This paper proposes a variable sampling interval $n{p}_x-\overline{X}$ control chart for monitoring the process mean using combined attribute‐variable inspection. An economic design of the proposed chart using Taguchi's quadratic loss function is presented. The proposed model minimizes the total expected cost per unit time while minimizing out‐of‐control average time‐to‐signal and maintaining reasonable in‐control average time‐to‐signal. The numerical results indicate that, compared with the corresponding fixed sampling interval control chart scheme, the proposed control chart yields better performance in terms of both shorter time to signal a process shift and less total expected cost per unit time. Sensitivity analyses of the cost model are also carried out by using a fractional factorial experimental design.

中文翻译：

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结合属性变量检验将二次损失函数法集成到VSI控制图的经济设计中

本文提出了一个可变的采样间隔 $ñp_X-\overline{X}$使用组合的属性-变量检查来监控过程平均值的控制图。提出了使用田口二次损失函数对建议图表进行经济设计的方法。所提出的模型使单位时间的总预期成本最小化，同时使失控平均信号时间最小化，并保持合理的失控平均信号时间。数值结果表明，与相应的固定采样间隔控制图方案相比，该建议的控制图在较短的信号发送过程偏移时间和较少的每单位时间总预期成本方面具有更好的性能。成本模型的敏感性分析也通过使用分数阶乘实验设计进行。