Abstract

In this paper, a new variable parameters chart for the process mean with a statistic that integrates information from the study and auxiliary variables is proposed. The proposed variable parameters chart with auxiliary information (AI) (abbreviated as VP-AI) is optimally designed to minimize the out-of-control steady-state (i) average time to signal (ATS₁) and (ii) expected average time to signal (EATS₁) values when the mean shift sizes are known and unknown, respectively. The Markov chain approach is adopted to derive the formulae of the performance measures ATS₁, standard deviation of the time to signal (SDTS₁) and EATS₁. The VP-AI chart significantly outperforms the standard VP chart; thus, justifying the incorporation of auxiliary information to enhance the ability of the VP chart. The VP-AI chart is also compared with the Shewhart AI, synthetic AI, exponentially weighted moving average (EWMA) AI, run sum AI and variable sample size and sampling interval (VSSI) AI charts. The VP-AI chart significantly outperforms the Shewhart AI, synthetic AI and VSSI AI charts for all levels of shifts. Meanwhile, the VP-AI chart outperforms the EWMA AI and run sum AI charts for most shifts. The VP-AI chart is found to be more robust than the EWMA-AI chart when the correlation coefficient is misspecified or the bivariate normality assumption is violated as long as the size of the shift is moderate or large. A real application which monitors spring elasticity is used to illustrate the VP-AI chart’s implementation.

摘要

在本文中，提出了一种新的过程均值变量参数图表，该图表具有整合研究和辅助变量信息的统计量。建议的带有辅助信息 (AI)（缩写为 VP-AI）的可变参数图表经过优化设计，以最大限度地减少失控稳态 (i) 平均发出信号时间 (ATS ₁ ) 和 (ii) 预期平均时间分别在平均偏移大小已知和未知时发出 (EATS ₁ ) 值。马尔科夫链方法被采用来导出的性能措施式ATS ₁，的时间到信号标准偏差（SDTS ₁）和EATS ₁. VP-AI 图明显优于标准 VP 图；因此，证明结合辅助信息以增强 VP 图的能力是合理的。VP-AI 图还与 Shewhart AI、合成 AI、指数加权移动平均 (EWMA) AI、运行总和 AI 以及可变样本大小和采样间隔 (VSSI) AI 图表进行了比较。VP-AI 图表在所有级别的班次中都明显优于 Shewhart AI、合成 AI 和 VSSI AI 图表。同时，VP-AI 图表优于 EWMA AI 和大多数班次的运行总和 AI 图表。当相关系数被错误指定或违反双变量正态性假设时，只要偏移的大小适中或很大，VP-AI 图就会比 EWMA-AI 图更稳健。