There exist many processes where the quality characteristic does not follow a normal distribution, and the conditions for the application of central limit theorem are not satisfied; for example, because collecting data in a subgroup is impossible or the distribution is highly skewed. Thus, researchers have developed the control charts according to the specific distribution that models the quality characteristic. In this paper, some control charts are designed to monitor an exponentially distributed lifetime. The life testing is conducted according to the failure censoring while during the test; once observing a failure item, it is replaced by a new one so that the total number of items inspected during the test remains constant. Under the condition of the test, it is discussed that the elapsed time until observing the r’th failure has Erlang distribution. According to the relation of Erlang and chi-square distributions, the chart limits are computed to satisfy a specified value of type I error. Examples are presented and the curves of average run length are derived for the one-sided and two-sided control charts. Also, a comparative study is conducted to show the performance and superiority of the proposed control charts.

中文翻译：

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设计失效删失可靠性试验下的可变控制图和替换

存在许多质量特性不服从正态分布，不满足中心极限定理应用条件的过程；例如，因为不可能在子组中收集数据或分布高度偏斜。因此，研究人员根据对质量特征建模的特定分布开发了控制图。在本文中，设计了一些控制图来监控指数分布的寿命。寿命试验按试验过程中的失效截尾进行；一旦观察到一个不合格项目，它就会被一个新项目取代，以便在测试期间检查的项目总数保持不变。在测试条件下，讨论了观察到第 r 次故障之前经过的时间具有 Erlang 分布。根据 Erlang 和卡方分布的关系，计算图表限制以满足 I 类错误的指定值。给出了示例，并推导出了单侧和双侧控制图的平均运行长度曲线。此外，还进行了比较研究，以显示所提出的控制图的性能和优越性。