Using evolutionary artificial neural networks in monitoring binary and polytomous logistic profiles

A statistical profile is a relationship between a quality characteristic (a response) and one or more explanatory variables to characterize quality of a process or a product. Monitoring profiles or checking the stability of profiles over time, has been extensively studied under the normal response variable, but it has paid a little attention to the profile with the non-normal response variable denoted by generalized linear models (GLM). Whereas, some of the potential applications of profile monitoring are cases where the response can be modelled using logistic profiles entailing binary, nominal and ordinal models. Also, most of existing control charts in this field have been developed by statistical approach and employing machine learning techniques have been rarely addressed in the related literature. Hence, to implement on-line process monitoring of logistic profiles, a novel artificial neural network (ANN) as a control chart with a heuristic training procedure is proposed in this paper. Performance of the proposed approach is investigated and compared using simulation studies in binary and polytomous models based on average run length (ARL) criterion. Simulation results revealed a good performance of the proposed approach. Nevertheless, to enhance the detection ability of the proposed approach more, the idea of combining run-rule which is a supplementary tool for making more sensitive control chart with final statistic is also implemented in this paper. Furthermore, a diagnostic method with machine learning schemes is employed to identify the shifted parameters in the profile. Results indicate the superior performance of the proposed approaches in most of the simulations. Finally, an example is used to illustrate the implementation of the proposed charting scheme.     

A general framework for monitoring complex processes with both in-control and out-of-control information

Processes monitoring using multivariate quality variables remains an important and challenging problem in statistical process control (SPC). Although multivariate SPC has been extensively studied in the literature, the challenges associated with designing robust and flexible control schemes have yet to be adequately addressed. This paper develops a general monitoring framework for detecting location shifts in complex processes by employing data mining methods. The historical in-control (IC) and out-of-control (OC) data are combined to set up a support vector machine (SVM) model. The working status of the process is indicated by the probabilistic outputs of the SVM classifier and the multivariate exponentially weighted moving average strategy is applied to construct the control chart. A fast diagnostic procedure can be implemented as soon as the control chart gives an alarm. Our numerical studies show that the proposed control chart is able to deliver satisfactory IC and OC run-length performance regardless of the underlying distributions and data types. An example using real data from an industrial application demonstrates the effectiveness of the proposed method.     

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.     

Control chart based on likelihood ratio for monitoring linear profiles

A control chart based on the likelihood ratio is proposed for monitoring the linear profiles. The new chart which integrates the EWMA procedure can detect shifts in either the intercept or the slope or the standard deviation, or simultaneously by a single chart which is different from other control charts in literature for linear profiles. The results by Monte Carlo simulation show that our approach has good performance across a wide range of possible shifts. We show that the new method has competitive performance relative to other methods in literature in terms of ARL, and another feature of the new chart is that it can be easily designed. The application of our proposed method is illustrated by a real data example from an optical imaging system.     

Simple linear profiles monitoring in the presence of within profile autocorrelation

Quality of some processes or products can be characterized effectively by a function referred to as profile. Many studies have been done by researchers on the monitoring of simple linear profiles when the observations within each profile are uncorrelated. However, due to spatial autocorrelation or time collapse, this assumption is violated and leads to poor performance of the proposed control charts. In this paper, we consider a simple linear profile and assume that there is a first order autoregressive model between observations in each profile. Here, we specifically focus on phase II monitoring of simple linear regression. The effect of autocorrelation within the profiles is investigated on the estimate of regression parameters as well as the performance of control charts when the autocorrelation is overlooked. In addition, as a remedial measure, transformation of Y-values is used to eliminate the effect of autocorrelation. Four methods are discussed to monitor simple linear profiles and their performances are evaluated using average run length criterion. Finally, a case study in agriculture field is investigated.     

A double-max MEWMA scheme for simultaneous monitoring and fault isolation of multivariate multistage auto-correlated processes based on novel reduced-dimension statistics

In this article, a double-max multivariate exponentially weighted moving average (DM-MEWMA) chart is proposed to jointly monitor the parameters of a multivariate multistage auto-correlated (MMAP) process. While the process is assumed to work in a linear state-space form, two modified statistics are combined into a novel statistic to monitor the mean vector and the covariance matrix of the MMAP simultaneously. Besides, prior knowledge of variation propagation is used so that the chart has both a fault identification power and capability of working with the sample size of one. A statistical test shows that the two proposed statistics are independent of the process dimension. Monte Carlo simulation indicates that the DM-MEWMA chart has quite robust performance in detecting changes. Moreover, when the number of stages increases, it outperforms some existing alternative methods. In addition, fault identification comparison demonstrates that most of the moderate mean and variability shifts can be isolated by the DM-MEWMA chart.     

An improved attribute control chart for monitoring non-conforming proportion in high quality processes

Processes with very low rate of nonconformities are frequently observed in practice. These processes are known as “high quality processes”. Traditionally, the study of the rate of nonconformities was carried out using the conventional 3-sigma p control chart (Shewhart), constructed by the normal approximation. But this p chart suffers a serious inaccuracy in the modeling process and in control limits specification when the true rate of nonconforming items is small. This paper shows that, with simple adjustments to the control limits of the p-chart, achieving equal or even better improvement while still working on the original data scale, is feasible. In particular, an improved p chart which can provide a large improvement over the usual p chart for attributes is presented. This new chart, based on the Cornish–Fisher quantile correction, is also better than a previous simpler correction proposed in the literature. The improved p chart is compared with both, normal-based chart and modified p chart with one correction term and the benefits of including a new term of correction for monitoring high-quality processes is illustrated with real data.     

A generalized Conforming Run Length control chart for monitoring the mean of a variable

The attribute Conforming Run Length (CRL) control chart has attracted increasing research interests in Statistical Process Control (SPC). It decides the process status based on the interval or distance between two nonconforming units. This article proposes a Generalized CRL chart (namely GCRL chart) for monitoring the mean of a measurable quality characteristic x under 100% inspection. To run a GCRL chart, each unit will be classified as a passing or nonpassing unit depending on whether the sample value of x falls within or beyond a pair of lower and upper inspection limits LIL and UIL. When a nonpassing unit is detected, the GCRL chart checks the distance between the current and last nonpassing units in order to determine the process status (in control or out of control). The inspection limits LIL and UIL are determined by an optimization design. The GCRL chart not only solves a dead-corner problem suffered by the conventional CRL chart, but also considerably outperforms the latter for detecting mean shifts. The most interesting finding is that the attribute GCRL chart excels the variable X chart to a significant degree in SPC for variables. It suggests that the simple attribute chart may replace the variable chart in some SPC applications. The design of the GCRL chart has to be carried out by a computer program, but the design can be completed almost in no time in a personal computer.     

Design and optimization of EWMA control charts for in-control,indifference, and out-of-control regions

The design of quality control charts is normally carried out considering a process shift size that is considered important to be detected. The EWMA control chart is one of the best available options to use when good performance is needed to detect small process shifts. This paper presents a method for design of EWMA charts for control processes, in which the detection of small shifts is not necessary, and at the same time is effective in detecting important shifts. In such cases the EWMA control chart can also be designed successfully to deal with these requirements. A Markov chain approach is also applied to determine the ARL of the modified EWMA control chart. The implementation and interpretations are provided and numerical examples are used to illustrate the application procedure. We also investigate some basic properties of the proposed scheme. Genetic algorithms have been used to carry out this design.     

Detection of chatter vibration in a drilling process using multivariate control charts

Time series analysis and multivariate control charts are used to devise a real-time monitoring strategy in a drilling process. The process is used to produce holes with high length-to-diameter ratio, good surface finish and straightness. It is subject to dynamic disturbances that are classified as either chatter vibration or spiralling. A new nonparametric control chart for multivariate processes is proposed. It is used to detect chatter vibration which is dominated by single frequencies. The results showed that the proposed monitoring strategy can detect chatter vibration and that some alarm signals are related to changing physical conditions of the process.     

Application of integrated recurrent neural network with multivariate adaptive regression splines on SPC-EPC process

The integration of statistical process control and engineering process control has been reported as an effective way to monitor and control the autocorrelated process. However, because engineering process control compensates for the effects of underlying disturbances, the disturbance patterns become very hard to recognize, especially when various abnormal control chart patterns are mixed and co-existed in the engineering process. In this study, a new control chart pattern recognition model which integrates multivariate adaptive regression splines and recurrent neural network is proposed to not only address the problem of feature selection (i.e., lagged process measurements) but also improve the pattern recognition accuracy. The performance of the proposed method is evaluated by comparing the recognition results of multivariate adaptive regression splines and recurrent neural network with the results of four competing approaches (multivariate adaptive regression splines-extreme learning machine, multivariate adaptive regression splines-random forest, single recurrent neural network, and single random forest) on the simulated individual process data. The experimental study shows that the proposed multivariate adaptive regression splines and recurrent neural network approach can not only solve the problem of variable selection but also outperform other competing models. Moreover, according to the lagged process measurements selected by the proposed approach, lagged observations that exerted significant impact on the construction of the control chart pattern recognition model can be identified successfully. This study has significant implications for research and practice in production management and provides a valuable reference for manufacturing process managers to better understand and develop strategies for control chart pattern recognition.     

A multivariate control chart for simultaneously monitoring process mean and variability

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and the EWMA procedure, the new chart provides quite robust and satisfactory performance in various cases, including detection of the decrease in variability and individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.     

Application of artificial neural networks in linear profile monitoring

In many quality control applications the quality of process or product is characterized and summarized by a relation (profile) between a response variable and one or more explanatory variables. Such profiles can be modeled using linear or nonlinear regression models. In this paper we use artificial neural networks to detect and classify the shifts in linear profiles. Three monitoring methods based on artificial neural networks are developed to monitor linear profiles. Their efficacies are assessed using average run length criterion.     

A new monitoring design for uni-variate statistical quality control charts

In this research, an iterative approach is employed to analyze and classify the states of uni-variate quality control systems. To do this, a measure (called the belief that process is in-control) is first defined and then an equation is developed to update the belief recursively by taking new observations on the quality characteristic under consideration. Finally, the upper and the lower control limits on the belief are derived such that when the updated belief falls outside the control limits an out-of-control alarm is received. In order to understand the proposed methodology and to evaluate its performance, some numerical examples are provided by means of simulation. In these examples, the in and out-of-control average run lengths (ARL) of the proposed method are compared to the corresponding ARL’s of the optimal EWMA, Shewhart EWMA, GEWMA, GLR, and CUSUM[11] methods within different scenarios of the process mean shifts. The simulation results show that the proposed methodology performs better than other charts for all of the examined shift scenarios. In addition, for an autocorrelated AR(1) process, the performance of the proposed control chart compared to the other existing residual-based control charts turns out to be promising.     

Using recurrent neural networks to detect changes in autocorrelated processes for quality monitoring

With the growing of automation in manufacturing, process quality characteristics are being measured at higher rates and data are more likely to be autocorrelated. A widely used approach for statistical process monitoring in the case of autocorrelated data is the residual chart. This chart requires that a suitable model has been identified for the time series of process observations before residuals can be obtained. In this work, a new neural-based procedure, which is alleviated from the need for building a time series model, is introduced for quality control in the case of serially correlated data. In particular, the Elman’s recurrent neural network is proposed for manufacturing process quality control. Performance comparisons between the neural-based algorithm and several control charts are also presented in the paper in order to validate the approach. Different magnitudes of the process mean shift, under the presence of various levels of autocorrelation, are considered. The simulation results indicate that the neural-based procedure may perform better than other control charting schemes in several instances for both small and large shifts. Given the simplicity of the proposed neural network and its adaptability, this approach is proved from simulation experiments to be a feasible alternative for quality monitoring in the case of autocorrelated process data.     

A multivariate synthetic double sampling T2 control chart

In this article, we propose a multivariate synthetic double sampling T² chart to monitor the mean vector of a multivariate process. The proposed chart combines the double sampling (DS) T² chart and the conforming run length (CRL) chart. On the whole, the proposed chart performs better than its standard counterparts, namely, the Hotelling’s T², DS T², and synthetic T² charts, in terms of the average run length (ARL) and average number of observations to sample (ANOS). The proposed chart also outperforms the multivariate exponentially weighted moving average (MEWMA) chart for moderate and large shifts but the latter is more sensitive than the former towards small shifts. For a variable sample size chart, like the synthetic DS T² chart, ANOS is a more meaningful performance measure than ARL. ANOS relates to the actual number of observations sampled but ARL merely deals with the number of sampling stages taken. Interpretation based on ARL is more complicated as either n₁ or n₁ + n₂ observations are taken in each sampling stage.     

Cumulative quantity control chart for the mixture of inverse Rayleigh process

The engineering processes are made up of a number of the phenomenons working together that may lead to defects with multiple causes. In order to model such types of multiple cause defect systems we may not rely on simple probability models and hence, the need arises for mixture models. The commonly used control charts are based on simple models with the assumption that the process is working under the single cause defect system. This study proposes a control chart for the two component mixture of inverse Rayleigh distribution. The proposed chart namely IRMQC chart is based on mixture cumulative quantity using the quantity of product inspected until specified numbers of defects are observed. The single cause chart is also discussed as a special case of the proposed mixture cumulative quantity chart. The control structure of the proposed chart is designed, and its performance is evaluated in terms of some useful measures, including average run length (ARL), expected quality loss (EQL) and relative ARL (RARL). An illustrative example along a case study, is also given to highlight the practical aspects of the proposal.     

Mean shifts detection and classification in multivariate process: a neural-fuzzy approach

For monitoring multivariate quality control process, traditional multivariate control charts have been proposed to detect mean shifts. However, a persistent problem is that such charts are unable to provide any shift-related information when mean shifts occur in the process. In fact, the immediate classification of the magnitude of mean shifts can greatly narrow down the set of possible assignable causes, hence facilitating quick analysis and corrective action by the technician before many nonconforming units are manufactured. In this paper, we propose a neural-fuzzy model for detecting mean shifts and classifying their magnitude in multivariate process. This model is divided into training and classifying modules. In the training module, a neural network (NN) model is trained to detect various mean shifts for multivariate process. Then, in the classifying module, the outputs of NN are classified into various decision intervals by using a fuzzy classifier and an additional two-point-in-an-interval decision rule to determine shift status. An example is presented to illustrate the application of the proposed model. Simulation results show that it outperforms the multivariate T²control chart in terms of out-of-control average run length under fixed type I error. In addition, the correct classification percentages are also studied and the general guidelines are given for the proper use of the proposed model.     

带法向约束的圆平均非线性细分曲线设计

目的 对采样设备获取的测量数据进行拟合,可实现原模型的重建及功能恢复。但有些情况下,获取的数据点不仅包含位置信息,还包含法向量信息。针对这一问题,本文提出了基于圆平均的双参数4点binary非线性细分法与单参数3点ternary插值非线性细分法。方法 首先将线性细分法改写为点的重复binary线性平均,然后用圆平均代替相应的线性平均,最后用加权测地线平均计算的法向量作为新插入顶点的法向量。基于圆平均的双参数4点binary细分法的每一次细分过程可分为偏移步与张力步。基于圆平均的单参数3点ternary细分法的每一次细分过程可分为左插步、插值步与右插步。结果 对于本文方法的收敛性与C¹连续性条件给出了理论证明;数值实验表明,与相应的线性细分相比,本文方法生成的曲线更光滑且具有圆的再生力,可以较好地实现3个封闭曲线重建。结论 本文方法可以在带法向量的初始控制顶点较少的情况下,较好地实现带法向约束的离散点集的曲线重建问题。     

A weighted support vector machine method for control chart pattern recognition

Manual inspection and evaluation of quality control data is a tedious task that requires the undistracted attention of specialized personnel. On the other hand, automated monitoring of a production process is necessary, not only for real time product quality assessment, but also for potential machinery malfunction diagnosis. For this reason, control chart pattern recognition (CCPR) methods have received a lot of attention over the last two decades. Current state-of-the-art control monitoring methodology includes K charts which are based on support vector machines (SVM). Although K charts have some profound benefits, their performance deteriorate when the learning examples for the normal class greatly outnumbers the ones for the abnormal class. Such problems are termed imbalanced and represent the vast majority of the real life control pattern classification problems. Original SVM demonstrate poor performance when applied directly to these problems. In this paper, we propose the use of weighted support vector machines (WSVM) for automated process monitoring and early fault diagnosis. We show the benefits of WSVM over traditional SVM, compare them under various fault scenarios. We evaluate the proposed algorithm in binary and multi-class environments for the most popular abnormal quality control patterns as well as a real application from wafer manufacturing industry.