A variable parameter Shewhart control scheme for joint monitoring of process mean and variance

This paper presents a new Statistical Process Control model for the economic optimization of a variable-parameter control chart monitoring a process operation where two assignable causes may occur, one affecting the mean and the other the variance of the process. Therefore, it is possible for the process to operate in statistical control, when none of the two assignable causes has occurred, or under the effect of one or both the assignable causes. By making the assumption that the occurrence rate of each assignable cause is exponential, a Markov chain approach is utilized to determine the probabilities that the process operates at any of the above possible states. The model uses an economic (or an economic/statistical) optimization criterion for the time to the next sampling instance, the size of the next sample, as well as the control limits of the inspection. That is, all design parameters of the control scheme are selected so as to minimize the total expected quality-related costs. The superiority of the proposed model is estimated by comparing its expected quality control cost vs. the outcome of the Fp (Fixed-parameter) Shewhart control chart, the Variable Sample Size (VSS) control chart, the Variable Sampling Interval (VSI) and the Variable Sample Size and Sampling Interval (VSSI) control chart, for a benchmark of examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant.     

An adaptive Bayesian scheme for joint monitoring of process mean and variance

This paper presents a new model for the economic optimization of a process operation where two assignable causes may occur, one affecting the mean and the other the variance. The process may thus operate in statistical control, under the effect of either one of the assignable causes or under the effect of both assignable causes. The model employed uses the Bayes theorem to determine the probabilities of operating under the effect of each assignable cause. Based on these probabilities, and following an economic optimization criterion, decisions are made on the necessary actions (stop the process for investigation or not) as well as on the time of the next sampling instance and the size of the next sample. The superiority of the proposed model is estimated by comparing its economic outcome against the outcome of simpler approaches such as Fp (Fixed-parameter) and adaptive Vp (Variable-parameter) Shewhart charts for a number of cases. The numerical investigation indicates that the economic improvement of the new model may be significant.     

A joint design of production run length,maintenance policy and control chart with multiple assignable causes

Although economic production quantity, statistical process monitoring and maintenance are three major concepts in process optimization of industrial environments, they have been often investigated separately in literature. Furthermore, in studies that consider these three concepts simultaneously, it is assumed that there is only one assignable cause in the production process. This simplified assumption is unlikely to occur in real production processes due to the usual complexity of manufacturing systems, which may lead to a poor performance in both economic and statistical criteria if the assignable cause originating the shift is different from the one anticipated at the design of the chart. To overcome these drawbacks, this paper develops an integrated model ofeconomic production quantity, statistical process monitoring and maintenance in the presence ofmultiple assignable causes. The particle swarm optimization algorithm is used to minimize the expected total cost per production cycle, subject to statistical quality constraints. Also, a comparative study is performed to illustrate the effect of considering multiple assignable causes on model’s costs. Finally, a sensitivity analysis is conducted on the expected total cost per production cycle and process variable values to extend insights into the matter.     

Economic design of autoregressive moving average control chart using genetic algorithms

When designing control charts, it is usually assumed that the observations from the process at different time points are independent. However, this assumption may not be true for some production processes, e.g., the continuous chemical processes. The presence of autocorrelation in the process data can result in significant effect on the statistical performance of control charts. Jiang, Tsui, and Woodall (2000) developed a control chart, called the autoregressive moving average (ARMA) control chart, which has been shown suitable for monitoring a series of autocorrelated data. In the present paper, we develop the economic design of ARMA control chart to determine the optimal values of the test and chart parameters of the chart such that the expected total cost per hour is minimized. An illustrative example is provided and the genetic algorithm is applied to obtain the optimal solution of the economic design. A sensitivity analysis shows that the expected total cost associated with the control chart operation is positively affected by the occurrence frequency of the assignable cause, the time required to discover the assignable cause or to correct the process, and the quality cost per hour while producing in control or out of control, and is negatively influenced by the shift magnitude in process mean.     

Fuzzy logic based assignable cause diagnosis using control chart patterns

Control chart patterns, besides determining the presence of assignable causes, also provide hints on the nature of assignable cause(s) present. Relating the patterns exhibited on the control chart to assignable causes is an ambiguous and vague task especially when multiple patterns co-exist. In this work, a rule based fuzzy inference system is developed for control chart to prioritize the control chart causes based on the accumulated evidence. When a process goes out of control, search for assignable causes can be assisted by the priorities assigned to the causes. For an in-control process, developing patterns can be tracked and preventive action can be taken to prevent the process from going out of control.     

OWave control chart for monitoring the process mean

In this paper a control chart for monitoring the process mean, called OWave (Orthogonal Wavelets), is proposed. The statistic that is plotted in the proposed control chart is based on weighted wavelets coefficients, which are provided through the Discrete Wavelets Transform using Daubechies $\mathit{db}2$ wavelets family. The statistical behavior of the wavelets coefficients when the mean shifts are occurring is presented, and the distribution of wavelets coefficients in the case of normality and independence assumptions is provided. The on-line algorithm of implementing the proposed method is also provided. The detection performance is based on simulation studies, and the comparison result shows that OWave control chart performs slightly better than Fixed Sample Size and Sampling Intervals control charts ($\overline{X}$, EWMA, CUSUM) in terms of Average Run Length. In addition, illustrative examples of the new control chart are presented, and an application to Tennessee Eastman Process is also proposed.     

A framework for Expert System development in statistical quality control

We have proposed a framework for developing expert systems for statistical process control applications. The knowledge base is partitioned into three sets: domain-independent, analysis rules, which determne whether or not the sample observations indicate a lack-of-control; intrpretive rules, which analyze the patterns in the chart in terms of process changes; and domain-dependent diagnostic rules, which assist in determining assignable causes and corrective action. This structure allows some portability between applications and customizing to specific applications.     

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.     

Effective recognition of control chart patterns in autocorrelated data using a support vector machine based approach

The effective recognition of unnatural control chart patterns (CCPs) is a critical issue in statistical process control, as unnatural CCPs can be associated with specific assignable causes adversely affecting the process. Machine learning techniques, such as artificial neural networks (ANNs), have been widely used in the research field of CCP recognition. However, ANN approaches can easily overfit the training data, producing models that can suffer from the difficulty of generalization. This causes a pattern misclassification problem when the training examples contain a high level of background noise (common cause variation). Support vector machines (SVMs) embody the structural risk minimization, which has been shown to be superior to the traditional empirical risk minimization principle employed by ANNs. This research presents a SVM-based CCP recognition model for the on-line real-time recognition of seven typical types of unnatural CCP, assuming that the process observations are AR(1) correlated over time. Empirical comparisons indicate that the proposed SVM-based model achieves better performance in both recognition accuracy and recognition speed than the model based on a learning vector quantization network. Furthermore, the proposed model is more robust toward background noise in the process data than the model based on a back propagation network. These results show the great potential of SVM methods for on-line CCP recognition.     

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.     

On-line control chart pattern detection and discrimination—a neural network approach

Unnatural patterns in the control charts can be associated with a specific set of assignable causes for process variation. Hence pattern recognition is very useful in identifying process problem. A common difficulty in existing control chart pattern recognition approaches is that of discrimination between different types of patterns which share similar features. This paper proposes an artificial neural network based model, which employs a pattern discrimination algorithm to recognise unnatural control chart patterns. The pattern discrimination algorithm is based on several special-purpose networks trained for specific recognition tasks. The performance of the proposed model was evaluated by simulation using two criteria: the percentage of correctly recognised patterns and the average run length (ARL). Numerical results show that the false recognition problem has been effectively addressed. In comparison with previous control chart approaches, the proposed model is capable of superior ARL performance while the type of the unnatural pattern can also be accurately identified.     

A hybrid learning-based model for on-line detection and analysis of control chart patterns

Unnatural control chart patterns (CCPs) are associated with a particular set of assignable causes for process variation. Therefore, effectively recognizing CCPs can substantially narrow down the set of possible causes to be examined, and accelerate the diagnostic search. In recent years, neural networks (NNs) have been successfully used to the CCP recognition task. The emphasis has been on the CCP detection rather than more detailed quantification of information of the CCP. Additionally, a common problem in existing NN-based CCP recognition methods is that of discriminating between various types of CCP that share similar features in a real-time recognition scheme. This work presents a hybrid learning-based model, which integrates NN and DT learning techniques, to detect and discriminate typical unnatural CCPs, while identifying the major parameter (such as the shift displacement or trend slope) and starting point of the CCP detected. The performance of the model was evaluated by simulation, and numerical and graphical results that demonstrate that the proposed model performs effectively and efficiently in on-line CCP recognition task are provided. Although this work considers the specific application of a real-time CCP recognition model for the individuals (X) chart, the proposed learning-based methodology can be applied to other control charts (such as the X-bar chart).     

Mixture control chart patterns recognition using independent component analysis and support vector machine

Effective recognition of control chart patterns (CCPs) is an important issue since abnormal patterns exhibited in control charts can be associated with certain assignable causes which affect the process. Most of the existing studies assume that the observed process data which needs to be recognized are basic types of abnormal CCPs. However, in practical situations, the observed process data could be mixture patterns, which consist of two basic CCPs combined together. In this study, a hybrid scheme using independent component analysis (ICA) and support vector machine (SVM) is proposed for CCPs recognition. The proposed hybrid ICA-SVM scheme initially applies an ICA to the mixture patterns in order to generate independent components (ICs). The hidden basic patterns of the mixture patterns can be discovered in these ICs. The ICs can then serve as the input variables of the SVM for building a CCP recognition model. Experimental results revealed that the proposed scheme is able to effectively recognize mixture control chart patterns and outperform the single SVM models, which did not use an ICA as a preprocessor.     

Recognition of concurrent control chart patterns using wavelet transform decomposition and multiclass support vector machines

Statistical process control charts have been widely utilized for monitoring process variation in many applications. Nonrandom patterns exhibited by control charts imply certain potential assignable causes that may deteriorate the process performance. Though some effective approaches to recognition of control chart patterns (CCPs) have been developed, most of them only focus on recognition and analysis of single patterns. A hybrid approach by integrating wavelet transform and improved particle swarm optimization-based support vector machine (P-SVM) for on-line recognition of concurrent CCPs is developed in this paper. A statistical correlation coefficient is used to determine whether the input pattern is a single or concurrent CCP. Based on wavelet transform, a raw concurrent pattern signal is decomposed into two basic pattern signals, which can be recognized by multiclass SVMs. The performance of the hybrid approach is evaluated by simulation experiments, and numerical and graphical results are provided to demonstrate that the proposed approach can perform effectively and efficiently in on-line CCP recognition task.     

Improved statistical features-based control chart patterns recognition using ANFIS with fuzzy clustering

Neural Computing and Applications - Various types of abnormal control chart patterns can be linked to certain assignable causes in industrial processes. Hence, control chart patterns recognition...     

Economic model of x̄-CHART under non-normality and measurement errors

This paper investigates the effect of non-normality and measurement errors on the economic design of $\text{x}\text{?}\text{-}\text{control}$ charts. The measurable quality characteristic of the product is assumed to be non-normally distributed random variable. The process is subject to a single assignable cause with exponentially distributed occurrence time. This assignable cause shifts the process from in-control state to out-of-control state. Each observation involves some deviation from true value due to measurement error. This deviation, characterized by bias and imprecision, is considered to be a normally distributed random variate. The production cycle for the process model consists of: (1 ) the in-control period, (2) the out-of-control period due to occurrence of the assignable cause, (3) the search period due to false alarm, and (4) the search and correction time due to true alarm. An expected-cost model is formulated which comprises the fixed and variable cost of sampling, the cost of searching for the assignable cause when it does and does not exist, and the adjustment and correction costs. The economic design of $\text{x}\text{-}\text{?}\text{rmchart}$ involves optimal determination of the design parameters; the sample size, the sampling interval and the control limits coefficients so as to minimize the expected total cost. The optimal value of the design parameters are obtained using a computerized search technique. Consequently the effect of non-normality parameters and measurement errors on the design parameters and on the loss-cost function is explained through numerical examples.     

A neural network approach to characterize pattern parameters in process control charts

Abnormal patterns on manufacturing process control charts can reveal potential quality problems due to assignable causes at an early stage, helping to prevent defects and improve quality performance. In recent years, neural networks have been applied to the pattern recognition task for control charts. The emphasis has been on pattern detection and identification rather than more detailed pattern parameter information, such as shift magnitude, trend slope, etc., which is vital for effective assignable cause analysis. Moreover, the identification of concurrent patterns (where two or more patterns exist together) which are commonly encountered in practical manufacturing processes has not been reported. This paper proposes a neural network-based approach to recognize typical abnormal patterns and in addition to accurately identify key parameters of the specific patterns involved. Both single and concurrent patterns can be characterized using this approach. A sequential pattern analysis (SPA) design was adopted to tackle complexity and prevent interference between pattern categories. The performance of the model has been evaluated using a simulation approach, and numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart pattern recognition and accurately identifies the key parameters of the recognized pattern(s) in both single and concurrent pattern circumstances.     

一种基于SPC的软件过程质量分析方法

一个项目的开发活动是很多软件过程的集合,不同软件过程之间关联性很强,成功地分析特定软件过程质量的关键是确保软件过程分析的独立性,剔除来自于其他过程的影响。传统Shewhart控制图基于统计假设检验理论,能够区分软件过程中的偶然因素和系统因素,但Shewhart控制图是全控图,无法区分过程之间的影响。为解决这种问题,定义软件过程的总质量和分质量,把系统因素细分为外部系统因素和内部系统因素,并总结软件过程质量诊断表,以使用控制图和选控图来帮助诊断导致软件过程质量异常的偏差源。     

Intelligent monitoring of a frequency-trimming process

In the development of a process diagnostic system to monitor the condition of the frequency-trimming process in the production of crystal resonators, fuzzy logic can be applied in the recognition of unnatural statistical patterns in the control charts. The heuristics for reasoning are based on the principles behind statistical process control. Using expert experience and knowledge to troubleshoot the causes of problems, one can associate a characteristic chart pattern with a set of known physical causes. As these causes related to the unnatural statistical patterns are not independent of each other, it is difficult to precisely associate the chart distribution patterns with the known causes. Furthermore, as the trimming process is dynamic, the causes of problems dealt with will vary with time. Hence, by means of neural networks, it is possible to associate fuzzily deduced chart patterns with plausible causes to achieve optimum operating conditions.     

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.