Effect of Phase I Estimation on Phase II Control Chart Performance with Profile Data

This paper illustrates how phase I estimators in statistical process control (SPC) can affect the performance of phase II control charts. The deleterious impact of poor phase I estimators on the performance of phase II control charts is illustrated in the context of profile monitoring. Two types of phase I estimators are discussed. One approach uses functional cluster analysis to initially distinguish between estimated profiles from an in‐control process and those from an out‐of‐control process. The second approach does not use clustering to make the distinction. The phase II control charts are established based on the two resulting types of estimates and compared across varying sizes of sustained shifts in phase II. A simulated example and a Monte Carlo study show that the performance of the phase II control charts can be severely distorted when constructed with poor phase I estimators. The use of clustering leads to much better phase II performance. We also illustrate that the performance of phase II control charts based on the poor phase I estimators not only have more false alarms than expected but can also take much longer than expected to detect potential changes to the process. Copyright © 2014 John Wiley & Sons, Ltd.     

Cluster‐Based Bounded Influence Regression

A regression methodology is introduced that obtains competitive, robust, efficient, high‐breakdown regression parameter estimates as well as providing an informative summary regarding possible multiple outlier structure. The proposed method blends a cluster analysis phase with a controlled bounded influence (BI) regression phase, thereby referred to as cluster‐based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point‐addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster ‘half‐set’ of observations, with the remaining observations comprising one or more minor clusters. An initial regression estimator arises from the main cluster, with a group‐additive DFFITS argument used to carefully activate the minor clusters through a BI regression frame work. CBI achieves a 50% breakdown point, is regression equivariant, scale and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo results demonstrate the performance advantage of CBI over other popular robust regression procedures regarding coefficient stability, scale estimation and standard errors. The dendrogram of the clustering process and the weight plot are graphical displays available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical view point towards data analysis and the marriage of estimation with diagnostic summary. Copyright © 2013 John Wiley & Sons, Ltd.     

MRI brain image classification—a hybrid approach

The present article proposes a novel computer‐aided diagnosis (CAD) technique for the classification of the magnetic resonance brain images. The current method adopt color converted hybrid clustering segmentation algorithm with hybrid feature selection approach based on IGSFFS (Information gain and Sequential Forward Floating Search) and Multi‐Class Support Vector Machine (MC‐SVM) classifier technique to segregate the magnetic resonance brain images into three categories namely normal, benign and malignant. The proposed hybrid evolutionary segmentation algorithm which is the combination of WFF(weighted firefly) and K‐means algorithm called WFF‐K‐means and modified cuckoo search (MCS) and K‐means algorithm called MCS‐K‐means, which can find better cluster partition in brain tumor datasets and also overcome local optima problems in K‐means clustering algorithm. The experimental results show that the performance of the proposed algorithm is better than other algorithms such as PSO‐K‐means, color converted K‐means, FCM and other traditional approaches. The multiple feature set comprises color, texture and shape features derived from the segmented image. These features are then fed into a MC‐SVM classifier with hybrid feature selection algorithm, trained with data labeled by experts, enabling the detection of brain images at high accuracy levels. The performance of the method is evaluated using classification accuracy, sensitivity, specificity, and receiver operating characteristic (ROC) curves. The proposed method provides highest classification accuracy of greater than 98% with high sensitivity and specificity rates of greater than 95% for the proposed diagnostic model and this shows the promise of the approach. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 226–244, 2015     

A General Framework for Constructing Control Charts

A general framework for the construction of control charts is presented. The method is based on using the density of the sample subgroup statistic as a measure of how unusual newly observed subgroups are. This methodology includes, as special cases, many common control chart techniques. The method is also easily applied to multivariate and multimodal situations. A non‐parametric control chart is implemented by estimating the density of the sample subgroup statistic using a kernel estimator of the bootstrap distribution of the observed subgroup statistics. Several examples of the method are presented in the parametric and non‐parametric situations. The potential performance of the non‐parametric version of the method is demonstrated through an empirical study of average run length properties. Copyright © 2005 John Wiley & Sons, Ltd.     

基于密度的轮廓控制参数识别方法研究

正确识别受控轮廓集并确定轮廓控制参数是轮廓控制的基础。当轮廓内部存在相关关系时,异常轮廓对目前轮廓控制参数识别方法的干扰较大。因此,为降低异常轮廓对轮廓控制参数识别方法的影响,提出一种基于密度的受控轮廓集识别方法。该方法包括基于线性混合模型的轮廓建模、基于密度的初始受控轮廓集确定、基于逐次迭代方法的受控轮廓集识别和轮廓控制参数确定等。基于蒙特卡洛模拟分析所提方法中初始受控轮廓数目和密度参数对识别性能的影响。此外,比较分析所提方法与已有方法的识别性能。模拟仿真显示,基于密度的轮廓控制参数识别方法的识别性能要优于其他方法。     

Estimation of Complicated Profiles in Phase I,Clustering and S‐estimation Approaches

Some quality characteristics are well defined when expressed as a function of an independent variable. This function is usually called a profile. If the functional form of the profile is known, parametric methods could be used to monitor the profile representing a process. However, some processes are complicated, and it is not suitable to use parametric models. In these cases, nonparametric methods may be used to monitor the profiles. One of the powerful nonparametric profile monitoring methods is to use wavelets. In this paper, the issue of estimating the complicated profiles in phase I is studied. In order to monitor the process using wavelets, it is required to estimate the vector of wavelet coefficients. Classical estimators are usually used to estimate the coefficients vector. These estimators should be used when the data do not contain outliers. However, it is possible that the data set is contaminated and includes some outliers. Thus, it is better to use robust estimators that are insensitive to the presence of outliers. In this paper, two robust estimators for estimating the complicated profiles using wavelets are proposed. In the first approach, the dimension of the coefficients vector is reduced by means of PCA incorporated into clustering. The second approach is based on the S‐estimation method. An extensive simulation study is performed using matlab ® software to evaluate the proposed methods and to compare the results with an existing classical method. The results show the well performance of the suggested methods in estimating the model parameters when the data set is not contaminated and in the presence of outliers. Copyright © 2016 John Wiley & Sons, Ltd.     

A nonparametric CUSUM chart for process dispersion

In the present article, we propose a nonparametric cumulative sum control chart for process dispersion based on the sign statistic using in‐control deciles. The chart can be viewed as modified control chart due to Amin et al, 6 which is based on in‐control quartiles. An average run length performance of the proposed chart is studied using Markov chain approach. An effect of non‐normality on cumulative sum S² chart is studied. The study reveals that the proposed cumulative sum control chart is a better alternative to parametric cumulative sum S² chart, when the process distribution is non‐normal. We provide an illustration of the proposed cumulative sum control chart.     

A semiparametric profile monitoring via residuals

Profile monitoring is a vast area of research underneath the statistical process monitoring (SPM). Several methods for univariate and multivariate process control are found in literature to monitor the profile data, including parametric, nonparametric, and some semiparametric methods. The main idea behind monitoring the linear profiles in mixed effects is to model the possible individual differences between similar set of profiles for future monitoring. In this paper, nonparametric and semiparametric approaches are proposed to model the profile data in a linear mixed effect setting by considering the residuals from a parametric model. A simulation study was carried out to compare the efficiency of the proposed methods. At first step, the residuals from a parametric linear mixed model are obtained. A nonparametric approach (NPR) is then used to model these residuals. Finally, a semiparametric method (MMRRPM) is proposed as a convex combination of the parametric (P) and nonparametric estimations based on the residuals (NPR) to model the profile data in mix effects. Two Hoteling's T² statistics were computed for each technique based on fitted values and the estimated random effects. The results show that the proposed methods are most effective to monitor the autocorrelated profile data compared with the state‐of‐the‐art.     

Using independent component analysis to monitor 2‐D geometric specifications

Functional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2‐dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non‐normality of the error term is present. The performance of this method is evaluated and compared with a regression‐ and PCA‐based approach through simulation of the average run length criterion. The results reveal that the proposed ICA‐based approach is robust against non‐normality in the in‐control analysis, and its out‐of‐control performance is on par with that of the PCA‐based method in case of normal and near‐normal error terms.     

One‐sided control chart based on support vector machines with differential evolution algorithm

The statistical learning classification techniques have been successfully applied to statistical process control problems. In this paper, we proposed a one‐sided control chart based on support vector machines (SVMs) and differential evolution (DE) algorithm to monitor a process with multivariate quality characteristics. The SVM classifier provides a continuous distance from the boundary, and the DE algorithm is used to obtain the optimal parameters of the SVM model by minimizing mean absolute error (MAE). The average run length of the proposed chart is computed using the Monte Carlo simulation approach. Several simulated cases are conducted using a multivariate normal distribution with 10 and 20 dimensions and three different process shift scenarios. In addition, we consider two non‐normal distribution cases. The ARL performance of the proposed chart is better than the distance‐based SVM chart. A real example is used to illustrate the application of the proposed control chart.     

Combining classifiers through fuzzy cognitive maps in natural images

A new automatic hybrid classifier for natural images by combining two base classifiers through the fuzzy cognitive maps (FCMs) approach is presented in this study. The base classifiers used are fuzzy clustering (FC) and the parametric Bayesian (BP) method. During the training phase, different partitions are established until a valid partition is found. Partitioning and validation are two automatic processes based on validation measurements. From a valid partition, the parameters of both classifiers are estimated. During the classification phase, FC provides for each pixel the supports (membership degrees) that determine which cluster the pixel belongs to. These supports are punished or rewarded based on the supports (probabilities) provided by BP. This is achieved through the FCM approach, which combines the different supports. The automatic strategy and the combined strategy under the FCM framework make up the main findings of this study. The analysis of the results shows that the performance of the proposed method is superior to other hybrid methods and more accurate than the single usage of existing base classifiers.     

Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

This paper presents a design stage method for assessing performance reliability of systems with multiple time‐variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time‐dependent limit‐state functions. System failure is defined as the non‐conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second‐order bounds. Further, for numerical efficiency probabilities are evaluated by first‐order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Sum of Squares Control Charts for Monitoring of Multivariate Multiple Linear Regression Profiles in Phase II

In this paper, we propose four control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression profiles in Phase II. The proposed control charts include sum of squares exponential weighted moving average (SS‐EWMA) and sum of squares cumulative sum (SS‐CUSUM) for monitoring regression parameters and corresponding covariance matrix and SS‐EWMARe and SS‐CUSUMRe control charts for monitoring mean vector and covariance matrix of residual. Proposed methods are able to identify the out‐of‐control parameter responsible for shift. The performance of the proposed control charts is compared with existing method through Monte‐Carlo simulations. Moreover, the diagnostic performance of the proposed control charts is evaluated through simulation studies. The results show better performance of the proposed control charts rather than competing control chart. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry. Copyright © 2016 John Wiley & Sons, Ltd.     

Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model

A non‐gradient‐based approach for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the non‐gradient‐based topology optimization method in flow problems, this research focuses on two single‐objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and one multi‐objective optimization problem, which combines earlier two single‐objective optimization problems. The shape of flow channels is represented by the level set function. The pressure loss and the heat transfer performance of the channels are evaluated by the Building‐Cube Method code, which is a Cartesian‐mesh CFD solver. The proposed method resulted in an agreement with previous study in the single‐objective problems in its topology and achieved global exploration of non‐dominated solutions in the multi‐objective problems. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd     

Phase I control chart based on a kernel estimator of the quantile function

To measure the statistical performance of a control chart in Phase I applications, the in‐control average run length (ARL) is the most frequently used parameter. In typical start up situations, control limits must be computed without knowledge of the underlying distribution of the quality characteristic. Assumptions of an underlying normal distribution can increase the probability of false alarms when the underlying distribution is non‐normal, which can lead to unnecessary process adjustments. In this paper, a control chart based on a kernel estimator of the quantile function is proposed. Monte Carlo simulation was used to evaluate the in‐control ARL performance of this chart relative to that of the Shewhart individuals control chart. The results indicate that the proposed chart is more robust to deviations in the assumed underlying distribution (with respect to the in‐control ARL) and results in an alternative method of designing control charts for individual units. Copyright © 2011 John Wiley & Sons, Ltd.     

A Direct Data-Cluster Analysis Method Based on Neutrosophic Set Implication

Raw data are classified using clustering techniques in a reasonable manner to create disjoint clusters. A lot of clustering algorithms based on specific parameters have been proposed to access a high volume of datasets. This paper focuses on cluster analysis based on neutrosophic set implication, i.e., a k-means algorithm with a threshold-based clustering technique. This algorithm addresses the shortcomings of the k-means clustering algorithm by overcoming the limitations of the threshold-based clustering algorithm. To evaluate the validity of the proposed method, several validity measures and validity indices are applied to the Iris dataset (from the University of California, Irvine, Machine Learning Repository) along with k-means and threshold-based clustering algorithms. The proposed method results in more segregated datasets with compacted clusters, thus achieving higher validity indices. The method also eliminates the limitations of threshold-based clustering algorithm and validates measures and respective indices along with k-means and thresholdbased clustering algorithms.     

Statistical monitoring of nonlinear product and process quality profiles

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T² control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T² control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T² statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non‐parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models. Journal of Quality Technology 2002; 34:118–129). Copyright © 2007 John Wiley & Sons, Ltd.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust Multivariate Control Chart for Outlier Detection Using Hierarchical Cluster Tree in SW2

The goal of this paper is to develop a new multivariate control chart that can effectively detect potential outlier(s) in multi‐dimensional data while keeping the masking and swamping effects under control. The hierarchical clustering tree plays a central role in the proposed control chart, in an attempt to improve the Sullivan and Woodall's second method, known as the SW2 method. Historical multivariate datasets taken from the literature are used as the benchmarks to illustrate the performance of the proposed control charts in comparison to nine existing methods for outlier detection. The two criteria, the masking and swamping rates, are used as yardsticks for the evaluation purpose. An additional simulation study by means of Monte Carlo experiments further verifies that the proposed control chart that incorporates the hierarchical clustering tree performs much better in outlier detection and swamping prevention than the original SW2 and minimum volume ellipsoid methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Knowledge based cluster ensemble for cancer discovery from biomolecular data

The adoption of microarray techniques in biological and medical research provides a new way for cancer diagnosis and treatment. In order to perform successful diagnosis and treatment of cancer, discovering and classifying cancer types correctly is essential. Class discovery is one of the most important tasks in cancer classification using biomolecular data. Most of the existing works adopt single clustering algorithms to perform class discovery from biomolecular data. However, single clustering algorithms have limitations, which include a lack of robustness, stability, and accuracy. In this paper, we propose a new cluster ensemble approach called knowledge based cluster ensemble (KCE) which incorporates the prior knowledge of the data sets into the cluster ensemble framework. Specifically, KCE represents the prior knowledge of a data set in the form of pairwise constraints. Then, the spectral clustering algorithm (SC) is adopted to generate a set of clustering solutions. Next, KCE transforms pairwise constraints into confidence factors for these clustering solutions. After that, a consensus matrix is constructed by considering all the clustering solutions and their corresponding confidence factors. The final clustering result is obtained by partitioning the consensus matrix. Comparison with single clustering algorithms and conventional cluster ensemble approaches, knowledge based cluster ensemble approaches are more robust, stable and accurate. The experiments on cancer data sets show that: 1) KCE works well on these data sets; 2) KCE not only outperforms most of the state-of-the-art single clustering algorithms, but also outperforms most of the state-of-the-art cluster ensemble approaches.