Design of control charts with m‐of‐m runs rules
Design of control charts with m‐of‐m runs rules
复制标题
具有 m-of-m 运行规则的控制图设计
DOI：
10.1002/qre.1023
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发表时间：
2009
影响因子：
2.3
通讯作者：
M. Cho
中科院分区：
文献类型：
--
作者：
T. Lim;M. Cho
本文研究了补充了m-of-m游程规则的X线图的经济统计性质。图表的失控条件是一个点超过控制限或连续m个点超过警告限。采样过程由具有2 m个状态的马尔可夫链建模。马尔可夫链的每个状态的稳态概率和每个状态的平均游程长度（ARL）以显式公式导出。然后推导出平稳平均游程长度（SALR），从而建立一个经济统计模型。使用该模型，通过最小化的成本函数的平均信号时间（ATS）的约束，优化设计参数。在SARL和成本函数方面，将补充了m-of-m运行规则的X射线图与Shewhart X射线图进行了比较。还分析了设计参数对代价函数的敏感性。根据这些观察结果，给出了使用m-of-m运行规则执行X射线图的一般指导原则。应该强调的是，即使样本量有限，补充运行规则也可能提供可行且有效的解决方案，而ShewhartX射线图可能不会。版权所有© 2009约翰威利父子有限公司。
This paper investigates economic–statistical properties of the X̄ charts supplemented with m‐of‐m runs rules. An out‐of‐control condition for the chart is either a point beyond a control limit or a run of m‐of‐m successive points beyond a warning limit. The sampling process is modeled by a Markov chain with 2m states. The steady‐state probability for each state and the average run length (ARL) from each state of the Markov chain are derived in explicit formulas. Then the stationary average run length (SALR) is derived so as to develop an economic–statistical model. Using this model, the design parameters are optimized by minimizing the cost function with constraints on the average time to signal (ATS). The X̄ chart supplemented with m‐of‐m runs rules is compared with the Shewhart X̄ chart in terms of the SARL and the cost function. Sensitivity of the design parameters with respect to the cost function is also analyzed. General guidelines for implementing the X̄ chart with m‐of‐m runs rules are presented from those observations. It should be emphasized that supplementing run rules may provide feasible and efficient solutions even if the sample size is limited, while the Shewhart X̄ chart may not. Copyright © 2009 John Wiley & Sons, Ltd.