考虑Taguchi损失函数时自适应指数加权平滑控制图的经济统计设计

Considering Taguchi loss function on economic-statistical design of adaptive exponentially weighted moving average control chart

为解决指数加权平滑(EWMA)控制图惯性问题而提出的自适应EWMA(adaptive EWMA,AEWMA)控制图的统计特性已经被广泛研究,但AEWMA控制图经济特性的研究却从未见有成果发表.针对该问题,在考虑Taguchi损失函数的基础上,给出了AEWMA控制图经济统计设计的模型.提出了一种在偏移区间上对AEWMA控制图进行优化设计的方法,用该方法优化设计的AEWMA控制图与针对固定偏移优化设计的EWMA控制图进行了比较.结果表明该方法设计的AEWMA控制图仍然保持其解决EWMA控制图惯性问题的特性,AEWMA控制图的经济特性同样优于EWMA控制图.分析了AEWMA控制图经济统计设计的参数灵敏度,总结了AEWMA控制图的参数变化与损失、平均链长以及最优参数组合之间的关系.

The statistical properties of adaptive exponentially weighted moving average（AEWMA） control chart,which is proposed to deal with the inertia problem of EWMA control chart,have been thoroughly investigated by many authors.However,the research results on economic properties of AEWMA control chart have never been reported in the publications.In this paper,an economic-statistical design model based on Taguchi loss function is proposed for AEWMA control chart.The optimal algorithm based on the range of shift is developed for economic-statistical design of AEWMA chart.The effectiveness of the optimal algorithm is validated by the comparison between AEWMA chart and EWMA chart.The comparison results show that the designed AEWMA chart is still able to deal with the inertia problem of EWMA chart,and the economic properties of AEWMA chart outperforms the EWMA chart.Finally,the sensitivity analysis of AEWMA chart is performed,and the relationship between parameter changes and cost,average run length and optimal decision variables of AEWMA chart are summarized respectively.