Abstract

The repetitive sampling scheme is utilized in control charts to enhance their detection ability in process shifts. Their performance is usually evaluated under the assumption that the process parameters are known. In this article, we investigate the performance of the $\overline{X}$ and S² charts under repetitive sampling when the process parameters are estimated from a preliminary in-control (Phase I) sample. We also present the exact expressions of the average run-length (ARL), standard deviation of run-length (SDRL) and average sample number (ASN) measures. A numerical analysis demonstrates that the effect of parameters estimation is significant when the Phase I sample and the sample size are small.

摘要

控制图中采用重复抽样方案，以增强其在过程班次中的检测能力。它们的性能通常在工艺参数已知的假设下进行评估。在本文中，我们研究了$\overline{X}$和S ²图在重复抽样下，当过程参数从初步控制（阶段 I）样本中估计时。我们还提供了平均游程 ( ARL )、游程标准差 ( SDRL ) 和平均样本数 ( ASN ) 度量的精确表达式。数值分析表明，当第一阶段样本和样本量较小时，参数估计的效果显着。