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.     

Nonparametric control scheme for monitoring phase II nonlinear profiles with varied argument values

Profile monitoring is used to check the stability of the quality of a product over time when the product quality is best represented by a function at each time point.However,most previous monitoring approaches have not considered that the argument values may vary from profile to profile,which is common in practice.A novel nonparametric control scheme based on profile error is proposed for monitoring nonlinear profiles with varied argument values.The proposed scheme uses the metrics of profile error as the statistics to construct the control charts.More details about the design of this nonparametric scheme are also discussed.The monitoring performance of the combined control scheme is compared with that of alternative nonparametric methods via simulation.Simulation studies show that the combined scheme is effective in detecting parameter error and is sensitive to small shifts in the process.In addition,due to the properties of the charting statistics,the out-of-control signal can provide diagnostic information for the users.Finally,the implementation steps of the proposed monitoring scheme are given and applied for monitoring the blade manufacturing process.With the application in blade manufacturing of aircraft engines,the proposed nonparametric control scheme is effective,interpretable,and easy to apply.     

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.     

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.     

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.     

质量控制图在线智能诊断分析系统

在计算机集成制造系统环境下，为了有效实现工序质量控制，提出了质量控制图的在线智能诊断分析系统框架，它由控制图模式识别、参数估计、专家诊断分析系统和加工参数调整系统四个模块组成。在该系统中，采用了一种适用于模式识别与分类的新型神经网络模型——局部有监督特征映射网络，将其应用于该系统的控制图模式识别和参数估计中。仿真实验和应用实例表明，识别和分类结果与实际相符，并可以保证实时性。     

Cause-selecting control charts based on Huber’s M-estimator

Cause-selecting chart (CSC) is effective in monitoring and diagnosing multistage processes. It discriminates between the overall and specific qualities by establishing the relationship between input and output measurements. In practice, the model relating the input and output variables must be estimated. To this end, historical data are used, which often contain outliers. The presence of outliers has a deleterious effect on the control charting procedure. To alleviate the encountered problem, a robust monitoring approach based on Huber’s M-estimator is proposed. Subsequently, the performance of the robust and non-robust CSCs is investigated using the average run length criterion while conducting a simulation study. The results reveal that the Huber-based CSC is superior to the traditional CSC due to its prompt detection of out-of-control conditions.     

模型估计对序数响应轮廓控制图的影响

复杂制造或服务过程的质量特性可用函数关系即轮廓描述.针对序数响应轮廓的监控,基于非参数回归模型提出了广义似然比控制图.在受控模型未知且需要估计的现实情况下,采用局部线性核估计、样条和Newton Raphson 3种模型估计方法,并考虑不同的样本量、估计方法的不同参数设置,研究模型估计对控制图性能的影响.仿真以及案例分...     

A comparison study of three non-parametric control charts to detect shift in location parameters

Control charts are used as a statistical process control or SPC tool to identify the presence of assignable cause of variation in the process. Despite immense use and acceptability of parametric control charts, non-parametric control charts are an emerging area of recent development in the theory of SPC. The main advantage of non-parametric control charts is that they do not require any knowledge about the underlying distribution of the variable. In this work, we have summarized the different non-parametric control charts for controlling location from a literature survey, viz. control charts based on the sign test, control charts based on the Hodges–Lehmann estimator and control charts based on the Mann–Whitney statistic and compared their efficiency to detect the shift in location while in out of the control state under different situations and identified the best method under the prevailing situation.     

Modifying simple linear profiles monitoring schemes in phase II to detect decreasing step shifts and drifts

In profile monitoring, a relationship between a response variable and one or more explanatory variables is monitored. Different methods were developed for phase II monitoring of simple linear profiles. While some of the methods can be used to detect both increasing and decreasing shifts in the regression parameters, others need to be modified to enable detection of decreasing shifts in a process. In this paper, necessary modifications of the phase II methods for simple linear profile monitoring are proposed to improve their performance in detecting decreasing shifts. The paper also presents a performance comparison of several phase II methods.     

Statistical design of variable sample size and sampling interval $\bar{X}$\bar{X}control charts with run rules

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.     

Statistical design of variable sample size and sampling interval\bar Xcontrol charts with run rulescontrol charts with run rules

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.     

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.     

基于鲁棒参数控制方法的可变控制线控制图

针对在制造过程中应用鲁棒参数控制时,其过程均值和方差都会经常改变,且无法直接使用现有的控制图技术进行统计过程控制,提出了基于应用鲁棒参数控制的可变控制线控制图的设计方法.它不同于传统的适应性控制图设计方法,是该研究通过对过程均值和方差变化的有效估计,给出了可变控制线的调节律算法,为控制图自动跟踪过程变化提供了一种可行的方法.通过实例分析,验证了上述方法的有效性和实用性.     

Economic design of two-stage control charts with skewed and dependent measurements

In many instances, the cost is high to monitor primary quality characteristic called performance variable, but it could be more economical to monitor its surrogate. To cover asymmetric processes in an alternating fashion of two-stage charting design using either performance variable or surrogate variable, both process variables are modeled by a skew normal distribution, respectively. The proposed two-stage control charts are constructed with an economic viewpoint using Markov chain approach. Two algorithms are provided to implement the proposed charting method. The application of the proposed charting method and its advantages over the existing methods are presented through an illustrating example.     

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 robust \overline {\hbox{X}} control chart based on M-estimators in presence of outliers

Specifying the control limits is an important step in designing a control chart. The control limits are determined by the estimates of mean and/or standard deviation of the process. In the $ \overline {\hbox{X}} $ control chart, when outliers exist in the data, using the classical estimators to estimate parameters may cause the limits to become wider or to shift in the same direction. Robust estimators which are not affected by outliers are used in this research to determine the control limits for $ \overline {\hbox{X}} $ control chart. The mean and the dispersion estimators which are currently applied to define control limits are evaluated, and their performances in control charting are compared with the proposed method by vast simulation and real data examples. Based on the results, it is revealed that when M-estimators with bisquare ρ functions is used to estimate the mean and the dispersion of the process, the control chart has the best performance among the other robust and classical control charts.     

Parameter estimation of integrating and time delay processes using single relay feedback test

Autotuning using relay feedback is widely used to identify low order integrating plus dead time (IPDT) systems as the method is simple and is operated in closed-loop without interrupting the production process. Oscillatory responses from the process due to ideal relay input are collected to calculate ultimate properties of the system that in turn are used to model the responses as functions of system model parameters. These theoretical models of relay response are validated. After adjusting the phase shift, input and output responses are used to find land mark points that are used to formulate algorithms for parameter estimation of the process model. The method is even applicable to distorted relay responses due to load disturbance or measurement noise. Closed-loop simulations are carried out using model based control strategy and performances are calculated.     

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.     

基于稳健回归分析的转子系统不平衡量识别

不平衡是造成转子系统振动过大、影响其安全运行的重要因素。传统的最小二乘算法(least squares,简称LS)在不平衡量识别过程中存在对外界干扰或异常值敏感的问题,改进的加权最小二乘算法(weighted least squares,简称WLS)虽然能够降低异常值的影响,但需要经验积累并对振动数据进行深入分析。提出一种基于稳健回归分析的转子系统不平衡量识别方法,通过构建优化的目标函数自动消除异常值的影响,得到正常状态下转子系统不平衡量的最佳估值。实验结果表明,该方法能够有效消除外界干扰和异常值的影响,准确识别出转子系统不平衡量。