费用约束条件下带有竞争风险的逐级删失模型的优化  

Planning progressive censoring life tests with competing risks under cost constraints

作　　者：杨明杰 杨春燕[1] YANG Ming-jie;YANG Chun-yan(School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650091

出　　处：《云南大学学报（自然科学版）》2020年第5期811-818,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11561072,11561075,11661081)。

摘　　要：对带有竞争风险的产品,研究了带有随机移走的定时截尾逐级删失寿命试验在费用约束条件下的优化设计.假定产品的失效是由多个独立的原因导致的,不同失效原因下,产品寿命服从不同参数的指数分布且相互独立,推导了似然函数和Fisher信息阵,建立了费用函数.对给定的试验预算,通过极小化Fisher信息阵的逆的行列式(D-optimality)得到了试验产品数、观测次数以及观测间隔的最优取值.并利用MonteCarlo方法进行了敏感性分析,考察了不同的寿命参数,移走概率以及费用系数的变化对最优解的影响.The optimal plans of life tests is investigated under cost constraints when the competing risks data are progressive Type I interval censored with binomial removals. It is assumed that the lifetimes of the individual causes are statistically independent and exponentially distributed with different parameters. The maximum likelihood and the Fisher information matrix are derived. A cost function is set up. For given restricted budgets, the number of test units, the number of inspection and the lengths of inspection intervals are determined to minimize the determinant of asymptotic variance of the estimated lifetime parameters(D-optimality). Furthermore, the sensitivity analysis is conducted through Monte-Carlo simulation to investigate the effects of different lifetime parameters, removal probabilities, as well as cost coefficients on the optimal plans.

关 键 词：竞争风险 指数分布 随机移走 逐级删失 费用约束 

分 类 号：O213.2[理学—概率论与数理统计]