剩余寿命和休止时间在可靠性理论、可靠性工程以及应用概率领域中都有广泛的应用。在独立同分布元件构成的协同系统中，协同系统寿命可靠性函数的基于signature的混合表达结构已经被证实在研究协同系统的年龄性质以及对不同协同系统进行随机比较时是非常有效的，本项目中，我们考虑将该方法延伸到更一般情形。当构成协同系统的元件为独立不同分布或具有某种相依关系时，本项目主要研究如何利用如上基于signature 的混合表达方法来寻找协同系统剩余寿命、休止时间、条件剩余寿命和条件休止时间的分布结构，以及如何进一步在两个具有不同结构或不同元件寿命分布的协同系统之间建立相关的随机比较关系？本课题的研究对了解协同系统结构和元件间的相依关系对协同系统剩余寿命和休止时间的影响有重要意义。

Both residual life and inactivity time have widely application in theory of reliability, reliability engineering and the field of applied probability. In coherent system with independent and identical components, signature-based representation of the reliability function of system's life has been proved to be very useful in studying the ageing characteristics of coherent system and in comparing the performance of different coherent systems. In this project, we consider extending this method to a more general case. When the components of coherent system are independent but not identical or under some specified form of dependence, this project mainly study how to apply the above signature-based representation to finding the distribution sturctures of residual life, inactivity time, conditional residal life and conditional inactivity time of coherent system , and how to further establish the related stochastic comparisons between two coherent systems with different structures or different component lifes? Research of this subject will be benefit for understanding the influence of system's structure and components' dependence to residual life and inactivity time of coherent system.