The distribution of consumer lifetimes, high‐voltage of current in semiconductor transistors, and the risk associated with monitoring health care often come with a threshold. A two‐parameter (or shifted) exponential distribution is, in general, regarded as a better statistical model in such situations compared with a traditional (one‐parameter) exponential model. Research on inferential problems associated with two‐parameter exponential distributions, including monitoring schemes for the parameters of this model, is active. Currently, all existing monitoring schemes for origin and scale parameters of a shifted exponential distribution assume that the process parameters are known (Case‐K). The actual values of the process parameters are, however, rarely known in practice. The traditional method of estimating parameters from a set of a (Phase‐I) reference sample and plug them in for Phase‐II monitoring affects the performance of a monitoring scheme. Skewed processes, like the two‐parameter exponential process, exacerbate this problem. The present article shows that even a reference sample of size 50,000 cannot guarantee nominal in‐control performances of monitoring schemes when the actual process parameters are unknown (Case‐U). To address this problem, we develop monitoring schemes based on max and distance statistics for simultaneously monitoring the two parameters of a shifted exponential process in Case‐U. We show that the proposed schemes perform well. We illustrate the practical application of the proposed procedures by analyzing data about the production of an electronic component.

中文翻译：

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使用未知和估计的参数同时监视偏移指数过程的起源和规模

消费者寿命的分布，半导体晶体管中的高压电流以及与监视医疗保健相关的风险通常带有阈值。与传统的（一参数）指数模型相比，在这种情况下，通常认为两参数（或移位）指数分布是更好的统计模型。关于与两参数指数分布相关的推理问题的研究，包括对该模型参数的监控方案，正在积极开展。当前，所有现有的偏移指数分布的原始和比例参数监视方案都假定过程参数是已知的（Case-K）。然而，在实践中很少知道过程参数的实际值。从一组（阶段-I）参考样本估计参数并将其插入以进行阶段-II监视的传统方法会影响监视方案的性能。偏斜的过程（如两参数指数过程）加剧了这一问题。本文显示，即使实际过程参数未知（案例U），即使参考样本大小为50,000，也不能保证监视方案的名义控制性能。为解决此问题，我们开发了基于最大和距离统计信息的监视方案，以同时监视Case-U中移位指数过程的两个参数。我们证明了所提出的方案表现良好。我们通过分析有关电子零件生产的数据来说明所建议程序的实际应用。