ARMA型过程能力指数的统计推断方法研究

The Study on Statistical Inference Method for ARMA Type Process Capability Index

过程能力指数主要是用来评判一个生产过程是否充分。在传统上,计算过程能力指数要求数据来自独立同分布的样本,但随着互联网和物联网兴起,现代数据的收集、分析、推断与决策方法逐渐体现出时序性的特点。工业自动化的产品生产过程的自相关性往往会影响对过程能力的评价。由于作为评价过程能力的指数是一个基于样本观测值的统计量(点估计),需要对其进行统计推断(区间估计),这在传统的过程能力评价中没有引起足够的重视,当过程自相关时,更需要对其进行统计检验。在以往的研究中,只针对特定的自相关模型给出评价。本文给出了基于ARMA模型的过程能力指数自适应计算方法,并构建了其置信区间。理论和模拟及实证分析均表明所提的方法比传统的方法能更准确的评价过程的实际生产能力。

Process capability index refers to the level of process capability satisfied with the product quality standard requirements(specification range,etc.).The calculation of traditional process capability index requires data from independent and identically distribution,but with the rise of the Internet and the Internet of Things,the methods of collection,analysis,inference and decision-making for modern data gradually involve the characteristics of time series.The autocorrelation of producing process of the product in industrial automation often affects the evaluation of process capability.As the index of process capability evaluation is a statistic(point estimation)based on sample observations,it needs to be statistically inferred(interval estimation),which has not been paid enough attention in traditional process capability evaluation.When the process data exhibit autocorrelation,it needs to be statistically tested.In previous studies,evaluations were made only for specific auto-correlated models.In this paper,an adaptive calculation method of process capability index based on ARMA model is presented,and its confidence interval is also constructed.Theoretical,simulative and empirical analysis show that the proposed method can more accurately evaluate the actual production capacity of the process than the traditional method.