比例失效率模型以及脆弱模型的随机比较与年龄性质

Stochastic comparisons and ageing properties in proportional hazard rate model or frailty model

失效率在年龄性质及生存分析研究中是特别重要的指标之一,基于现实生活中应用的需要,以失效率及脆弱变量为线索,依次应运而生的比例失效率模型及脆弱模型被广泛应用到可靠性理论特别是年龄性质,生存分析及风险分析的实践研究中.关于比例失效率模型及脆弱模型的研究近年来受到国内外学者的普遍关注,并取得一系列丰硕的成果.应用随机序,首先讨论比例失效率模型的年龄性质及其在随机序下的封闭性,然后研究脆弱模型在基变量不同时的随机比较及年龄性质,认为比例失效率模型在年龄性质及随机序下是封闭的.

The hazard rate function plays an important role in ageing properties and survivor analysis.Based on practical applications,the hazard rate function and frailty random variable as clues,the proportional hazard rate model and the frailty model are successively emerged.Those models are widely used in reliability theory especially in ageing properties,survival analysis and risk analysis.In recent years,domestic and foreign scholars paid more attention to those models,and obtained a series of achievements.In this work,the ageing properties and the preservation about stochastic order in proportional hazard rate model are firstly studied.Then aging properties and stochastic comparison under different baseline random variables of frailty model are investigated.The results show that ageing properties and stochastic orders are preserved under proportional hazard rate model.