具有可变抽样区间的残差MEWMA控制图

为了提高控制图监控多元自相关过程小波动的效率,研究具有可变抽样区间(VSI)的残差MEWMA控制图。首先,对残差MEWMA控制图进行可变抽样区间设计,用蒙特卡罗模拟方法计算其平均报警时间。其次,对所设计的可变抽样区间残差MEWMA与固定抽样区间的残差MEWMA进行比较研究。结果表明,可变抽样区间残差MEWMA控制图监控效率优于固定抽样区间的残差MEWMA控制图,能更快地发现过程中的变化。然后,通过对比研究得出,VSI残差MEWMA控制图的受控性能优于VSI MEWMA控制图。最后,研究平滑系数对过程监控性能的影响,得出过程波动较小时,采用较小的平滑系数;分析自相关系数对过程监控性能的影响关系,得出对于相同波动,相关系数越小,VSI MEWMA残差控制图的监控效果越好。     

可变样本容量和抽样区间的质量控制图

常规控制图是每隔固定时间从过程抽取固定容量的样本对过程进行监督,本文根据Ｐｒａｂｈｕ等的联合可变样本容量和抽样区间的ｘ图的模型设计可变样本容量和抽样区间的中位值ｘ和极差Ｒ控制图,计算了在可变样本容量和抽样区间下发信号前的平均时间,并同常规、可变样本容量与可变抽样区间图作比较。所设计的ｘ和Ｒ图能缩短过程失控时间而减少不合格品数。     

考虑质量损失和预防维修策略下的VSI EWMA标准差控制图经济决策模型

为了提高控制图监控效率和降低过程质量损失成本,提出一种监控过程标准差的可变抽样区间(VSI)指数加权移动平均(EWMA)控制图联合经济设计方法。首先,在考虑质量损失和预防维修决策的前提下,构建VSI EWMA标准差控制图的联合经济决策模型,使期望损失函数最小确定控制图设计参数的最优值。其次,以期望损失函数为适应性函数,采用遗传算法寻找联合经济决策模型的最优解。然后,对VSI EWMA标准差控制图联合经济决策模型进行灵敏度分析,研究了控制图模型参数对设计参数与期望损失函数的影响关系。最后,最优性分析表明基于联合经济决策模型设计的VSI EWMA控制图具有较小的期望损失,在经济性方面优于静态EWMA控制图以及平均报警时间为准则设计的VSI EWMA控制图。     

VSI Q控制图应用研究

VSI Q控制图可以解决经典休哈特控制图在样本数据缺乏的情况下不能应用的问题,并且可以加快检出速度.具体方法是将样本数据转换成服从标准正态分布的统计数据,再利用可变抽样区间技术确定抽样间隔时间.应用研究证明,VSI Q控制图在缺乏样本数据时也能用于监控生产过程,快速检测出异常.     

变采样间隔中位数控制图设计

针对过程数据存在异常值的问题,采用中位数统计量()代替传统均值()统计量,提出一种变采样间隔(Variable Sampling Interval ,VSI )控制图来监控过程均值偏移。首先推导出VSI 控制图的平均报警时间和报警时间标准差等性能指标;保证过程处于受控状态的统计性能指标,得到VSI 控制图的最优决策变量,进一步获得其失控状态下的最优性能指标。仿真结果表明,VSI 控制图的性能明显优于传统控制图,当过程均值偏移较小时,其优势更加明显。     

非对称抽样区间x^-图

许多生产过程不满足休哈特图所基于的假设,过程均值向上飘移与向下飘移的发生具有不等概率,向上漂移幅度不同于向下漂移幅度.提出一种非对称抽样区间(x)图来监控此类过程,计算了控制图的效率测度--平均报警时间,与对称抽样区间图及非对称控制限图的比较显示此方案可以更快发现过程的变化.     

基于ARMA(n,n-1)模型的统计质量控制图

将ARMA(n,n-1)模型应用到具有自相关性的生产过程中,提出了基于该模型的统计控制图.使用蒙特卡洛方法进行数据模拟,与其它文献比较可得,当生产过程平稳时,ARMA(n,n-1)控制图的性能要远远地超过ARMA(1,1)控制图;当生产过程不平稳时,ARMA(n,n-1)控制图也能达到预期目的.并在此基础上,设计了AR...     

基于马尔可夫链模型的B&L VP (X)控制图统计性能分析

在已有VP(X)控制图基础上,增加了B&L转换规则,构建了基于马尔可夫链模型的B&L VP(X)控制图统计性能分析模型,给出了统计性能指标ATS、AATS以及ANSW的表达式.针对2组设计参数,将构建的模型与现有VP(X)控制图进行了比较分析,结果表明当平均运行时间相同时,本文构建的模型在缩短报警时间和减少转换次数方面,都有着明显的优势,而且随着转换参数L的增大,这种优势会增大.     

《测量不确定度评定与表示》系列讲座 第六讲 蒙特卡洛法评定测量不确定度简介

正一、什么是蒙特卡洛法蒙特卡洛法缩写为MCM,MCM是一种概率传播的方法,即通过对输入量Xi的概率密度函数(PDF)离散抽样,由测量模型传播输入量的概率分布,计算获得输出量Y的概率密度函数(PDF)的离散抽样值,进而由输出量的离散分布数值获取输出量的最佳估计值、标准不确定度和包含区间。该最佳估计值、标准不确定度和包含区间的可信程度随PDF抽样数的增加而提高。图1描述了由输入量Xi(i=1,……,N)的PDF,通过模型传播,给出输出量Y的PDF的过程的示意图。图     

面粉冲装称量机构变脉冲积分化控制

目的 针对面粉自动冲装称量生产加工要求,改进设计一种可实现多款称量功能的冲粉称量机构,并进行可变脉冲积分化控制设计,实现自动冲装称量应用.方法 采用可编程序控制器(PLC)的高速脉冲输出功能,设计分段高速脉冲控制驱动步进电机解决冲粉称量的生产控制要求,即在精确称量阶段通过设计匀速递减可变脉冲来快速无限逼近积分控制过程以达到精准称量.结果 该设计有效地抑制了称量中干扰和步进电机的高频振颤现象,最大过冲量小于3 g.结论 与传统的粉末自动冲装称量控制应用相比,该控制无整定参数且精准称量时间更短,设计更便于采用PLC编程来实现,称量精度更逼近称量传感器的分辨率.     

An adaptive exponentially weighted moving average chart for the mean with variable sampling intervals

The AEWMA control chart is an adaptive EWMA (exponentially weighted moving average) type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. To improve the detection performance of the FSI (fixed sampling interval) AEWMA control chart 7 in terms of the ATS(average time to signal), this paper proposes a new VSI (variable sampling interval) AEWMA control chart. A Markov chain approach is used to calculate the ATS values of the new VSI AEWMA control chart, and comparative results show that the proposed control chart performs better than the standard FSI AEWMA control chart and than other VSI control charts over a wide range of shifts.     

An economic design model for X¯ charts with random sampling policies

Recent literature contains many papers on the study of variable (but deterministic) sampling interval (VSI) policies for X¯ control charts. VSI policies perform better than their corresponding classical fixed-sampling-interval (FSI) policies. Results are also available in the literature for an adaptive VSI policy, an enhancement of the VSI policy, where the sample size also changes with the sampling interval. However, for many industrial (especially continuous) processes where X¯ charts are used, maintaining deterministic time intervals between samples is not possible owing to inherent randomness of the processes. In this paper we propose a new variable sampling policy, named random sampling policy (RSP), for X¯ charts in which the sampling intervals and the sample sizes (considered a function of the sampling intervals) are treated as random variables. An economic modeling framework for design of RSP with run rules is developed. Within the proposed modeling framework, special cases of RSP, such as VSI and FSI policies with and without run rules, can also be evaluated. An application of the economic model is demonstrated through design of RSP parameters for two numerical example problems.     

Adaptive CUSUM and EWMA charts with auxiliary information and variable sampling intervals for monitoring the process mean

The variable sampling interval (VSI) feature enhances the sensitivity of a control chart that is based on fixed sampling interval (FSI). In this paper, we enhance the sensitivities of the auxiliary information-based (AIB) adaptive Crosier cumulative sum (CUSUM) (AIB-ACC) and adaptive exponentially weighted moving average (EWMA) (AIB-AE) charts using the VSI feature when monitoring a mean shift which is expected to lie within a given interval. The Monte Carlo simulations are used to compute zero-state and steady-state run length properties of these control charts. It is found that the AIB-ACC and AIB-AE charts with VSI feature are uniformly more sensitive than those based on FSI feature. Real datasets are also considered to demonstrate the implementation of these control charts.     

Nonparametric signed‐rank control charts with variable sampling intervals

Variable sampling interval (VSI) charts have been proposed in the literature for normal theory (parametric) control charts and are known to provide performance enhancements. In the VSI setting, the time between monitored samples is allowed to vary depending on what is observed in the current sample. Nonparametric (distribution‐free) control charts have recently come to play an important role in statistical process control and monitoring. In this paper a nonparametric Shewhart‐type VSI control chart is considered for detecting changes in a specified location parameter. The proposed chart is based on the Wilcoxon signed‐rank statistic and is called the VSI signed‐rank chart. The VSI signed‐rank chart is compared with an existing fixed sampling interval signed‐rank chart, the parametric VSI ‐chart, and the nonparametric VSI sign chart. Results show that the VSI signed‐rank chart often performs favourably and should be used.     

The Run Sum Hotelling's χ2 Control Chart with Variable Sampling Intervals

Control charts are widely used for process monitoring and quality control in manufacturing industries. Implementing variable sampling interval (VSI) control schemes on control charts rather than traditional fixed sampling interval procedure can significantly improve the control chart's efficiency. In this paper, the VSI run sum (RS) Hotelling's χ² chart is proposed. The optimal scores and parameters of the proposed chart are determined using an optimization technique to minimize the following: (i) out‐of‐control average time to signal (ATS); (ii) adjusted ATS (AATS), when the exact shift size can be specified; (iii) expected ATS; or (iv) expected AATS, when the exact shift size cannot be specified. The Markov chain method is used to evaluate the zero‐state ATS and expected ATS, and steady‐state AATS and expected AATS of the proposed chart. The results show that the VSI RS Hotelling's χ² chart significantly outperforms the standard RS Hotelling's χ² chart and the former also performs well compared with other competing charts. By adding more scoring regions, the efficiency of the VSI RS Hotelling's χ² chart can be further enhanced. An illustrative example using data from a manufacturing process is presented to demonstrate the application of the VSI RS Hotelling's χ² chart. The application of the proposed chart in a quality improvement program can be extended to management and service industries. Copyright © 2016 John Wiley & Sons, Ltd.     

The Design of the Variable Sampling Interval Generalized Likelihood Ratio Chart for Monitoring the Process Mean

This paper considers the problem of monitoring a normally distributed process variable in which some sustained shift in the mean may occur. A generalized likelihood ratio (GLR) control chart with a variable sampling interval (VSI) scheme is proposed to quickly detect a wide range of such shifts. The performance of the VSI GLR chart is evaluated, and the results show that using the VSI feature can greatly reduce the expected detection time. Design methodology for the VSI GLR chart is provided so that practitioners can easily use this chart in applications. An illustrative example is given to explain how to apply the VSI GLR chart. Copyright © 2013 John Wiley & Sons, Ltd.     

Variable sampling interval exponentially weighted moving average median chart with estimated process parameters

The variable sampling interval exponentially weighted moving average median chart with estimated process parameters is proposed. The charting statistic, optimal design, performance evaluation, and implementation of the proposed chart are discussed. The average of the average time to signal (AATS) criterion is adopted to evaluate the performance of the proposed chart. The estimated process parameter‐based VSI EWMA median (VSI EWMA median‐e) chart is compared with the estimated process parameter‐based Shewhart median (SH median‐e), EWMA median (EWMA median‐e), and variable sampling interval run sum median (VSI RS median‐e) charts, in terms of the AATS criterion, where the VSI EWMA median‐e chart is shown to be superior. When process parameters are estimated, the standard deviation of the average time to signal (SDATS) criterion is used to evaluate the AATS performance of the VSI EWMA median‐e chart. Based on the SDATS criterion, the minimum number of phase‐I samples required by the VSI EWMA median‐e chart so that its performance is close to the known process parameters VSI EWMA median chart is recommended.     

Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts

We investigate in this paper a new type of control chart called VSI EWMA‐RZ by integrating the variable sampling interval feature (VSI) with the exponentially weighted moving average (EWMA) scheme to monitor the ratio of two normal random variables. Because the distribution of the ratio is skewed, we suggest designing two separated one‐sided charts instead of one two‐sided chart. A new coefficient is introduced allowing us to be free to choose a sampling interval provided that it optimizes the performance of the control chart. We also make a direct comparison between the VSI EWMA‐RZ charts and standard EWMA‐RZ control charts. The numerical simulations show that the proposed charts outperform the standard EWMA charts in detecting process shifts. An application is illustrated for the implementation of the VSI EWMA‐RZ control charts in the food industry.     

EWMA control charts with variable sample sizes and variable sampling intervals

Traditional control charts for process monitoring are based on taking samples of fixed size from the process using a fixed sampling interval. Variable Sample Size (VSS) and Variable Sampling Interval (VSI) control charts vary the sampling rate from the process as a function of the data from the process. VSS and VSI control charts sample at a higher rate when there is evidence of a change in the process, and are thus able to detect process changes faster than traditional control charts. This paper considers general VSS and VSI control charts and develops integral equation and Markov chain methods for finding the statistical properties of these charts. EWMA charts with the VSS and/or the VSI features are studied in detail, and different ways of defining the EWMA control statistic are investigated. It is shown that using either the VSS or VSI feature in an EWMA control chart substantially improves the ability to detect all but very large shifts in the process mean. The VSI feature usually gives more improvement in detection ability than the VSS feature, and using both features together sometimes gives more improvement than using either one separately. Guidelines are given for choosing the possible sample sizes and the possible sampling intervals for these charts. EWMA charts with the VSS and/or VSI feature are compared to CUSUM charts and Shewhart X¯ charts with the VSS and/or VSI features.