Universal and individual two‐sided tolerance intervals that take the inherent structure of normal mixture distributions into account are introduced in this paper for the purpose of monitoring the overall population and specific subpopulations. On the basis of generalised fiducial inference, a Markov chain Monte Carlo sampler is proposed to generate realisations from the generalised fiducial distributions of unknown parameters for obtaining the required tolerance intervals. Based on the simulation results, it is shown that the proposed method can maintain the empirical coverage rates sufficiently close to the nominal level. In addition, a lake acidity monitoring study is used to illustrate the proposed method.

中文翻译：

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正常混合物分布的大约两侧公差间隔

本文介绍了考虑正常混合物分布的固有结构的通用和单个两侧公差区间，目的是监视总体种群和特定亚群。在广义基准推断的基础上，提出了一个马尔可夫链蒙特卡洛采样器，从未知参数的广义基准分布中生成实现，以获得所需的公差区间。根据仿真结果表明，该方法可以保持经验覆盖率足够接近标称水平。此外，湖水酸度监测研究用于说明该方法。