Shifts In Process Mean Research Articles

Multivariate Process Monitoring and Diagnosis: A Case Study

In manufacturing industries, monitoring and diagnosis of multivariate process out-of-control condition become more challenging. Process monitoring refers to the identification of process status either it is running within a statistically in-control or out-of-control condition, whereas process diagnosis refers to the identification of the source variables of out-of-control process. In order to achieve these requirements, the application of an appropriate statistical process control framework is necessary for rapidly and accurately identifying the signs and source out-of-contol condition with minimum false alarm. In this research, a framework namely, an Integrated Multivariate Exponentially Weighted Moving Average with Artificial Neural Network was investigated in monitoring-diagnosis of multivariate process mean shifts in manufacturing audio video device component. Based on two-stages monitoring-diagnosis technique, the proposed framework has resulted in efficient performance.

A Framework for Multivariate Process Monitoring and Diagnosis

Monitoring and diagnosis of mean shifts in manufacturing processes become more challenging when involving two or more correlated variables. Unfortunately, most of the existing statistical process control frameworks are only effective in shift detection but suffers high false alarm, that is, imbalanced performance monitoring. The problem becomes more complicated when dealing with small shift particularly in identifying the causable variables. In this research, a framework to address balanced monitoring and accurate diagnosis was investigated. Design considerations involved extensive simulation experiments to select input representation based on raw data and statistical features, recognizer design structure based on synergistic model, and monitoring-diagnosis approach based on two stages technique. The study focuses on correlated process mean shifts for cross correlation function, ρ = 0.1 ~ 0.9 and mean shift, μ = ± 0.75 ~ 3.00 standard deviations. The proposed design, that is, an Integrated Multivariate Exponentially Weighted Moving Average with Artificial Neural Network gave superior performance, namely, average run length, ARL1 = 3.18 ~ 16.75 (for out-of-control process), ARL0 = 452.13 (for in-control process) and recognition accuracy, RA = 89.5 ~ 98.5%. This research has provided a new perspective in realizing balanced monitoring and accurate diagnosis of multivariate correlated process mean shifts.

An economic design of the VSSI control charts for the means of positively Skewed distributions

Variable sample size and sampling interval (VSSI) control charts have been shown superior to standard Shewhart (SS) control charts for detection of a small or moderate shift in process mean. However, they might utilize more resources by a more frequent sampling rate and a large sample size to improve its performance. Recently, some economic models were used to express the long-run cost per hour of operating the VSSI control charts and gain insight into the way to design the charts. The usual assumption for the models is the normality of the underlying data or measurements. However, this assumption may not be true in practice. In this paper, an economic design of the VSSI control charts for skewed non-normal data is conducted by using the Markov chain approach and genetic algorithms. Two types of VSSI charts are considered and compared with the SS charts over several numerical examples: the symmetric control limits and asymmetric control limits. Moreover, effects of non-normality on the performance of the VSSI charts with respect to the costs of operating the charts are studied. It is shown that the reduction in cost can be achieved by using the VSSI charts instead of the SS charts. However, an increase on the skewness coefficient results in a decrease on the cost savings. In addition, the asymmetric control limits is a better choice with respect to the costs and the false alarm rate. Key words: Skewed non-normal, control chart, genetic algorithms, economic design.

Fault Identification in Industrial Processes Using an Integrated Approach of Neural Network and Analysis of Variance

Due to its importance in process improvement, the issue of determining exactly when faults occur has attracted considerable attention in recent years. Most related studies have focused on the use of the maximum likelihood estimator (MLE) method to determine the fault in univariate processes, in which the underlying process distribution should be known in advance. In addition, most studies have been devoted to identifying the faults of process mean shifts. Different from most of the current research, the present study proposes an effective approach to identify the faults of variance shifts in a multivariate process. The proposed mechanism comprises the analysis of variance (ANOVA) approach, a neural network (NN) classifier, and an identification strategy. To demonstrate the effectiveness of our proposed approach, a series of simulated experiments is conducted, and the best results from our proposed approach are addressed.

On-line classifying process mean shifts in multivariate control charts based on multiclass support vector machines

In multivariate statistical process control (MSPC), most multivariate control charts can effectively monitor anomalies based on overall statistic, however, they cannot provide guidelines to classify the source(s) of out-of-control signals. Classifying the source(s) of process mean shifts is critical for quality control in multivariate manufacturing process since the immediate identification of them can greatly help quality engineer to narrow down the set of possible root causes and take corrective actions. This study presents an improved particle swarm optimisation with simulated annealing-based selective multiclass support vector machines ensemble (PS-SVME) approach, in which some selective multiclass SVMs are jointly used for classifying the source(s) of process mean shifts in multivariate control charts. The performance of the proposed PS-SVME approach is evaluated by computing its classification accuracy. Simulation experiments are conducted and a real application is illustrated to validate the effectiveness of the developed approach. The analysis results indicate that the developed PS-SVME approach can perform effectively for classifying the source(s) of process mean shifts.

The Detection Method of Small Shifts Based on Stationary Autocorrelated Process

When control charts are used to monitor a process, a standard assumption is that observations from the process at different times are independent random variables. However, the independence assumption is often not reasonable for processes of interest in many applications because the dynamics of the process product autocorrelation in the process observations. The presence of significant autocorrelation in the process observations can have a large impact on traditional control charts developed under the independence assumption. A method of monitoring little shifts in stationary autocorrelated process is discussed in this paper. At first, auto-regressive moving-average model is used to fit stationary autocorrelated process. Then, process autocorrelation can be removed by residual method, and exponentially weighted moving average charts are constructed to monitor little shifts of process mean and variance. Comparing with other methods, we can illustration that this EWMA residuals charts have better efficiency for stationary autocorrelated processes.

Pattern Recognition of Process Mean Shift using Combined ANN Recognizer

Neural Network (ANN) based model has been proposed for diagnosis of process mean shift. These are mainly generalized-based where only a single classifier was applied in the diagnosis of abnormal pattern. In this paper, we analyze the performance of a combined recognizer consisting of small-sized artificial neural networks on varying number of nodes in the hidden layer trained with Levenberg Marquardt and Quasi-Newton Algorithm. The results of our study illustrate the effectiveness of the combined recognizer and showed that combined recognizer performed better when number of hidden nodes is small, say, less than 15 in terms of recognition accuracies and mean square error as compared to the single recognizer.

Minimal Euclidean distance chart based on support vector regression for monitoring mean shifts of auto-correlated processes

Though traditional control charts have been widely used as effective tools in statistical process control (SPC), they are not applicable in many industrial applications where the process variables are highly auto-correlated. In this study, one new minimal Euclidean distance (MED) based monitoring approach is proposed for enhancing the monitoring mean shifts of auto-correlated processes. Support vector regression (SVR) is used to predict the values of a variable in time series. Through calculating minimal Euclidean distance (MED) values over time series, a novel MED chart is developed for monitoring mean shifts, and it can provide a comprehensive and quantitative assessment for the current process state. The performance of the proposed MED control chart is evaluated based on average run length (ARL). Simulation experiments are conducted and one industrial case is illustrated to validate the effectiveness of the developed MED control chart. The analysis results indicate that the developed MED control chart is more effective than other control charts for small process mean shifts in auto-correlated processes, and it can be used as a promising tool for SPC.

The Revised m-of-k Runs Rule Based on Median Run Length

Runs rules are used to increase the sensitivity of the Shewhart control chart in detecting small and moderate process mean shifts. Most of the charts incorporating runs rules are designed based on the average run length (ARL). It is known that the shape of the run length distribution changes according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control to approximately symmetric when the shift is large. Since the shape of the run length distribution changes with the magnitude of the shift in the mean, the median run length (MRL) provides a more meaningful explanation about the in-control and out-of-control performances of a control chart. In this article, we propose the design of the revised m-of-k runs rule based on MRL. In addition, the standard deviation of the run length (SDRL) of the revised m-of-k rule will also be studied. The revised m-of-k runs rule, suggested by Antzoulakos and Rakitzis (2008), was originally designed based on ARL. The Markov chain technique is employed to obtain the MRLs. Compared with the standard chart, the MRL results show that the revised rules give better performances for small and moderate mean shifts, while maintaining the same sensitivity towards large mean shifts. The MRL results are in accordance with the results obtained by Antzoulakos and Rakitzis (2008), where the rules are designed based on ARL.

Pattern recognition for bivariate process mean shifts using feature-based artificial neural network

In multivariate quality control, the artificial neural networks (ANN)-based pattern recognition schemes generally performed better for monitoring bivariate process mean shifts and provided more efficient information for diagnosing the source variable(s) compared to the traditional multivariate statistical process control charting. However, these schemes revealed disadvantages in term of reference bivariate patterns in identifying the joint effect and excess false alarms in identifying stable process condition. In this study, feature-based ANN scheme was investigated for recognizing bivariate correlated patterns. Feature-based input representation was utilized into an ANN training and testing towards strengthening discrimination capability between bivariate normal and bivariate mean shift patterns. Besides indicating an effective diagnosis capability in dealing with low correlation bivariate patterns, the proposed scheme promotes a smaller network size and better monitoring capability as compared to the raw data-based ANN scheme.

An optimal design algorithm of the SPRT chart for minimizing weighted ATS

Abstract The Sequential Probability Ratio Test (SPRT) chart is a very effective control chart. It is much faster to detect out-of-control cases compared with the X ¯ and CUSUM charts, even their VSSI (Variable Sample Sizes and Sampling Intervals) versions. The new contribution of this paper is the development of an algorithm for the optimal design of the SPRT chart based on the Average Extra Quadratic Loss (AEQL). More importantly, the results of the systematic comparative studies show that this design algorithm is indeed effective. Using the design algorithm proposed here yields charts that significantly outperform other designs in terms of the proposed AEQL performance criteria for detecting process mean shifts. Moreover, this paper conducts a designed experiment to study the effect of the Average Sample Number (ASN) (i.e., the average sample size) on the chart's performance. It is found that, in order to achieve higher overall detection effectiveness, the ASN of the SPRT chart should be set substantially smaller compared with that recommended by the existing guidelines.

An Effective Procedure for Calculating Weibull Production Yield with Mean Shift

Abstract Motorola, Inc. introduced its six sigma production quality initiative to the world in the 1980 s. Six sigma production quality is estimated by assuming a 1.5σ shift to the process mean. Bothe provided a statistical reason for considering such a shift in the normal process mean, and he also provided a much more accurate capability calculation to measure the production yield (Bothe, D. R., “Statistical Reason for the 1.5σ Shift,” Qual. Eng., Vol. 14(3), 2002, pp. 479–487). In this paper, we consider Weibull processes, which cover a wide class of non-normal processes. We calculate the mean shift adjustments under various sample sizes n and Weibull parameters, with the power fixed at 0.5. Then, we implement the derived results to develop an effective procedure to accurately calculate the production yield. Finally, to demonstrate the applicability of the proposed approach, the proposed procedure is applied to a real manufacturing process with mean shift.

Multiscale monitoring of autocorrelated processes using wavelets analysis

This article proposes a new method to develop multiscale monitoring control charts for an autocorrelated process that has an underlying unknown ARMA(2, 1) model structure. The Haar wavelet transform is used to obtain effective monitoring statistics by considering the process dynamic characteristics in both the time and frequency domains. Three control charts are developed on three selected levels of Haar wavelet coefficients in order to simultaneously detect the changes in the process mean, process variance, and measurement error variance, respectively. A systematic method for automatically determining the optimal monitoring level of Haar wavelet decomposition is proposed that does not require the estimation of an ARMA model. It is shown that the proposed wavelet-based Cumulative SUM (CUSUM) chart on Haar wavelet detail coefficients is only sensitive to the variance changes and robust to process mean shifts. This property provides the separate monitoring capability between a variance change and a mean shift, which shows its advantage by comparison with the traditional CUSUM monitoring chart. For the purpose of mean shift detection, it is also shown that using the proposed wavelet-based Exponentially Weighted Moving Average (EWMA) chart to monitor Haar wavelet scale coefficients will more successfully detect small mean shifts than direct-EWMA charts.

Demerit-GWMA Control Chart with Fast Initial Response

Complex Products may present more than one type of defects and these defects are not always of equal severity. These defects are classified according to their seriousness and effect on product quality and performance. Demerit systems are very effective systems to monitoring the different types of defects. So, classical demerit control chart used to monitor counts of several different types of defects simultaneously in complex products. Recently, H.W. Kang et al.[7] introduced Demerit-GWMA(generally weighted moving average) and Demerit-EWMA control charts that can detect small shifts of the process mean more sensitively than the classical demerit control charts. In this paper, we present an effective method for process control using the Demerit-GWMA statistics with fast initial response. Moreover, we evaluate exact performance of the Demerit-GWMA control chart with fast initial response(FIR), Demerit-GWMA and Demerit-EWMA according to changing sample size or parameters.

Optimal Process Shift Design in Selective and Adaptive Production Systems

Selective and Adaptive Production Systems (SAPS) are widely used in the mechanical component manufacturing to deliver high precision products from relatively low precision sub-assemblies. By involving component inspection and partitioning, SAPS increase the product quality at the cost of decreasing the logistics performance of the system. In this paper, the integrated analysis of quality and production logistics performance in SAPS is addressed. A method to derive the optimal number of process mean shifts to meet desired levels of component matching is presented. Moreover, a system level simulation model is developed to validate the impact of the proposed shift design on the overall system performance. The proposed method outperforms existing shift design approaches and paves the way to the efficient design and control of SAPS.

An integrated MEWMA-ANN scheme towards balanced monitoring and accurate diagnosis of bivariate process mean shifts

Various artificial neural networks (ANN)-based pattern recognition schemes have been developed for monitoring and diagnosis of bivariate process variation in mean shifts. In comparison with the traditional multivariate statistical process control (MSPC) charts, these advanced schemes generally perform better in identifying process mean shifts and provide more effective information towards diagnosing the root causes. However, it seemly less effective for multivariate quality control (MQC) application due to disadvantages in reference bivariate patterns and imbalanced monitoring performance. To achieve ‘balanced monitoring and accurate diagnosis’, this study proposes an integrated multivariate exponentially weighted moving average (MEWMA)-ANN scheme for two-stages monitoring and diagnosis of some reference bivariate patterns. Raw data and statistical features input representations were applied into training of the Synergistic-ANN recognizer for improving patterns discrimination capability. The proposed scheme has resulted in better monitoring – diagnosis performances with smaller false alarm, quick mean shift detection and higher diagnosis accuracy compared to the basic scheme.

A single-featured EWMA-X control chart for detecting shifts in process mean and standard deviation

The combined EWMA-X chart is a commonly used tool for monitoring both large and small process shifts. However, this chart requires calculating and monitoring two statistics along with two sets of control limits. Thus, this study develops a single-featured EWMA-X (called SFEWMA-X) control chart which has the ability to simultaneously monitor both large and small process shifts using only one set of statistic and control limits. The proposed SFEWMA-X chart is further extended to monitoring the shifts in process standard deviation. A set of simulated data are used to demonstrate the proposed chart's superior performance in terms of average run length compared with that of the traditional charts. The experimental examples also show that the SFEWMA-X chart is neater and easier to visually interpret than the original EWMA-X chart.

Process Capability Evaluation for Square Bumps with Mean Shift

Abstract Process capability indices have been widely used in manufacturing industries to provide numerical measures of process potential and performance. In in-plant applications, some inevitable process mean shift may be undetected when the statistical process control charts are applied, particularly, in the bumping process for square bumps. Bothe in 2002 provided a statistical reason for considering such a shift in the process mean to accommodate the undetected mean shifts for normally distributed processes when evaluating process capability. In this paper, we consider a bumping process for square bumps in which the data can be formulated as a non-central chi-square distribution, a class of non-normal distributions. To evaluate the popular yield-based process capability Cpk more accurately, we accommodate the magnitudes of undetected mean shifts using the modified capability evaluation formula and tabulate the detection powers under various subgroup sizes and non-central chi-square parameters. Based on the modified process capability evaluation, we can provide a more reliable process capability evaluation of capability index Cpk for square bumps and make more correct decisions. For illustration purpose, a real application in a bumping factory which is located on the Science-based Industrial Park in Hsinchu, Taiwan, is presented.

The synthetic [Xbar] chart with estimated parameters

A synthetic [Xbar] chart consists of an integration of a Shewhart [Xbar] chart and a conforming run length chart. This type of chart has been extensively used to detect a process mean shift under the assumption of known process parameters. However, in practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. The goals of this article are to (i) evaluate (using a Markov chain model) the performances of the synthetic [Xbar] chart when the process parameters are estimated; (ii) compare it with the case where the process parameters are assumed known to demonstrate that these performances are quite different when the number of samples used during Phase I is small; and (iii) suggest guidelines concerning the choice of the number of Phase I samples and to provide new optimal constants, especially dedicated to the number of samples used in practice.

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.