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.     

A transformation-based multivariate chart to monitor process dispersion

Multivariate monitoring techniques such as multivariate control charts are used to control the processes that contain more than one correlated characteristic. Although the majority of previous researches are focused on controlling only the mean vector of multivariate processes, little work has been performed to monitor the covariance matrix. In this research, a new method is presented to detect possible shifts in the covariance matrix of multivariate processes. The basis of the proposed method is to eliminate the correlation structure between the quality characteristics by transformation technique and then use an S chart for each variable. The performance of the proposed method is then compared to the ones from other existing methods and a real case is presented.     

Bootstrap method approach in designing multi-attribute control charts

In a production process, when the quality of a product depends on more than one correlated characteristic, multivariate quality control techniques are used. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In monitoring the quality of a product or process in multi-attribute environments in which the attributes are correlated, several issues arise. For example, a high number of false alarms (type I error) occur and the probability of not detecting defects (type II error) increases when the process is monitored by a set of independent uni-attribute control charts. In this paper, to overcome these problems, first we develop a new methodology to derive control limits on the attributes based on the bootstrap method in which we build simultaneous confidence intervals on the attributes. Then, based upon the in-control and out-of-control average run length criteria we investigate the performance of the proposed method and compare it with the ones from the Bonferroni and Sidak’s procedure using simulation. The results of the simulation study show that the proposed method performs better than the other two methods. At the end, we compare the bootstrap method with the T ² control chart for attributes.     

A heuristic threshold policy for fault detection and diagnosis in multivariate statistical quality control environments

In this paper, a heuristic threshold policy is developed to detect and classify the states of a multivariate quality control system. In this approach, a probability measure called belief is first assigned to the quality characteristics and then the posterior belief of out-of-control characteristics is updated by taking new observations and using a Bayesian rule. If the posterior belief is more than a decision threshold, called minimum acceptable belief determined using a heuristic threshold policy, then the corresponding quality characteristic is classified out-of-control. Besides using a different approach, the main difference between the current research and previous works is that the current work develops a novel heuristic threshold policy, in which in order to save sampling cost and time or when these factors are constrained, the number of the data gathering stages is assumed limited. A numerical example along with some simulation experiments is given at the end to demonstrate the application of the proposed methodology and to evaluate its performances in different scenarios of mean shifts.     

Condition monitoring scheme via one-class support vector machine and multivariate control charts

A condition-based maintenance (CBM) has been widely employed to reduce maintenance cost by predicting the health status of many complex systems in prognostics and health management (PHM) framework. Recently, multivariate control charts used in statistical process control (SPC) have been actively introduced as monitoring technology. In this paper, we propose a condition monitoring scheme to monitor the health status of the system of interest. In our condition monitoring scheme, we first define reference data set using one-class support vector machine (OC-SVM) to construct the control limit of multivariate control charts in phase I. Then, parametric control chart or non-parametric control chart is selected according to the results from multivariate normality tests. The proposed condition monitoring scheme is applied to sensor data of two anemometers to evaluate the performance of fault detection power.

     

On-machine wire electrical discharge dressing (WEDD) of metal-bonded grinding wheels

Traditional multivariate control charts such as Hotelling’s χ ² and T ² control charts are designed to monitor vectors of variable quality characteristics. However, in certain situations, data are expressed in linguistic terms and, under these circumstances, variable or attribute multivariate control charts are not suitable choices for monitoring purposes. Fuzzy multivariate control charts such as fuzzy Hotelling’s T ² could be considered as efficient tools to overcome the problems of linguistic observations. The purpose of this paper is to develop a fuzzy multivariate exponentially weighted moving average (F-MEWMA) control chart. In this paper, multivariate statistical quality control and fuzzy set theory are combined to develop the proposed method. Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling uncertain systems in industry, nature, and humanity. Through a numerical example, the performance of the proposed control chart was compared to the fuzzy Hotelling’s T ² control chart. Results indicate uniformly superior performance of the F-MEWMA control chart over Hotelling’s T ² control chart.     

Decision-making in detecting and diagnosing faults of multivariate statistical quality control systems

A new methodology is proposed in this paper to both monitor an overall mean shift and classify the states of a multivariate quality control system. Based on the Bayesian rule (Montgomery, Introduction to statistical quality control, 5th edn. Wiley, New York, USA, 2005), the belief that each quality characteristic is in an out-of-control state is first updated in an iterative approach and the proof of its convergence is given. Next, the decision-making process of the detection and classification the process mean shift is modeled. Numerical examples by simulation are provided in order to understand the proposed methodology and to evaluate its performance. Moreover, the in-control and out-of-control average run length (Montgomery, Introduction to statistical quality control, 5th edn. Wiley, New York, USA, 2005) of the proposed method are compared with the ones from the well-known Multivariate Cumulative Sum (MCUSUM), Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling T ² methods in different scenarios of mean shifts. The results of the simulation study show that the proposed methodology performs better than other methods for all shifts of the process mean. Additionally, the estimated probabilities of making correct classifications by the proposed approach are encouraging.     

A new link function in GLM-based control charts to improve monitoring of two-stage processes with Poisson response

In this paper, a new procedure is developed to monitor a two-stage process with a second stage Poisson quality characteristic. In the proposed method, log and square root link functions are first combined to introduce a new link function that establishes a relationship between the Poisson variable of the second stage and the quality characteristic of the first stage. Then, the standardized residual statistic, which is independent of the quality characteristic in the previous stage and follows approximately standardized normal distribution, is computed based on the proposed link function. Then, Shewhart and exponentially weighted moving average (EWMA) cause-selecting charts are utilized to monitor standardized residuals. Finally, two examples and a case study with a Poisson response variable are investigated, and the performance of the charts is evaluated by using average run length (ARL) criterion in comparison with the best literature method.     

A CUSUM-based method for monitoring simple linear profiles

In most statistical process control applications, the quality of a process or product is characterized by univariate or multivariate quality characteristics and monitored by the corresponding univariate and multivariate control charts, respectively. However, sometimes, the quality of a process or a product is better characterized by a relationship between a response variable and one or more explanatory variables. This relationship, which can be linear, nonlinear, or even a complicated model, is referred to as a profile. So far, several methods have been proposed for monitoring simple linear profiles. In this paper, a new method based on cumulative sum statistics is proposed to enhance monitoring of linear profiles in phase II. The performance of the proposed method is evaluated by average run length criterion. A comprehensive comparison is also conducted between the performance of the proposed method and the existing methods for monitoring simple linear profiles. The results show that the proposed method performs satisfactorily. In addition, the effects of reference value, sample size, and corrected sum of squares of explanatory variables on the performance of the proposed method are investigated.     

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts (one for each quality characteristic). A numerical example illustrates the proposed control charts.     

A neural network-based control scheme for monitoring start-up processes and short runs

Traditional control charts are commonly used as a monitoring tool in long-run processes. However, such control charts, due to the need for phase I analysis, are not suitable for start-up processes or short runs. Q control charts have been developed to help monitor start-up processes and short runs. In this article, a back propagation network is proposed for detecting a mean shift in start-up processes and short runs. In-control run length distribution of the control scheme is estimated using simulation study to provide information about the possibility of a false alarm within a specified number of observations. Performance of the proposed control scheme is assessed using different performance measures. It is shown numerically that the proposed control scheme outperforms the CUSUM of Q charts in detecting small to moderate mean shifts.     

基于深度置信网络的大数据制造过程实时智能监控

针对基于浅层学习模型的过程监控方法难以对大数据制造过程运行状态进行实时智能监控的问题,提出了基于深度置信网络的大数据制造过程实时智能监控方法。利用灰度图建立大数据制造过程质量图谱,以精准表达其过程的运行状态;构建用于识别大数据制造过程质量图谱的深度置信网络;应用离线训练好的深度置信网络模型对当前监控窗口内的过程质量图谱进行识别,实现大数据制造过程实时智能监控。最后,应用该方法对某注塑件大数据制造过程进行实时质量智能监控,结果表明：所提方法的识别性能明显优于基于主成分分析与BP神经网络、支持向量机的识别模型,能有效应用于大数据制造过程实时质量智能监控。     

Estimating process capability indices of multivariate nonnormal processes

The capability analysis of production processes where there are more than one correlated quality variables is a complicated task. The problem becomes even more difficult when these variables exhibit nonnormal characteristics. In this paper, a new methodology is proposed to estimate process capability indices (PCIs) of multivariate nonnormal processes. In the proposed methodology, the skewness of the marginal probability distributions of the variables is first diminished by a root transformation technique. Then, a Monte Carlo simulation method is employed to estimate the process proportion of nonconformities (PNC). Next, the relationship between PNC and PCI is found, and finally, PCI is estimated using PNC. Several multivariate nonnormal distributions such as Beta, Weibull, and Gamma are taken into account in simulation experiments. A real-world problem is also given to demonstrate the application of the proposed procedure. The results obtained from both the simulation studies and the real-world problem show that the proposed method performs well and is able to estimate PCI properly.     

Monitoring process variability using exponentially weighted moving sample variance control charts

Exponentially weighted moving average (EWMA) control charts are regarded as one of the most convenient tools in detecting small process shifts. Although EWMA control charts have been extensively used to monitor the mean of quality characteristics, there are few studies concentrating on the monitoring of process variability by using weighted moving control charts. In this paper, we propose an exponentially weighted moving sample variance (EWMSV) control chart for monitoring process variability when the sample size is equal to 1. The results are compared numerically with other similar methods using the average run length (ARL). Through an example, the practical considerations are presented to implement EWMSV control charts.     

Monitoring polynomial profiles in quality control applications

In some statistical process control applications, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. Sometimes, this relationship can be characterized by a polynomial profile. There are some methods in the literature which can be easily extended and used for monitoring polynomial profiles. In this paper, a new method is proposed for monitoring kth order polynomial profiles in phase II. In the proposed method, the polynomial profiles are transformed to orthogonal polynomial profiles, and the parameters of the transformed model are monitored by separate exponentially weighted moving average control charts. Based on the relationship between the parameters of the main and transformed model, the step shifts in the parameters of main model lead to larger step shifts in the parameters of the transformed model. Hence, this transformation leads to quicker detection in phase II. The performance of the proposed method is compared with the existing methods using numerical simulation runs in terms of average run length criterion.     

面向多品种小批量制造过程的NAD-EWMA控制图多目标优化设计方法

针对面向多品种小批量制造过程设计质量控制图面临的样本数量少、分布不确定问题,提出一种基于非参数、自适应、动态EWMA控制图的多目标优化设计方法。基于非参数统计理论与自适应控制的思想,构建与样本数据分布无关的控制图统计量,并设计一种基于聚类距离的动态抽样方法实现样本抽样;在此基础上,考虑统计性、经济性建立控制图多目标优化设计模型,基于改进人工鱼群算法与云清晰综合评价方法实现对模型求解,进而构建面向多品种小批量制的非参数自适应动态EWMA控制图。最后,以航天复杂构件制造过程为例,对制造过程进行动态监控。结果表明,所提方法能够快速监控到质量异常,监控性能高,验证了该方法的有效性和可行性,为多品种小批量制造过程实际的质量监控提供一种有效的途径。     

A new EWMA monitoring design for multivariate quality control problem

In this paper, a new approach is proposed to detect shifts of a multivariate quality control system. To do this, first, the decomposition method in multivariate normal distribution is introduced. Then, a control statistics is defined, and its properties are explained. In order to understand the proposed methodology and to evaluate its performance, a numerical example is provided by simulation. Moreover, the in- and out-of-control average run length of the proposed method are compared with the ones from the well-known multivariate cumulative sum and multivariate exponential weighted moving average in different scenarios of shifts. The results of the simulation study show that the proposed methodology performs better than the other methods in detecting the shifts of the standard deviation and correlation.     

Change point estimation in phase I monitoring of logistic regression profile

In statistical process control, an important issue in phase I is to identify the time of a change in process parameters. Control charts monitor the process over time, but the time an alarm is signaled by a control chart is not necessarily the real time of change in the process. Finding the real time of change, called as change point, is important because it leads to saving cost and time in detecting the assignable cause. Recently, profile monitoring in which a response variable and one or more explanatory variables are modeled by a regression function is attracted by many researchers. One type of profiles considered in the literature is a logistic profile where the distribution of the response variable is binary. In this paper, we develop two methods including likelihood ratio test and clustering to estimate the real time of a step change in phase I monitoring of the logistic profiles. The performance of the proposed methods is evaluated and compared through simulation studies. The results show the efficiency of both estimator methods. A real case is also studied to show the applicability of the proposed methods in practice.     

On efficient phase II process monitoring charts

Control charts act as the most effective statistical process control (SPC) tools for the monitoring of manufacturing processes. In this study, we propose and investigate a set Shewhart-type variability control chart based on the utilization of auxiliary information for efficient phase II process monitoring. The design parameters of the proposals are derived under correlated setups for the monitoring of variability parameter. The properties of these charting structures are evaluated in terms of average run length and some other related measures. The performance abilities of these charts are compared with each other and also with some existing counterparts. The comparisons revealed that the proposed charts are very efficient at detecting shifts in the variability parameter and have the ability to perform better than the competing charts in terms of run length characteristics. We have also used real datasets to illustrate the application of the proposed structures in practical situations.     

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。