二阶自相关过程Shewhart 型控制图的性能评价

针对二阶自相关过程,分别采用有限马氏链内嵌法和积分法给出了Shewhart型修正控制图和残差控制图平均运行链长的计算方法,并通过其数值结果的比较分析,得到结论:当自相关过程系数均为正值时,修正图的性能较好;当过程系数均取负值时,残差图较为适用;当过程系数符号相异时,两图性能可采用所给方法具体比较.该结论为控制图的选择和应用提供了理论依据.

Performance evaluation of Shewhart type charts for AR(2) process

Limited Markov chain embedded method and integration method are given to calculate the respective average run
length of modified Shewhart chart and Shewhart residual chart for 2-order autoregressive process. Performance of both charts
with different parameters are discussed and compared by numerical results. Some conclusions show that, modified chart is
more applicable when both parameters are positive, residual chart is more applicable when both parameters are negative,
otherwise both charts need to be compared through the proposed method. The conclusion provides academic basis to choose
and apply control charts.