Exact Run Length Evaluation on a Two-Sided Modified ExponentiallyWeighted Moving Average Chart for Monitoring

A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

In practice,the control charts for monitoring of process mean are based on the normality assumption.But the performance of the control charts is seriously affected if the process of quality characteristics departs from normality.For such situations,we have modified the already existing control charts such as Shewhart control chart,exponentially weighted moving average(EWMA)control chart and hybrid exponentially weighted moving average(HEWMA)control chart by assuming that the distribution of underlying process follows Power function distribution(PFD).By considering the situation that the parameters of PFD are unknown,we estimate them by using three classical estimation methods,i.e.,percentile estimator(P.E),maximum likelihood estimator(MLE)and modified maximum likelihood estimator(MMLE).We construct Shewhart,EWMA and HEWMA control charts based on P.E,MLE and MMLE.We have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.

Memory-Type Control Charts Through the Lens of Cost Parameters

A memory-type control chart utilizes previous information for chart construction.An example of a memory-type chart is an exponentially-weighted moving average(EWMA)control chart.The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts.Meanwhile,the EWMA median chart is robust against outliers.In light of this,the economic model of the EWMA and EWMA median control charts are commonly considered.This study aims to investigate the effect of cost parameters on the out-of-control average run lengthðARL_(1)Þin implementing EWMA and EWMA median control charts.The economic model was used to compute the ARL_(1) parameter.The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis.When the input parameters change based on a predetermined percentage,the ARL_(1) is affected.According to the results of the EWMA chart,nine input parameters had an effect andfive input parameters had no effect on the ARL_(1) parameter.Further,only seven of the 14 input parameters had an effect on the ARL_(1) of the EWMA median chart.However,the effect of each input parameter on the ARL_(1) was different.Moreover,the ARL_(1) for the EWMA median chart was smaller than the EWMA chart.This analysis is crucial to observe and determine the input parameters that have a significant impact on the ARL_(1) of the EMWA and EWMA median control charts.Hence,practitioners can obtain an overview of the influence of the input parameters on the ARL_(1) when implementing the EWMA and EWMA median control charts.

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

ON EVALUATING THE RUN LENGTH PROPERTIES OF CHARTS WITH ESTIMATED CONTROL LIMITS

X charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the X charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.

STATISTICAL PROPERTIES OF WAVE GROUPS DESCRIBED BY GROUP-INDUCED LONG WAVES

A new method using group-induced second-order long waves (GSLW) to describe wave groups is presented in this paper on the basis of the GSLW theory by Longuet- Higgins and Steward (1964) . In the method , the parabolic relationship between GSLW and the wave envelope is first deduced , and then the distribution function of GSLW amplitude is derived . Thus, the formulae in terms of the moments of GSLW and short wave spectra for the average time duration and the mean length of runs of wave heights exceeding a certain level can be derived . A new groupiness factor equivalent to half the mean wave number in wave groups is defined by taking into account the widths of spectra of GSLW and short waves . Compared with theoretical results of others , ours are closer to measured wave data .

REPRESENTATION OF STATISTICAL PROPERTIES OF WAVE GROUPS FOR SEA PROCESSES WITH DOUBLE-PEAKED SPECTRA

A method using group-induced second-order long waves(GSLW) to represent statistical properties of wave groups with double-peaked spectra is put forward in this paper on the basis of the GSLW theory. The GSLW is regarded as a weighted linear superimposition of the second-order long Wave induced by the low peak frequency section and that induced by the high peak frequency section. There is a parabolic relationship between the GSLW and the wave envelope. Then the probability density function and the distribution function of the GSLW amplitude are derived. Thus the formulas for the average time duration and the mean length of runs can be derived. Good agreement between theoretical results and measured values was achieved. as verified with the measured double-peaked spectra in different regions.

Control charts for the Pareto distribution

The Pareto distribution plays an important role in various areas of research. In this paper, the average run length （ARL） unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARLo, which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.

Comparison of Rectangular and Elliptical Control Region EWMA Schemes for Joint Quality Monitoring

The exponential weighted moving average technique used in process mean and variance monitoring charts was combined by Gan in 1997 and proposed two combined joint monitoring schemes one with rectangular control region and the other with elliptical control region. Performance of these two schemes may very depend on the shifts in mean or variance to be detected quickly. In this paper, performances of these two schemes are evaluated with respect to the average run length properties. The results reveal that elliptical scheme is little faster in detecting the shifts in process mean and increase in variance within a limit.

On-line Recognition of Abnormal Patterns in Bivariate Autocorrelated Process Using Random Forest

It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time.Meanwhile,the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics.This goes against the statistical I.I.D assumption in using the multivariate control charts,which may lead to the performance of multivariate control charts collapse soon.Meanwhile,the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation,and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities.This study proposed a pattern recognition model using Random Forest(RF)as pattern model to detect and identify the abnormalities in bivariate autocorrelated process.The simulation experiment results demonstrate that the model is superior on recognition accuracy(RA)(97.96%)to back propagation neural networks(BPNN)(95.69%),probability neural networks(PNN)(94.31%),and support vector machine(SVM)(97.16%).When experimenting with simulated dynamic process data flow,the model also achieved better average running length(ARL)and standard deviation of ARL(SRL)than those of the four comparative approaches in most cases of mean shift magnitude.Therefore,we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process.Although bivariate autocorrelated process is focused in this study,the proposed model can be extended to multivariate autocorrelated process control.

非参数自适应EWMA SR控制图及其变采样间隔设计

本文基于Wilcoxon符号秩(Signed Rank, SR)检验统计量,提出了一种非参数自适应指数加权移动平均(Adaptive Exponentially Weighted Moving Average, AEWMA)控制图。所提出的AEWMA SR控制图结合了非参数统计量的稳健受控性能以及自适应控制图良好的整体偏移检测特性。同时,为了提高固定采样间隔下的非参数AEWMA SR静态控制图对异常偏移的检测效率,本文进一步研究了可变采样间隔(Variable Sampling Intervals, VSI)下的非参数AEWMA SR动态控制图设计问题。使用了Markov链方法计算控制图的精确平均运行链长(Average Run Length, ARL)和平均报警时间(Average Time to Signal, ATS)等性能指标。通过仿真分析比较了VSI AEWMA SR控制图、FSI AEWMA SR控制图和VSI EWMA SR控制图的统计性能。结果表明,所提出的VSI AEWMA SR控制图能兼顾对于不同大小偏移的敏感性,且变采样间隔的动态策略能显著提高控制图的检测效率。

基于正态变换的变样本容量Shewhart比例控制图设计

为了提高Shewhart型比例控制图的监控效率,将其与变样本容量策略结合,提出一种新的比例控制图(VSS Shewhart-RZ*控制图)来监控二元正态变量之比。基于正态变换方法设计了新的比例统计量Z*,以消除样本容量变化对比例控制图设计及使用的不利影响。采用马尔科夫链方法计算了该控制图的平均运行长度和平均样本容量,给出该控制图的参数优化算法。通过仿真分析研究了该控制图的统计性能,并与Shewhart比例控制图进行比较,结果表明VSS Shewhart-RZ*控制图的性能明显优于传统固定样本容量Shewhart比例控制图。

楔形劲性复合桩水平承载特性的影响因素研究

为了分析楔形劲性复合桩的水平承载特性,以及不同桩身尺寸参数对其水平承载力的影响,采用数值模拟的方式建立三维有限元分析模型,对比分析楔角、平均截面含芯率和芯长比对楔形劲性复合桩水平承载特性的影响。结果表明,在线弹性阶段,同体积下1°楔角楔形劲性复合桩的水平承载力明显高于普通劲性复合桩,增大楔角能够有效减少桩身位移;增大楔角对水平承载能力的提升最大,平均截面含芯率次之,芯长比的影响最小。

自相关过程协方差阵的残差MEWMA控制图

本文研究多变量自相关过程协方差矩阵的质量监控问题.针对服从VAR(1)模型的多变量自相关过程,基于残差分析思想,将多变量指数加权移动平均(MEWMA)控制图用于对过程的监控.首先对残差MEWMA控制图统计量进行了推导,其次采用MonteCarlo仿真的方法,以平均运行链长为评价准则对残差MEWMA控制图的监控效果进行了分析.仿真结果表明,残差MEWMA控制图具有较好的监控效果.

直接成纤法芳纶－Ⅱ短纤维形态和性能的研究

利用聚对苯二甲酰对苯二胺（芳纶－Ⅱ树脂）的聚合物凝胶，在聚合的环境下就地直接成纤的方法制备了芳纶－Ⅱ短纤维。研究了在直接成纤法中，芳纶－Ⅱ树脂的对数比浓粘度（η＿（ｉｎｂ））与所制备的短纤维的长度和长径比之间的关系；建立了用短纤维一环氧树脂复合材料的性能表征短纤维性能的方法。在此基础上进一步研究了短纤维的长度和长径比对其性能的影响．结果表明，利用直接成纤法，由η＿（ｉｎｈ）≥３．５ｄＬ／ｇ的聚合物凝胶可以制备性能较好、适用于复合材料应用的芳纶－Ⅱ短纤维。

单边合格品链长t控制图设计

针对过程方差估计不精确的问题,采用t统计量代替传统统计量,提出一种单边合格品链长t控制图来监控过程均值偏移。采用马尔科夫链方法构建了该控制图的状态转移矩阵,并推导出其平均运行链长指标。在保证过程处于受控状态的统计性能基础上优化失控状态下的平均运行链长指标,从而获得控制图的最优决策变量和最优性能指标。仿真结果表明,SCRL&t控制图的性能明显优于传统合格品链长t控制图,当过程均值偏移较小时优势更加明显。

基于游程分析轮廓提取算法的改进

指出Capson游程分析轮廓提取算法存在的两点不足:一是所提取轮廓在水平方向凹形部分存在偏差;二是未考虑合并情况会导致提取复杂图案轮廓时出现部分轮廓丢失现象.通过增加分叉点和交汇点以及建立两种未考虑合并情况对应的规则,分别对这两点不足进行改进.实验表明,改进后的算法能精确提取任意复杂图案的全部内外轮廓,在提取高游程平均压缩率图像轮廓时耗时较少.该算法能实现流水线式并行轮廓提取,减少线阵扫描相机应用中等待数据获取的时间,提高在线检测速度,且成功应用于高精度PCB线路板缺陷检测系统,实现高分辨PCB图像轮廓快速准确提取.

带警戒限的均值控制图中平均链长的计算公式

带警戒限的均值控制图中 ,平均链长ARL(AverageRunLength)是其重要特性。本文利用转移概率流图TPFG(TransitionProbabilityFlowGraphs)

一种串行/并行两用的区域标记算法

通过设计一种游程与目标体间接关联的数据结构实现游程标记冲突的实时解决,提出一种基于游程的顺序扫描式区域标记算法,只需一次扫描分析即可获取游程区域表达,复杂度低,编码实现方便,易于扩展应用于并行计算系统中进行并行标记。实验结果表明,该算法与已有算法相比,拥有更高效的串行标记性能,在进行并行标记时具有近似线性的加速比。