可修系统的双变量剩余寿命模型及应用--基于出租车维修数据的研究

Residual life is defined as the length of time that a system will continue work until failure, given that this system has been working for a period of time. The concept of residual life has important theoretical and application value in reliability analysis. The project will systematically study the bivariate residual lives indexed by age and usage for repairable systems under imperfect repairs and with different maintenances. Firstly, for a single repairable system with only corrective maintenance, we will use two-dimensional stochastic point process to model the number of failures under imperfect repairs so as to obtain the form of the bivariate residual lives by either deduction or simulation. Secondly, for a single repairable system with both corrective and preventive maintenances, we will adopt competing risk model to deduce the expression of residual lives. Based on these two parts, a random effect will be introduced to describe different usage intensities of multi-systems so that the bivariate residual lives for multiple repairable systems could be developed. Finally, a set of real data will be used for model fitting and application. The theoretical value of this project is to enable people to study the failure and usage of systems from two dimensions, and to provide theoretical basis for extended product warranty for taxi. From application perspective, the real case could help people to receive a straightforward understanding of the theory.

剩余寿命，指的是在某系统已经工作一段时间的条件下，该系统继续工作直至故障的时间；这个概念在可靠性分析中具有重要的理论和应用价值。本项目将系统研究可修系统在不完全维修程度以及不同维修方式下以时间和使用程度为指标的双变量剩余寿命。首先，对于单个仅在故障时进行纠正性维修的可修系统，利用二维随机点过程通过对不完全维修下的故障次数进行建模从而推导或仿真获得双变量剩余寿命模型。其次，对于单个既有纠正性维修又有预防性维修的可修系统，同样在不完全维修下，利用竞争风险模型推导获得双变量剩余寿命。在这两者的基础上，引入随机效应来描述多个系统的不同使用强度，从而建立多个可修系统的双变量剩余寿命模型。最后项目利用实际数据对理论模型进行拟合应用。本项目的理论价值在于能够从两个维度来了解系统的故障及使用情况，同时能够为出租车的延长质保计划提供理论基础；在应用上，所给出的实际案例能够提供一个直观的理解。

本项目致力于在双变量剩余寿命的可靠性模型研究方面取得理论上的突破。通过本项目的实施，我们建立了不同的可靠性模型描述故障过程，讨论了参数的估计方法，也对剩余寿命的性质和计算进行了探讨。具体地，我们建立了一个随机过程来描述可修系统的故障发生过程，在此模型中，可修系统具有两种故障模式，一种是由于错误使用引起的故障，一种是正常使用下的故障，且两者相互影响；我们同时考虑使用二维分布，Marshall-Olkin 双变量Weibull模型作为竞争风险模型对相互影响的故障或失效模式进行建模，并提出更加优良的估计方法；我们还使用Weibull回归模型描述不同因素对系统寿命的影响，提出在不完全数据之下的参数估计修正方法；同时，我们还探讨了k-out-of-n系统剩余寿命分位点的性质；此外，我们也从退化分析的角度进行了研究，提出了带logistic分布测量误差的退化模型并计算了相应的剩余寿命。有关成果发表了4篇SCI文章，Reliability Engineering & System Safety, 2018, 171: 87-98; Communications in Statistics – Theory and Methods, 2018, 47; Journal of Statistical Computation and Simulation，2017, 87：2349-2371; Probability in the Engineering and Informational Sciences，2015, 29, 291-308；并还有2篇文章在审稿中。综上，我们完成了本项目的研究工作，并在开展课题过程中有新的发现和进展。