In this paper, we propose control charts for monitoring the Birnbaum‐Saunders (BS) median parameter (scale parameter) on the basis of three estimators. Comparison of the control charts in terms of average run length using probability control limits and those based on asymptotic distribution of three estimators for the median parameter is developed. We also present guidelines for practitioners about the minimum sample size needed to match out‐of‐control average run length with the asymptotic control limits in function of the median parameter after an extensive simulation study. Numerical example illustrates the applied monitoring of BS median parameter.

中文翻译：

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控制图，用于监控Birnbaum-Saunders分布的中值参数

在本文中，我们基于三个估计量，提出了用于监控Birnbaum-Saunders（BS）中值参数（比例参数）的控制图。建立了使用概率控制极限的控制图与平均游程长度的比较，以及基于三个估计量的中值参数的渐近分布的控制图的比较。在广泛的模拟研究之后，我们还为从业人员提供了指导准则，以指导将失控平均运行长度与中值参数函数的渐近控制极限相匹配所需的最小样本量。数值例子说明了对BS中值参数的应用监控。