期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 292, 期 3, 页码 1200-1208出版社
ELSEVIER
DOI: 10.1016/j.ejor.2020.11.036
关键词
Random effect; Cornish-fisher expansion; Generalized pivotal quantity; Confidence interval; Coverage probability
资金
- National Natural Science Foundation of China [11871431]
- Zhejiang Provincial Natural Science Foundation of China [LY18G010 003]
- First Class Discipline of Zhejiang - A (Zhejiang Gongshang University - Statistics)
- Key Project of Natural Science Foundation for Colleges and Universities of Anhui Province [KJ2019A0161]
- Pre-research Project of National Science Foundation of Anhui Ploytechnic University [Xjky08201903]
This paper introduces a generalized confidence interval method for the Gamma degradation model, evaluates its performance through Monte Carlo simulations, and illustrates it with two examples. The results show that the proposed approach outperforms traditional Wald CIs and bootstrap-p CIs in terms of coverage probabilities.
This paper focuses on investigating the Gamma degradation model with random effects. A generalized p-value procedure is proposed to test whether there exist some heterogeneities among the degradation processes of different units. Using the Cornish-Fisher expansion, an approximate confidence interval (CI) is obtained for the shape parameter. The generalized confidence intervals (GCIs) are derived for model parameters and commonly used reliability metrics (e.g., the quantile, the reliability function of the lifetime) based on the generalized pivotal quantity method. Those inference procedures are also extended to the accelerated degradation case. The performances of the proposed GCIs are assessed by Monte Carlo simulations. In the simulation, we compared our methods with the Wald CIs and bootstrap-p CIs under moderate and large sample sizes. It is found that the performance of the GCI procedures is better than the Wald CIs and bootstrap-p CIs in terms of coverage probabilities. Finally, the proposed procedures are illustrated by two examples. (C) 2020 Elsevier B.V. All rights reserved.
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