A new chart based on sample variances for monitoring the covariance matrix of multivariate processes

In this article, we propose a control chart for detecting shifts in the covariance matrix of a multivariate process. The monitoring statistic is based on the standardized sample variance of p quality characteristics we call the VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these p variances. The reasons to consider the VMAX statistic instead of the generalized variance |S| are faster detection of process changes and better diagnostic features, which mean that the VMAX statistic is better at identifying the out-of-control variable. User’s familiarity with sample variances is another point in favor of the VMAX statistic. An example is presented to illustrate the application of the proposed chart.     

A robust interactive approach to optimize correlated multiple responses

Setting of process variables to meet the required specification of quality characteristics is a common problem in the process quality control. To obtain the most satisfactory solution, a decision maker's (DM) preference information on the trade-offs among the quality characteristics should be incorporated into the optimization procedure. In this regard, several multiple response surface optimization (MRO) techniques have been proposed in recent years. Most of these techniques require that all the preference information is specified in advance which is very difficult in practice. Furthermore, most of them assume independency of quality characteristics where their variances are constant over the experimental space. An interactive approach to optimize multiple responses is presented that does not require any information about DM's preference before solving process. This method aims to identify process variables to consider correlation among quality characteristics and minimize the variation in deviation of responses from their targets. It also accommodates dispersion effects and specification limits as well as location effects in a unified framework based on desirability functions. The features of the proposed method are investigated and the results are compared with some existing techniques through a real numerical example. Obtained results indicate the superiority of proposed methodology with respect to the major existing MRO techniques.     

方差监测的自适应累积和车身质量控制图研究

针对车身制造质量检测工作量大、数据处理方式简单等特点,提出一种基于方差的改进累积和控制图（CUSUM）方法,用于监测车身制造质量的方差波动。其基本思想是对控制图参数k动态更新和迭代,并与方差波动量相联系,以便实时监测车身焊接尺寸过程方差的微小波动。通过对控制图的平均运行链长进行分析和实际案例研究,并与常规累积和控制图和指数加权移动平均控制图作对比,表明该方法对过程方差微小变异更为有效和敏感。     

Locating Error Considering Dimensional Errors Modeling for Multistation Manufacturing System

Multistation machining process is widely applied in contemporary manufacturing environment.Modeling of variation propagation in multistation machining process is one of the most important research scenarios.Due to the existence of multiple variation streams,it is challenging to model and analyze variation propagation in a multi-station system.Current approaches to error modeling for multistation machining process are not explicit enough for error control and ensuring final product quality.In this paper,a mathematic model to depict the part dimensional variation of the complex multistation manufacturing process is formulated.A linear state space dimensional error propagation equation is established through kinematics analysis of the influence of locating parameter variations and locating datum variations on dimensional errors,so the dimensional error accumulation and transformation within the multistation process are quantitatively described.A systematic procedure to build the model is presented,which enhances the way to determine the variation sources in complex machining systems.A simple two-dimensional example is used to illustrate the proposed procedures.Finally,an industrial case of multistation machining part in a manufacturing shop is given to testify the validation and practicability of the method.The proposed analytical model is essential to quality control and improvement for multistation systems in machining quality forecasting and design optimization.     

Online intelligent monitoring and diagnosis of aircraft horizontal stabilizer assemble processes

The ability to reduce variation for quality improvement in the aircraft horizontal stabilizer assembly processes plays an essential role in the success of an aircraft manufacturing enterprise in today’s globally competitive marketplace. Monitoring and identifying variation source(s) of out-of-control signals are important issues for variation reduction in horizontal stabilizer assembly process. Traditional quality control focuses on statistical process control using control charts. However, control charts cannot identify variation source(s) of out-of-control signals. One novel integrated system is developed for monitoring and diagnosis of horizontal stabilizer assembly processes. $ \left| \Sigma \right| $ control charts are firstly designed to be used as the detector of abnormal signals, and then, an improved particle swarm optimization with simulated annealing (PSOSA)-based selective neural network (NN) ensemble approach is explored for identifying the variation source(s) of out-of-control signals. Utilization of selective NN ensemble algorithm is able to improve the generalization performance of neural systems in comparison with using single NN recognizers, and PSOSA algorithm aims to improve the ability to escape from a local optimum. The data from the real-world aircraft horizontal stabilizer assembly processes are collected to validate the developed system. The results indicate that the developed system can perform effectively for monitoring and identifying out-of-control signals of variance increases in terms of correct classification percentage and average run length.     

Optimization of multi-response processes using the VIKOR method

Design of experiments and Taguchi methods are extensively adopted as off-line quality improvement techniques in industry. However, these methods were developed to optimize single-response processes. In many situations, multiple responses must be optimized simultaneously, since some product designs, especially in the integrated circuit industry, are becoming increasingly complex to meet customers’ demands. Although several procedures for optimizing multi-response processes have been developed in recent years, the associated quality measurement indices do not consider variations in the relative quality losses of multiple responses. These procedures may therefore result in an optimization in which quality losses associated with a few responses are very small but those associated with others are very large, even if the overall average quality loss is small. Such an optimization with a large variation of quality losses among the responses is usually unacceptable to engineers. Accordingly, this study employs the VIKOR method, which is a compromise ranking method used for multicriteria decision making (MCDM), to optimize the multi-response process. The proposed method considers both the mean and the variation of quality losses associated with several multiple responses, and ensures a small variation in quality losses among the responses, along with a small overall average loss. Two case studies of plasma-enhanced chemical vapor deposition and copper chemical mechanical polishing demonstrate the effectiveness of the proposed method.     

Multivariate process parameter change identification by neural network

Whenever there is an out-of-control signal in process parameter control charts, maintenance engineers try to diagnose the cause near the time of the signal which does not always lead to prompt identification of the source(s) of the out-of-control condition, and this in some cases yields to extremely high monetary loses for the manufacturer owner. This paper applies multivariate exponentially weighted moving average (MEWMA) control charts and neural networks to make the signal identification more effective. The simulation of this procedure shows that this new control chart can be very effective in detecting the actual change point for all process dimension and all shift magnitudes considered. This methodology can be used in manufacturing and process industries to predict change points and expedite the search for failure causing parameters, resulting in improved quality at reduced overall cost. This research shows development of MEWMA by usage of neural network for identifying the step change-point and the variable responsible for the change in the process mean vector.     

Adaptive sampling interval cause-selecting control charts

This article considers the statistical adaptive process control for two dependent process steps. We construct an adaptive sampling interval Z _X control chart to monitor the quality variable produced by the first process step, and use the adaptive sampling interval Z _e control chart to monitor the specific quality variable produced by the second process step. By using the proposed adaptive sampling interval control charts, we can quickly detect and distinguish which process step is out of control. The performance of the proposed adaptive sampling interval control charts is measured by the adjusted average time to signal (AATS), which was derived by a Markov chain approach, for an out-of-control process. An empirical automobile braking system example shows the application and the performance of the proposed adaptive sampling control charts in detecting shifts in process means. Some numerical results obtained demonstrated that the performance of the proposed adaptive sampling cause-selecting control charts outperforms the fixed sampling interval cause-selecting control charts.     

A CUSUM scheme with variable sample sizes for monitoring process shifts

The cumulative sum scheme (CUSUM) and the adaptive control chart are two approaches to improve chart performance in detecting process shifts. A weighted loss function CUSUM scheme (WLC) is able to monitor both the mean shift and the increasing variance shift by manipulating a single chart. This paper investigates the WLC scheme with a variable sample sizes (VSS) feature. A design procedure is firstly proposed for the VSS WLC scheme. Then, the performance of the chart is compared with that of four other competitive control charts. The results show that the VSS WLC scheme is more powerful than the other charts from an overall viewpoint. More importantly, the VSS WLC scheme is simpler to design and operate. A case study in the manufacturing industry is used to illustrate the chart application. The proposed VSS WLC scheme suits the scenario where the strategy of varying sample sizes is feasible and preferable to pursue a high capability of detecting process variations.     

A study of multivariate (\bar{X},S)control chart based on Kullback–Leibler information

Recently, Chou et al. [11] have considered the multivariate control chart for monitoring the process mean vector and covariance matrix for the related quality characteristics simultaneously by using log-likelihood ratio statistics. They have computed the approximation formula described with Bernoulli polynomials of degrees r≥30 by using software MATHEMATICA 4.0 for obtaining the control limit with sufficient accuracy for the specified type I error probability in the chart. However, they cannot have obtained the approximation formula for the power evaluation. By the way, Kanagawa et al. [12] have proposed the $(\bar{x},s)$ control chart for monitoring the mean and variance simultaneously based on Kullback–Leibler information when quality characteristics obey a univariate normal distribution. In this article, by adopting the procedure by Kanagawa et al., we propose the other approximation formula for determining simply the control limit with sufficient accuracy for the specified type I error probability. Furthermore, the power evaluation for the chart is also considered in theory.     

A new adaptive control chart for monitoring process mean and variability

Traditionally, an $\bar{X}$ chart is used to control the process mean, and an R chart is used to control the variance. However, these charts are not sensitive to the small shifts in the processes. The adaptive charts might be considered if the aim is to detect process changes quickly. In this paper, we propose a new adaptive single control chart which integrates the exponentially weighted moving average procedure with the generalized likelihood ratio test statistics for jointly monitoring both the process mean and variability. This new chart is effective in detecting the disturbances that shift the process mean, increase or decrease the process variance, or lead to a combination of both effects.     

基于SPC与EPC集成的制造过程质量监控与调整

针对质量监控与调整中噪声信息对测量数据质量影响的问题,提出了一种基于统计过程控制（SPC）与工程过程控制（EPC）集成的制造过程质量监控与调整方法。建立了基于波动状态的统计过程控制与工程过程控制集成模型,实现了在质量监控的同时进行波动补偿。在质量监控阶段,首先采用Kalman滤波方法对含有噪声信息的测量数据进行滤波处理,估计得到波动状态,再依据滤波状态建立指数加权移动平均控制图进行质量监控,通过平均运行长度验证了该质量监控方法的性能。在质量调整阶段,基于波动状态对制造过程进行了调整。运用生产实例验证了方法的有效性和准确性。     

Constructing multivariate process capability indices for short-run production

Job-shop factories (or short-run production facilities) are now becoming increasingly widespread as consumer requirements increase and production techniques are improved. The number of products in a short-run lot is small, so engineers cannot collect sufficient samples to determine the distribution of quality characteristics and estimate process parameters. Additionally, multiple quality characteristics must be simultaneously evaluated to determine product quality, when the complexity of the product design is high. In such a case, conventional process capability indices such as C_p and C_pk cannot satisfy practical requirements. Recently, multivariate process capability indices (MPCI) have been studied. However, these studies focus primarily on mass production and assume that quality characteristics are normally distributed in developing the MPCI. Studies to develop process capability indices, especially MPCI, for short-run production are few. On the basis of Clement’s method, this study develops a procedure for constructing MPCI for short-run production using the technique of principal component analysis. A case study confirms the effectiveness of the proposed procedure .     

The worst ill-conditioned silicon wafer slicing machine detected by using grey relational analysis

In the silicon slicing process, machine vibrations and the unstable wire knife motion cause the slicing precision to drift, or other ill-conditions. This process involves several synchronously occurring multiple quality characteristics, such as thickness (THK), bow, warp, total indicator reading (TIR), and total thickness variation (TTV), which must be closely monitored and controlled. In this research, grey relational analysis (GRA) is applied to prevent an ill-conditioned wire saw machine from producing an unconfirmed product that is screened from the synchronously occurring multiple quality characteristics. Five weights of those characteristics are determined by an entropy method. Finally, a case study and the exponential weighted moving average (EWMA) control chart are presented to demonstrate and verify the feasibility and effectiveness of the proposed method.     

Optimization of multiple responses using principal component analysis and technique for order preference by similarity to ideal solution

Optimizing multi-response problems has become an increasingly relevant issue when more than one correlated product quality characteristic must be assessed simultaneously in a complicated manufacturing process. This study proposes a novel optimization procedure for multiple responses based on Taguchi’s parameter design. The signal-to-noise (SN) ratio is initially used to assess the performance of each response. Principal component analysis (PCA) is then conducted on the SN values to obtain a set of uncorrelated components. The optimization direction for each component is determined based on the corresponding variation mode chart. Finally, the relative closeness to the ideal solution resulting from the technique for order preference by similarity to ideal solution (TOPSIS) is determined as an overall performance index (OPI) for multiple responses. Engineers can easily employ the proposed procedure to obtain the optimal factor/level combination for multiple responses. A case study involving optimization of the chemical-mechanical polishing of copper (Cu-CMP) thin films from an integrated circuit manufacturer in Taiwan is also presented to demonstrate the effectiveness of the proposed procedure.     

Monitoring multivariate–attribute processes based on transformation techniques

Control charts are widely used in monitoring the quality of a product or a process. In most of the cases, quality of a product or a process can be characterized by two or more correlated quality characteristics. Many control charts have been proposed for monitoring multivariate or multi-attribute quality characteristics, separately, but sometimes the correlated variables and attribute quality characteristics represents the quality of a process. In this paper, the use of four transformation methods is proposed to monitor the multivariate–attribute processes. In the first one, the distribution of correlated variables and attribute quality characteristics are transformed to approximate multivariate normal distribution, and then the transformed data are monitored by multivariate control charts including T ² and MEWMA. Based on the second transformation method, the correlated variables and attribute quality characteristics are transformed, such that the correlation between the quality characteristics approaches to zero, then univariate control charts are used in monitoring the transformed data. In the third and fourth proposed methods, a combination of two transformation methods is used to make the quality characteristics independent and to transform them to normal distribution. The difference between the third and fourth method is the order of using the transformation techniques. The performance of the proposed methods is evaluated by using simulation studies in terms of average run length criterion. Finally, the proposed approach is applied to a real dataset.     

Optimal control policy for dependent process steps with over-adjusted means and variances

Over-adjustment to processes may result in shifts in process mean and variance, ultimately affecting the quality of products. An economic adjustment model is developed for the joint design of X̄-S² control charts and ē-S_e² cause-selecting control charts to control both means and variances of two dependent process steps using the Markov chain approach. The objective is to determine the optimal control policy of the proposed control charts, which effectively detect and distinguish the shifts of means and variances on the dependent process steps and minimize the total quality control cost. Application of the proposed control charts is illustrated through a numerical example.     

Multi-variable measurements and optimization of GMAW parameters for API-X42 steel alloy using a hybrid BPNN–PSO approach

This research addresses multi criteria modeling and optimization procedure for Gas Metal Arc Welding (GMAW) process of API-X42 alloy. Experimental data needed for modeling are gathered as per L₃₆ Taguchi matrix. Model inputs include work piece groove angle as well as the five main GMAW process parameters. The proposed back propagation neural network (BPNN) simultaneously predicts weld bead geometry (WBG) and heat affected zone (HAZ). Image processing technique along with Bridge Cam and AWS gauges are used to take accurate measurements of WBGs and HAZs. The adequacy of the developed BPNN is established through comparisons against measured process outputs. Measurements indicate that the BPNN model simulates GMAW process with average errors of 0.33 to 0.82%. Next, the BPNN model is implanted into a particle swarm optimization (PSO) algorithm to simultaneously optimize HAZ and WBG characteristics. The hybrid BPNN–PSO determines process parameters values and groove angle so as a desired WBG is achieved while HAZ is minimized. Verification tests demonstrate that the proposed BPNN–PSO is quite efficient for in multi-criteria modeling and optimization of GMAW.     

An approach to optimize correlated multiple responses using principal component analysis and desirability function

While researchers have developed several approaches to attain design variable settings that simultaneously optimize multiple-quality characteristics, the multi-response optimization has become a common practice in complicated manufacturing processes. Most of these research works assume independency of responses where their variances are constant over the experimental space. However, there are many manufacturing processes in practice where the quality characteristics under consideration are correlated. In this study, an efficient approach based on principal component analysis and a conventional desirability function is proposed to optimize correlated multiple responses. This approach not only obtains optimal operating conditions, but also considers different variance and correlation levels of responses and enforces all objectives to satisfy constraints. Experimental results obtained using a standard example show the effectiveness of the proposed method.     

A hybrid root transformation and decision on belief approach to monitor multiattribute Poisson processes

Most of industrial applications of statistical process control involve more than one quality characteristics to be monitored. These characteristics are usually correlated, causing challenges for the monitoring methods. These challenges are resolved using multivariate quality control charts that have been widely developed in recent years. Nonetheless, multivariate process monitoring methods encounter a problem when the quality characteristics are of the attribute type and follow nonnormal distributions such as multivariate binomial or multivariate Poisson. Since the data analysis in the latter case is not as easy as the normal case, more complexities are involved to monitor multiattribute processes. In this paper, a hybrid procedure is developed to monitor multiattribute correlated processes, in which number of defects in each characteristic is important. Two phases are proposed to design the monitoring scheme. In the first phase, the inherent skewness of multiattribute Poisson data is almost removed using a root transformation technique. In the second phase, a method based on the decision on belief concept is employed. The transformed data obtained from the first phase are implemented on the decision on belief (DOB) method. Finally, some simulation experiments are performed to compare the performances of the proposed methodology with the ones obtained using the Hotelling T ² and the MEWMA charts in terms of in-control and out-of-control average run length criteria. The simulation results show that the proposed methodology outperforms the other two methods.