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.

Error Detection and Pattern Prediction Through Phase II Process Monitoring

The continuous monitoring of the machine is beneficial in improving its process reliability through reflected power function distribution.It is substantial for identifying and removing errors at the early stages of production that ultimately benefit the firms in cost-saving and quality improvement.The current study introduces control charts that help the manufacturing concerns to keep the production process in control.It presents an exponentially weighted moving average and extended exponentially weighted moving average and then compared their performance.The percentiles estimator and the modified maximum likelihood estimator are used to constructing the control charts.The findings suggest that an extended exponentially weighted moving average control chart based on the percentiles estimator performs better than exponentially weightedmoving average control charts based on the percentiles estimator and modified maximum likelihood estimator.Further,these results will help the firms in the early detection of errors that enhance the process reliability of the telecommunications and financing industry.

考虑风电不确定性的交直流配电网低碳分布鲁棒优化调度

为增加配电网风电的消纳能力,减少碳排放,建立了一种交直流配电网低碳分布鲁棒优化调度模型。分析风电预测误差和预测出力历史数据之间的正相关性,采用混合Copula函数,建立它们之间的联合概率分布,得到风电预测误差的条件概率分布。将交直流配电网解耦为交流和直流子网,以各自综合运行成本最小为优化目标,在交流子网优化模型中引入碳交易机制,建立交直流配电网分散协调优化模型。以得到的风电预测误差的条件概率分布为参考,构建了基于K-L散度的分布鲁棒模糊集。利用拉格朗日对偶理论,将优化模型转化为单层优化目标模型,并利用交替方向乘子法进行分散协调优化求解。基于修改后33节点交直流配电网模型的仿真结果表明所提模型能有效减少配电网侧碳排放量,显著提高风电消纳能力。