参数估计对检测简单线性曲线控制图的性能影响分析

The Performance of Control Chart for Monitoring Simple Linear Profiles When Parameters Are Estimated

关于简单线性曲线的在线监测方法多数假定受控参数是已知的,或者假定有足够多的历史样本来估计未知参数。Mahmoud[1]分析了参数估计对三种监测简单线性曲线方法的影响,但其部分模拟结果有一定差错。本文主要目的是研究参数估计对Zhang等[2]提出的基于似然比检验的监测简单线性曲线控制图的性能影响,并对Mahmoud[1]中的模拟方法进行纠正,同时对四种方法进行比较。模拟结果表明,若使用参数已知时的控制限,而历史样本数据较少时,控制图的性能会受到严重影响。

Most methods for on line monitoring simple linear profiles are based on the assumption that the in control parameters are known or can be estimated from a historical sample.The performance of three existing control charts for monitoring simple linear profiles with estimated parameters are reported by Mahmoud[1],but a part of simulation results are not correct.The main objective of this paper is to evaluate the effect of parameter estimation on the control chart proposed by Zhang et al.[2]based on likelihood ratio test,and we correct the simulation results of Mahmoud[1].The comparison between four methods is given.The simulation results show that the performance of the control charts significantly deteriorates if the estimated parameters are used with control limits intended for known parameters,especially when only a few PhaseⅠsamples are used to estimate the parameters.