (Shewhart‐SRS), synthetic‐SRS, double sampling‐SRS, Shewhart‐RSS, and Shewhart‐MRSS mean charts. The proposed synthetic charts generally outperform the exponentially weighted moving average (EWMA) chart based on SRS in the detection of large mean shifts. We also compare the performance of the synthetic‐ORSS dispersion chart with the existing powerful dispersion charts. It turns out that the synthetic‐ORSS chart also performs uniformly better than the Shewhart‐R, Shewhart‐S, synthetic‐R, synthetic‐S, synthetic‐D, cumulative sum (CUSUM) ln S², CUSUM‐R, CUSUM‐S, EWMA‐ln S², and change point CUSUM charts for detecting increases in the process dispersion. A similar trend is observed when the proposed synthetic charts are constructed under imperfect RSS schemes. Illustrative examples are used to demonstrate the implementation of the proposed synthetic charts. Copyright © 2014 John Wiley & Sons, Ltd.     

A EWMA Control Chart for Exponential Distributed Quality Based on Moving Average Statistics

We propose an exponentially weighted moving average (EWMA) control chart for monitoring exponential distributed quality characteristics. The proposed control chart first transforms the sample data to approximate normal variables, then calculates the moving average (MA) statistic for each subgroup, and finally constructs the EWMA statistic based on the current and the previous MA statistics. The upper and the lower control limits are derived using the mean and the variance of EWMA statistics. The in‐control and the out‐of‐control average run lengths are derived and tabularized according to process shift parameters and smoothing constants. It is shown that the proposed control chart outperforms the MA control chart for all shift parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Synthetic Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as a potentially powerful process monitoring tool of the statistical process control because of their excellent speed in detecting small to moderate shifts in the process parameters. Recently, new EWMA and synthetic control charts have been proposed based on the best linear unbiased estimator of the scale parameter using ordered ranked set sampling (ORSS) scheme, named EWMA‐ORSS and synthetic‐ORSS charts, respectively. In this paper, we extend the work and propose a new synthetic EWMA (SynEWMA) control chart for monitoring the process dispersion using ORSS, named SynEWMA‐ORSS chart. The SynEWMA‐ORSS chart is an integration of the EWMA‐ORSS chart and the conforming run length chart. Extensive Monte Carlo simulations are used to estimate the run length performances of the proposed control chart. A comprehensive comparison of the run length performances of the proposed and the existing powerful control charts reveals that the SynEWMA‐ORSS chart outperforms the synthetic‐R, synthetic‐S, synthetic‐D, synthetic‐ORSS, CUSUM‐R, CUSUM‐S, CUSUM‐ln S², EWMA‐ln S² and EWMA‐ORSS charts when detecting small shifts in the process dispersion. A similar trend is observed when the proposed control chart is constructed under imperfect rankings. An application to a real data is also provided to demonstrate the implementation and application of the proposed control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

Effective Control Charts for Monitoring the NGINAR(1) Process

In recent years, there has been a growing interest in the control of autocorrelated count data. Existing results focus on the Poisson integer‐valued autoregressive (INAR) process, but this process cannot deal with overdispersion (variance is greater than mean), which is a common phenomenon in count data. We propose to control the autocorrelated count data based on a new geometric INAR (NGINAR) process, which is an alternative to the Poisson one. In this paper, we use the combined jumps chart, the cumulative sum chart, and the combined exponentially weighted moving average chart to detect the shift of parameters in the process. We compare the performance of these charts for the case of an underlying NGINAR(1) process in terms of the average run lengths. One real example is presented to demonstrate good performances of the charts. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 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.