Monitoring the ratio between two random normal variables plays an important role in many industrial manufacturing processes. In this paper, we suggest designing two one‐sided Shewhart control charts monitoring this ratio. The numerical results show that the one‐sided charts have more advantages compared with the two‐sided Shewhart chart proposed previously in the literature. Moreover, we investigate the effect of measurement error on the performance of these control charts where the measurement error is supposed to follow a linear covariate error model. The change of model parameters from an in‐control condition to an out‐of‐control is presented without using a strict assumption about the independence of the shift size from measurement errors. A valuable finding from this study is that taking multiple measurements per item is not an effective way to reduce the negative effect of measurement error on the Shewhart charts' performance.

中文翻译：

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测量误差对两个单侧Shewhart控制图的影响，用于监控两个正态变量的比率

监视两个随机正态变量之间的比率在许多工业制造过程中起着重要作用。在本文中，我们建议设计两个监控该比率的单面Shewhart控制图。数值结果表明，与文献中先前提出的双面Shewhart图相比，单面图更具优势。此外，我们调查了测量误差对这些控制图性能的影响，在这些控制图中，测量误差应遵循线性协变量误差模型。提出模型参数从控制中状态到失控状态的变化，而没有严格考虑移位大小与测量误差之间的独立性。