Identifying source(s) of out-of-control signals in multivariate manufacturing processes using selective neural network ensemble

In multivariate statistical process control (MSPC), most multivariate quality control charts are shown to be effective in detecting out-of-control signals based upon an overall statistic. But these charts do not relieve the need for pinpointing source(s) of the out-of-control signals. Neural networks (NNs) have excellent noise tolerance and high pattern identification capability in real time, which have been applied successfully in MSPC. This study proposed a selective NN ensemble approach DPSOEN, where several selected NNs are jointly used to classify source(s) of out-of-control signals in multivariate processes. The immediate location of the abnormal source(s) can greatly narrow down the set of possible assignable causes, facilitating rapid analysis and corrective action by quality operators. The performance of DPSOEN is analyzed in multivariate processes. It shows improved generalization performance that outperforms those of single NNs and Ensemble All approach. The investigation proposed a heuristic approach for applying the DPSOEN-based model as an effective and useful tool to identify abnormal source(s) in bivariate statistical process control (SPC) with potential application for MSPC in general.     

Integrating economics into quality control charts

When control of a manufacturing process is needed, the common tool is Statistical Quality control (SQC). In the past, however, economic factors were the results after employing the SQC charts. Design of control charts refers to the specification of the sample size, the sampling frequency and the control limits for the chart. The authors have tested a model that uses economics as an integral part for the design of an X-bar control chart.

Douglas C. Montgomery developed a computer program for the optimal economic design of an X-bar control chart. The program is based on the cost model proposed by A.J. Duncan.

Montgomery's program was modified to select the optimal design parameters from a table of parameter values. Subroutines were developed to enable the user to enter the number of subgroups and the data points for each subgroup. The economically designed control chart is plotted using standard Graphical Kernel System (GKS) subroutines.     

On the performance of the conditional decision procedure in geometric charts

To improve the performance of control charts the conditional decision procedure (CDP) incorporates a number of previous observations into the chart’s decision rule. It is expected that charts with this runs rule are more sensitive to shifts in the process parameter. To signal an out-of-control condition more quickly some charts use a headstart feature. They are referred as charts with fast initial response (FIR). The CDP chart can also be used with FIR. In this article we analyze and compare the performance of geometric CDP charts with and with no FIR. To do it we model the CDP charts with a Markov chain and find closed-form ARL expressions. We find the conditional decision procedure useful when the fraction p of nonconforming units deteriorates. However the CDP chart is not very effective for signaling decreases in p.     

A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

Control charts are the most popular Statistical Process Control (SPC) tools used to monitor process changes. When a control chart produces an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of the process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the process change is known as change-point estimation problem. Most of the traditional change-point methods are based on maximum likelihood estimators (MLE) which need strict statistical assumptions. In this paper, first, we introduce clustering as a potential tool for change-point estimation. Next, we discuss the challenges of employing clustering methods for change-point estimation. Afterwards, based on the concepts of fuzzy clustering and statistical methods, we develop a novel hybrid approach which is able to effectively estimate change-points in processes with either fixed or variable sample size. Using extensive simulation studies, we also show that the proposed approach performs considerably well in all considered conditions in comparison to powerful statistical methods and popular fuzzy clustering techniques. The proposed approach can be employed for processes with either normal or non-normal distributions. It is also applicable to both phase-I and phase-II. Finally, it can estimate the true values of both in- and out-of-control states’ parameters.     

Multi-criteria design of an control chart

Control chart designs are widely studied because control charts are not only costly used but also play an important role in improving firms' quality and productivity. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. In this paper, a possible combination of design parameters is considered as a decision-making unit; it is characterized by three attributes: hourly expected cost, average run length of process being controlled, and detection power of the chart designed with the selected parameters. Accordingly, optimal design of control charts can be formulated as a multiple criteria decision-making (MCDM) problem. To solve the MCDM problem, a solution procedure on the basis of data envelopment analysis is proposed. Finally, an industrial application is presented to illustrate the solution procedure. Also, adjustment to control chart design parameters is suggested when there are process improvements or process deteriorations.     

Multi-criteria design of an X̄ control chart

Control chart designs are widely studied because control charts are not only costly used but also play an important role in improving firms' quality and productivity. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. In this paper, a possible combination of design parameters is considered as a decision-making unit; it is characterized by three attributes: hourly expected cost, average run length of process being controlled, and detection power of the chart designed with the selected parameters. Accordingly, optimal design of control charts can be formulated as a multiple criteria decision-making (MCDM) problem. To solve the MCDM problem, a solution procedure on the basis of data envelopment analysis is proposed. Finally, an industrial application is presented to illustrate the solution procedure. Also, adjustment to control chart design parameters is suggested when there are process improvements or process deteriorations.     

Using Bayesian networks for root cause analysis in statistical process control

Despite their fame and capability in detecting out-of-control conditions, control charts are not effective tools for fault diagnosis. There are other techniques in the literature mainly based on process information and control charts patterns to help control charts for root cause analysis. However these methods are limited in practice due to their dependency on the expertise of practitioners. In this study, we develop a network for capturing the cause and effect relationship among chart patterns, process information and possible root causes/assignable causes. This network is then trained under the framework of Bayesian networks and a suggested data structure using process information and chart patterns. The proposed method provides a real time identification of single and multiple assignable causes of failures as well as false alarms while improving itself performance by learning from mistakes. It also has an acceptable performance on missing data. This is demonstrated by comparing the performance of the proposed method with methods like neural nets and K-Nearest Neighbor under extensive simulation studies.     

Quality control expert systems: a review of pertinent literature

Statistical quality control (SQC) is an effective tool that ensures quality products and services by means of control charts, the essence of SQC, and sampling plans. While the computation of sample statistics and the development of control charts are routine exercises, the interpretation of chart patterns, trends and the associated diagnosis of assignable causes requires expert knowledge. The present trend is to develop a quality control system and apply it throughout the company (company-wide quality control CWQC or total quality control - TQC). This frequently means involvement of non-quality personnel in QC teams. Additionally, many companies are faced with a shortage of experienced quality controllers and individuals who can train and educate others on statistical quality control techniques. Quality control expert systems (QCESs) are considered as one way to alleviate these difficulties. In recent years, quality control expert systems have attracted the attention of both quality researchers and practitioners. This paper reviews existing quality control expert systems and recommends a set of quality engineering techniques that should be used to form a knowledge base, the heart of an expert system.     

A neural network ensemble-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes

In multivariate statistical process control, most multivariate quality control charts are shown to be effective in detecting out-of-control signals based upon an overall statistics. But these charts do not relieve the need for pinpointing source(s) of the out-of-control signals, which would be very useful for quality practitioners to locate the assignable causes that give rise to the out-of-control situation. In this study, a learning-based model has been investigated for monitoring and diagnosing out-of-control signals in a bivariate process. In this model, a selective neural network (NN) ensemble approach (DPSOEN, Discrete Particle Swarm Optimization) was developed for performing these tasks. The simulation results demonstrate that the proposed model outperforms the conventional multivariate control scheme in terms of average run length (ARL), and can accurately classify source(s) of out-of-control signals. Extensive experiment is also carried out to examine the effects of six statistical features on the performance of DPSOEN. Analysis from this study provides guidelines in developing NN ensemble-based Statistical process control recognition systems in multivariate processes.     

Optimal linear combination of Poisson variables for multivariate statistical process control

In this paper we analyze the monitoring of p Poisson quality characteristics simultaneously, developing a new multivariate control chart based on the linear combination of the Poisson variables, the LCP control chart. The optimization of the coefficients of this linear combination (and control limit) for minimizing the out-of-control ARL is constrained by the desired in-control ARL. In order to facilitate the use of this new control chart the optimization is carried out employing user-friendly Windows© software, which also makes a comparison of performance between this chart and other schemes based on monitoring a set of Poisson variables; namely a control chart on the sum of the variables (MP chart), a control chart on their maximum (MX chart) and an optimized set of univariate Poisson charts (Multiple scheme). The LCP control chart shows very good performance. First, the desired in-control ARL (ARL₀) is perfectly matched because the linear combination of Poisson variables is not constrained to integer values, which is an advantage over the rest of charts, which cannot in general match the required ARL₀ value. Second, in the vast majority of cases this scheme signals process shifts faster than the rest of the charts.     

A hybrid fuzzy adaptive sampling - Run rules for Shewhart control charts

In crisp run control rules, usually it is stated that a process moves very sharply from in-control condition to out-of-control act. This causes an increase in both false-alarm rate and control chart sensitivity. Moreover, the classical run control rules are not implemented on an intelligent sampling strategy that changes control charts’ parameters to reduce error probability when the process appears to have a shift in parameter values. This paper presents a new hybrid method based on a combination of fuzzified sensitivity criteria and fuzzy adaptive sampling rules, which make the control charts more sensitive and proactive while keeping false alarms rate acceptably low. The procedure is based on a simple strategy that includes varying control chart parameters (sample size and sample interval) based on current fuzzified state of the process and makes inference about the state of process based on fuzzified run rules. Furthermore, in this paper, the performance of the proposed method is examined and compared with both conventional run rules and adaptive sampling schemes.     

A new auxiliary information based cumulative sum median control chart for location monitoring

Control charts are commonly used tools in statistical process control for the detection of shifts in process parameters. Shewhart-type charts are efficient for large shift values, whereas cumulative sum (CUSUM) charts are effective in detecting medium and small shifts. Control chart use commonly assumes that data are free of outliers and parameters are known or correctly estimated based on an in-control process. In practice, these assumptions are not often true because some processes occasionally have outliers. Monitoring the location parameter is usually based on mean charts, which are seriously affected by violations of these assumptions. In this paper we propose several CUSUM median control charts based on auxiliary variables, and offer comparisons with their corresponding mean control charts. To monitor the location parameter, we examined the performance of mean and median control charts in the presence and absence of outliers. Both symmetric and non-symmetric processes were studied to examine the properties of the proposed control charts to monitor the location parameter using CUSUM control charts. We used different run length measures to study in-control and out-of-control performances of CUSUM charts. Results revealed that our proposed control charts perform much better than the traditional charts in the presence of outliers. A real application of our study was provided using data on concrete compressive strength as it relates to the quality of cement manufacturing.

     

基于多重相关状态采样的多元EWMA控制图

为提高控制图的监测效率,提出了一种基于多重相关状态采样的多元EWMA控制图,并利用改进后的马尔可夫链方法计算控制图的平均运行长度。根据不同参数下控制图的平均运行长度,分析了控制图在失控和受控状态下的性能表现,并与其它多元EWMA控制图进行比较。模拟结果表明,该控制图具有良好的监测能力。最后用一组模拟数据来说明该方法的使用。     

A new approach to detecting the process changes for multistage systems

The study aims to develop a new control chart model suitable for monitoring the process quality of multistage manufacturing systems.Considering both the auto-correlated process outputs and the correlation occurring between neighboring stages in a multistage manufacturing system, we first propose a new multiple linear regression model to describe their relationship. Then, the multistage residual EWMA and CUSUM control charts are used to monitor the overall process quality of multistage systems. Moreover, an overall run length (ORL) concept is adopted to compare the detecting performance for various multistage residual control charts. Finally, a numerical example with oxide thickness measurements of a three-stage silicon wafer manufacturing process is given to demonstrate the usefulness of our proposed multistage residual control charts in the Phase II monitoring. A computerized algorithm can also be written based on our proposed scheme for the multistage residual EWMA/CUSUM control charts and it may be further converted to an expert and intelligent system. Hopefully, the results of this study can provide a better alternative for detecting process change and serve as a useful guideline for quality practitioners when monitoring and controlling the process quality of multistage systems with auto-correlated data.     

Online monitoring and fault identification of mean shifts in bivariate processes using decision tree learning techniques

With modern data collection system and computers used for on-line process monitoring and fault identification in manufacturing processes, it is common to monitor more than one correlated process variables simultaneously. The main problems in most multivariate control charts (e.g., T ² charts, MCUSUM charts, MEWMA charts) are that they cannot give direct information on which variable or subset of variables caused the out-of-control signals. A Decision Tree (DT) learning based model for bivariate process mean shift monitoring and fault identification is proposed in this paper under the assumption of constant variance-covariance matrix. Two DT classifiers based on the C5.0 algorithm are built, one for process monitoring and the other for fault identification. Simulation results show that the proposed model can not only detect the mean shifts but also give information on the variable or subset of variables that cause the out-of-control signals and its/their deviate directions. Finally a bivariate process example is presented and compared with the results of an existing model.     

A control chart pattern recognition system using a statistical correlation coefficient method

This paper presents a control chart pattern recognition system using a statistical correlation coefficient method. Pattern recognition techniques have been widely applied to identify unnatural patterns in control charts. Most of them are capable of recognizing a single unnatural pattern for different abnormal types. However, before an unnatural pattern occurs, a change point from normal to abnormal may appear at any point in control charts for most practical cases. Moreover, concurrent patterns where two unnatural patterns simultaneously exist may also occur in a control chart pattern recognition system. Our statistical correlation coefficient approach is a simple mechanism for recognizing these unnatural control chart patterns with good performance. This approach is also an effective method for the control chart pattern recognition without a tedious training process.     

Self-oriented control charts for efficient monitoring of mean vectors

This work presents a procedure for monitoring the centre of multivariate processes by optimising the noncentrality parameter with respect to the maximum separability between the in- and out-of-control states. Similarly to the Principal Component Analysis, this procedure is a linear transformation but using a different criterion which maximises the trace of two scatter matrices. The proposed linear statistic is self-oriented in the sense that no prior information is given, then it is monitored by two types of control charts aiming to identify small and intermediate shifts. As the control charts performances depend only on the noncentrality parameter, comparisons are made with traditional quadratic approaches, such as the Multivariate Cumulative Sum (MCUSUM), the Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling’s T² control chart. The results show that the proposed statistic is a solution for the problem of finding directions to be monitored without the need of selecting eigenvectors, maximising efficiency with respect to the average run length.     

Neural networks for detecting cyclic behavior in autocorrelated process

In quality control area, cyclic behavior is one of the signals indicating an out-of-control situation in a manufacturing process. Neural network (NN)-based approaches have been proposed to detect the cyclical pattern in the data set collected from process. However, virtually all such proposed methods assume that the process data is independent and identically distributed when the process is under control. In other words, data from a manufacturing process is assumed uncorrelated. In this paper, a NN-based model for detecting the cyclical pattern in an autocorrelated process is proposed. After collecting the process data, this data set is preprocessed using the same information needed to calculate the fractal dimension of the data. It is then fed to a trained feedforward NN with a scaled conjugate gradient backpropagation training algorithm. An output of the model is the state of the process, i.e., whether the process is in-control or out-of-control with a particular cycle period. Such information can assist users of a manufacturing process to identify and remove the underlying causes of the out-of-control state. Our approach is thus suitable for automated manufacturing environment as a supplementary tool to traditional control charts. A Monte Carlo simulation was carried out to study performance of our proposed model. The results showed that the neural-based approach can quickly detect the cyclical pattern with better than 90% accuracy when the signal-to-noise ratio is greater than or equal 2.00. It performs well not only on autocorrelated data for a wide range of autoregressive coefficients, but also on uncorrelated data.     

An economically designed Sequential Probability Ratio Test control chart for short-run production

This paper proposes an economic model for the design of an SPRT (Sequential Probability Ratio Test) chart for monitoring the process mean in short-run production. The model expresses the short-run cost per unit of operating the SPRT chart as a function of the cost parameters associated with the operation. A simple algorithm capable of optimizing the charting parameters is also proposed. The model can be used to quantify cost reductions achievable by substituting a traditional control policy by SPRT control. Numerical examples illustrate the effectiveness of the proposed procedure. It is shown that the resulting cost reduction can range from modest to substantial as the out-of-control probability of the process increases.     

Notes on shift effects for T2-type charts on multivariate ARMA residuals

Statistical process control (SPC) needs to be aided by computers in order to deal with dynamic systems. Hence, more knowledge on the complexity of this issue is needed. This paper discusses in general the shift effects of residuals from vector autoregressive moving average process for Shewhart-type, i.e. Hotelling T²-type charts (we call it H charts). Three types of parameter shift were considered: mean shift, covariance shift, and coefficient shift. The estimation effects were addressed. The discussions begin with the shift effects for residuals then for T²-type chart on residuals. The out-of-control distributions of the chart statistic were provided in this paper.