Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2024-03-17 DOI:10.1002/asmb.2854

Shanya Baghel, Shuvashree Mondal

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引用次数: 0

Abstract

Recently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal-Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one-shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence-based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald-type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi-criteria-based optimal design. Population-based heuristic algorithm nondominated sorting-based multiobjective Genetic algorithm is exploited to solve this optimization problem.

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间隔监测下依赖竞争风险模型的稳健估算和最佳检查间隔的确定

近来，人们对生命周期预后问题中的依赖竞争风险建模越来越感兴趣。在这项工作中，我们建议用 Marshal-Olkin 双变量指数分布来模拟依赖性竞争风险。可观测数据包括不同时间间隔内不同原因导致的故障次数。故障次数数据常见于单次设备等情况，在这些情况下，受试者的状态是在不同的检查时间而不是确切的故障时间进行检查的。通过一种基于发散的稳健估算方法，即有约束和无约束的最小密度功率发散估算（MDPDE），对存在竞争风险时的寿命分布点估算进行了研究。研究得出了调整参数的最佳值。假设检验基于 Wald 型检验统计量。得出了点估计和检验统计量的影响函数，反映了稳健性的程度。这项工作的另一个主要贡献是根据预定目标确定最佳检测时间。本文介绍了基于多标准的最优设计的确定方法。利用基于种群的启发式算法非支配排序多目标遗传算法来解决这个优化问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.