Nonparametric simultaneous tolerance intervals - Roy,Gian Louisse A. (University of the Philippines, 2023)
ABSTRACT Tolerance interval play a relevant role in many medical and industrial applications. The ability to contain a specified proportion of sampled population values with high degree of confidence makes its computation meaningful. Whenever there are several populations, it may be of interest to perform simultaneous inference. For this reason, this study propose methods to construct accurate simultaneous tolerance intervals. Since in most cases of practical applications, distributional assumptions fail to hold, we derive these methods in the nonparametric setting. The proposed procedures and algorithms are then assessed by examining performance metrics such as estimated coverage probabilities and expected volumes. As a way of benchmarking, we also compare the proposed to the usual Bonferroni correction approach. Proposed methods are also illustrated through applications that utilize real-life datasets, particularly on setting reference limits in the field of laboratory medicine. The proposed methods show accurate results, with coverage probabilities close to the nominal level. Simultaneous tolerance intervals computed using our proposed methods are generally better than the ones obtained through a Bonferroni-corrected approach. For further studies, we suggest a potential approach to incorporate the effects of fixed covariates in the calculation of regression-based intervals. Moreover, for cases where improvement of the coverage probabilities is desired, a solution involving bootstrap calibration is recommended.