基于神经网络的SPC/EPC整合过程监测方法研究

为解决统计过程控制(SPC)/工程过程调整(EPC)整合引起的传统SPC控制图监测异常扰动效率低的问题,提出了采用神经网络技术监测SPC/EPC整合过程的策略,并对神经网络模型结构和参数设置进行分析,构建过程输入、过程输出及两者的协方差为输入参数,异常扰动发生与否为输出参数的3层神经网络模型。为验证该方法的性能,进行了大量的比较实验:即对相同的样本,分别采用Shewhar图、CUSUM图和上述神经网络模型进行监测。实验结果表明:神经网络模型能准确监测幅度大于2的阶跃扰动和大于2的过程漂移,平均运行步长(ARL)为1;传统SPC监测技术只能较准确地(监测率大于90%)监测幅度大于5的阶跃扰动和大于2的过程漂移,ARL大于2。与传统监测方法相比,该方法能快速有效地监测异常扰动的发生。     

An economic model for integrated APC and SPC control charts

As suggested by Box and Kramer [1] and others, it is possible to reduce both the special cause and common cause variations by applying Statistical Process Control (SPC) methods to monitor the output of an Automatic Process Control (APC) controlled process. In this paper, we develop an economic model for SPC monitoring of APC controlled processes. We also develop an economic loss-based criterion, the Average Quality Cost (AQC), to evaluate the performance of SPC charting methods. The AQC and the traditional average run length of three common SPC charts are investigated and compared.     

Efficient homogeneously weighted dispersion control charts with an application to distillation process

Monitoring disturbances in process dispersion using control chart is mostly based on the assumption that the quality characteristic follows normal distribution, which is not the case in many real-life situations. This paper proposes a set of new dispersion charts based on the homogeneously weighted moving average (HWMA) scheme, for efficient detection of shifts in process standard deviation (σ). These charts are based on a variety of σ estimators and are investigated for normal as well as heavy tailed symmetric and skewed distributions. The shift detection ability of the charts is evaluated using different run length characteristics, such as average run length (ARL), extra quadratic loss (EQL), and relative ARL measures. The performance of the proposed HWMA control charts is also compared with the existing EWMA dispersion charts, using different design parameters. Furthermore, an illustrative example is presented to monitor the vapor pressure in a distillation process.     

Economic design of the integrated multivariate EPC and multivariate SPC charts

The goal of engineering process control (EPC) is to minimize variability by adjusting some manipulative process variables. The goal of statistical process control (SPC) is to reduce variability by monitoring and eliminating assignable causes of variation. As suggested by Box and Kramer and others, it is possible to reduce both special cause and common cause variations by integrating EPC and SPC. In the integrated multivariate EPC (MEPC) and multivariate SPC (MSPC) charts, we propose some statistical and economic criteria, such as the average Euclidean distance from the target vector and the average quality cost (AQC) to evaluate the performance of the MEPC/MSPC charts. The traditional average run length (ARL), average Euclidean distance and AQC of three MSPC charts are investigated and compared. The results of the simulations show that the MEPC/MGWMA chart is more effective and more economical than both the MEPC/MEWMA chart and the MEPC/Hotelling multivariate chart in detecting small shifts of the mean vector. Copyright © 2006 John Wiley & Sons, Ltd.     

Monitoring the Weibull Shape Parameter by Control Charts for the Sample Range of Type II Censored Data

In this paper, we propose control charts to monitor the Weibull shape parameter β under type II (failure) censoring. This chart scheme is based on the sample ranges of smallest extreme value distributions derived from Weibull processes. We suggest one‐sided (high‐side or low‐side) and two‐sided charts, which are unbiased with respect to the average run length (ARL). The control limits for all types of charts depend on the sample size, the number of failures c under type II censoring, the desired stable‐process ARL, and the stable‐process value of β. This article also considers sample size requirements for phase I in retrospective charts. We investigate the effect of c on the out‐of‐control ARL. We discuss a simple approach to choosing c by cost minimization. The proposed schemes are then applied to data on the breaking strengths of carbon fibers. Copyright © 2011 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.     

Dual multivariate CUSUM charts with auxiliary information for process mean

It is customary to increase the sensitivity of a control chart using an efficient estimator of the underlying process parameter which is being monitored. In this paper, using an auxiliary information-based (AIB) mean estimator, we propose dual multivariate CUSUM (DMCUSUM) and mixed DMCUSUM (MDMCUSUM) charts, called the AIB-DMCUSUM and AIB-MDMCUSUM charts, with and without fast initial response features for monitoring the mean vector of a multivariate normally distributed process. The DMCUSUM chart combines two similar-type multivariate CUSUM (MCUSUM) charts while the MDMCUSUM chart combines two different-type MCUSUM charts, into a single chart. The objective of two multivariate subcharts in the DMCUSUM/MDMCUSUM chart is to simultaneously detect small-to-moderate and moderate-to-large shifts in the process mean vector. Monte Carlo simulations are used to compute the run length characteristics, including the average run length (ARL), extra quadratic loss, and integral of the relative ARL. Based on detailed run length comparisons, it turns out that the AIB-DMCUSUM and AIB-MDMCUSUM charts uniformly and substantially outperform the DMCUSUM and MDMCUSUM charts when detecting different sizes of shift in the process mean vector. A real dataset is used to explain the implementation of proposed AIB multivariate charts.     

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.     

Correction factors for Shewhart and control charts to achieve desired unconditional ARL

In this paper we derive correction factors for Shewhart control charts that monitor individual observations as well as subgroup averages. In practice, the distribution parameters of the process characteristic of interest are unknown and, therefore, have to be estimated. A well-known performance measure within Statistical Process Monitoring is the expectation of the average run length (ARL), defined as the unconditional ARL. A practitioner may want to design a control chart such that, in the in-control situation, it has a certain expected ARL. However, accurate correction factors that lead to such an unconditional ARL are not yet available. We derive correction factors that guarantee a certain unconditional in-control ARL. We use approximations to derive the factors and show their accuracy and the performance of the control charts – based on the new factors – in out-of-control situations. We also evaluate the variation between the ARLs of the individually estimated control charts.     

The revised Tennessee Eastman process simulator as testbed for SPC and DoE methods

Engineering process control and high-dimensional, time-dependent data present great methodological challenges when applying statistical process control (SPC) and design of experiments (DoE) in continuous industrial processes. Process simulators with an ability to mimic these challenges are instrumental in research and education. This article focuses on the revised Tennessee Eastman process simulator providing guidelines for its use as a testbed for SPC and DoE methods. We provide flowcharts that can support new users to get started in the Simulink/Matlab framework, and illustrate how to run stochastic simulations for SPC and DoE applications using the Tennessee Eastman process.     

On‐line Identification and Quantification of Mean Shifts in Bivariate Processes using a Neural Network‐based Approach

Many statistical process control (SPC) problems are multivariate in nature because the quality of a given process or product is determined by several interrelated variables. Various multivariate control charts (e.g. Hotelling's , multivariate cumulative sum and multivariate exponentially weighted moving average charts) have been designed for detecting mean shifts. However, the main shortcoming of such charts is that they can detect an unusual event but do not directly provide the information required by a practitioner to determine which variable or group of variables has caused the out‐of‐control signal. In addition, these charts cannot provide more detailed shift information, for example the shift magnitude, which would be very useful for quality practitioners to search the assignable causes that give rise to the out‐of‐control situation. This work proposes a neural network‐based model that can identify and quantify the mean shifts in bivariate processes on‐line. The performance evaluation performed by the simulation demonstrates that the proposed model outperforms the conventional multivariate control schemes in terms of average run length, and can accurately estimate the magnitude of the shift of each of the shifted variables in a real‐time mode. Extensive simulation is also carried out to examine the effects of correlation on the performance of the proposed model. A numerical example is presented to illustrate the usage of the proposed model. Although a mean shift identification and quantification tool for bivariate SPC is the particular application presented here, the proposed neural network‐based methodology can be applied to multivariate SPC in general. Copyright © 2006 John Wiley & Sons, Ltd.     

Monitoring of Proportional‐Integral Controlled Processes using a Bayesian Time Series Analysis Method

Recently, there has been interest in applying statistical process monitoring methods to processes controlled with feedback controllers in order to eliminate assignable causes and achieve reduced overall variability. In this paper, we propose a Bayesian change‐point method to monitor processes regulated with proportional‐integral controllers. The approach is based on fitting an exponential rise model to the control input actions in response to a step shift and employs a change‐point method to detect the change. Simulation studies show that the proposed method has better run‐length performance in detecting step shifts in controlled processes than Shewhart chart on individuals and special‐cause chart on residuals of time series model. Copyright © 2013 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.     

On designing an efficient control chart to monitor fraction nonconforming

Process control measures are mostly applied in production and manufacturing industries. The most important tool used in these disciplines is control chart. In manufacturing and production processes, when the quality characteristic of interest cannot be directly measured, it becomes essential to apply attribute control charts. To monitor fraction nonconforming of the output, quality practitioners mostly prefer p-chart. In this article, a new progressive mean (PM) control chart is being proposed for monitoring drift in proportion of nonconforming products. The design evaluations of the proposed chart are made and compared through different properties of run length distribution, such as average run length (ARL), standard deviation of run length (SDRL), and some percentile points. The performance of the proposed chart is assessed under zero-state and steady-state scenarios. The proposed PM chart is compared with p-chart, moving average (MA) chart, optimal CUSUM chart, modified exponentially weighted moving average (EWMA) chart, and runs rules p-charts for monitoring fraction nonconforming. The proposed chart spots efficiently sustained disturbances in the process as compared with their existing counterparts. Two illustrative examples are also provided; one from real-life application of nonconforming bearing and seal assemblies data and the other from simulated data for the implementation of PM chart.     

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.     

The Design of the ARL‐Unbiased S2 Chart When the In‐Control Variance Is Estimated

The S² chart has been known as a powerful tool to monitor the variability of the normal process. When the variance of the process is unknown, it needs to be estimated by Phase I samples. It is well known that there are serious effects of parameter estimation on the performance of the S² chart based on known parameter assumption. If the effects of parameter estimation are not considered, it can lead to an increase in the number of false alarms and a reduction in the ability of the chart to detect process changes except for very small shifts in the variance. Based on the criterion of average run length (ARL) unbiased, a S² control chart is developed when the in‐control variance is estimated. The performance of the proposed control chart is also evaluated in terms of the ARL and standard deviation of the run length. Finally, an example is used to illustrate the proposed control chart. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of control charts with m‐of‐m runs rules

This paper investigates economic–statistical properties of the X? charts supplemented with m‐of‐m runs rules. An out‐of‐control condition for the chart is either a point beyond a control limit or a run of m‐of‐m successive points beyond a warning limit. The sampling process is modeled by a Markov chain with 2m states. The steady‐state probability for each state and the average run length (ARL) from each state of the Markov chain are derived in explicit formulas. Then the stationary average run length (SALR) is derived so as to develop an economic–statistical model. Using this model, the design parameters are optimized by minimizing the cost function with constraints on the average time to signal (ATS). The X? chart supplemented with m‐of‐m runs rules is compared with the Shewhart X? chart in terms of the SARL and the cost function. Sensitivity of the design parameters with respect to the cost function is also analyzed. General guidelines for implementing the X? chart with m‐of‐m runs rules are presented from those observations. It should be emphasized that supplementing run rules may provide feasible and efficient solutions even if the sample size is limited, while the Shewhart X? chart may not. Copyright © 2009 John Wiley & Sons, Ltd.     

An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

We evaluate the performance of the Crosier's cumulative sum (C‐CUSUM) control chart when the probability distribution parameters of the underlying quality characteristic are estimated from Phase I data. Because the average run length (ARL) under estimated parameters is a random variable, we study the estimation effect on the chart performance in terms of the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL). Previous evaluations of this control chart were conducted while assuming known process parameters. Using the Markov chain and simulation approaches, we evaluate the in‐control performance of the chart and provide some quantiles for its in‐control ARL distribution under estimated parameters. We also compare the performance of the C‐CUSUM chart to that of the ordinary CUSUM (O‐CUSUM) chart when the process parameters are unknown. Our results show that large number of Phase I samples are required to achieve a quite reasonable performance. Additionally, the performance of the C‐CUSUM chart is found to be superior to that of the O‐CUSUM chart. Finally, we recommend the use of a recently proposed bootstrap procedure in designing the C‐CUSUM chart to guarantee, at a certain probability, that the in‐control ARL will be of at least the desired value using the available amount of Phase I data. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of Autocorrelation on Performance of the MCUSUM Control Chart

Control charts are designed to detect assignable causes of variation that may occur in production processes. When traditional control charts are used there is the implicit assumption that observations are independently and identically distributed over time. It is also assumed that the probability distribution representing the observations has a known functional form and is constant over time. However, in practice, observations generated by continuous as well as discrete production processes are often serially correlated. Autocorrelation not only violates the independence assumption of traditional control charts but also can affect the performance of control charts adversely. This point has received considerable attention in the past few decades. In this paper, we investigate the performance of the multivariate cumulative sum (MCUSUM) control chart in the presence of autocorrelation. Using an average run length (ARL) criterion, it is shown that autocorrelation can deteriorate the performance of MCUSUM control charts. A solution based on a time series model is presented that improves ARL properties of MCUSUM control charts. Copyright © 2005 John Wiley & Sons, Ltd.     

Risk‐based metrics for performance evaluation of control charts

Control charts are commonly evaluated in terms of their average run length (ARL). However, since run length distributions are typically strongly skewed, the ARL gives a very limited impression about the actual run length performance. In this study, it is proposed to evaluate a control chart's performance using risk metrics, specifically the value at risk and the tail conditional expectation. When a control chart is evaluated for an in‐control performance, the risk is an early occurrence of a false alarm, whereas in an out‐of‐control state, there is a risk of a delayed detection. For these situations, risk metric computations are derived and exemplified for diverse types of control charts. It is demonstrated that the use of such risk metrics leads to important new insights into a control chart's performance. In addition to the cases of known process parameters for control chart design, these risk metrics are further used to analyze the estimation uncertainty in evaluating a control chart's performance if the design parameters rely on a phase 1 analysis. Benefits of the risk‐based metrics are discussed thoroughly, and these are recommended as supplements to the traditional ARL metric.