摘要
针对样本数据不足及依赖专家信度评估系统可靠性的问题,文章基于概率论和不确定理论,建立了离散时间下随机不确定多状态系统的可靠性数学模型.假设系统在各状态的逗留时间独立且服从参数为不确定变量的几何分布,系统仅在相邻状态发生转移,利用离散Markov过程方法给出了具有M+1个状态的系统在状态i及以上的可靠度函数、平均寿命及平均剩余寿命的解析表达式.最后,给出了四状态汽轮机发电系统的数值算例,并与参数为常数的多状态系统模型进行了比较分析,得到系统的可靠性指标均对参数为不确定变量的情况具有一定的敏感性.
In order to solve the problem of insufficient sample data and relying on the expert experience to analyze the reliability of the system,in this paper,a random uncertain multi-state system reliability model in discrete time is established based on probability theory and uncertainty theory.The sojourn time of the system in each state are assumed to be independent distributed with geometric distributions which distribution parameters are uncertain variables,and the system only transfers in adjacent states.Using the discrete Markov process method,some formulas are given to calculate the reliability function,mean time to failure and mean residual life of system with M+ 1 states in state i or above.Finally,a numerical example of a four state steam turbine power generation system is given and compared with crisp value model.It is concluded that the reliability indexes of the system are sensitive to uncertain parameters.
作者
张婷婷
胡林敏
王桂荣
ZHANG Tingting;HU Linmin;WANG Guirong(School of Science,Yanshan University,Qinhuangdao 066004)
出处
《系统科学与数学》
CSCD
北大核心
2021年第7期2006-2017,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(72071175)
河北省自然科学基金(A2018203088)资助课题
关键词
不确定理论
离散时间
多状态系统
可靠性指标
Uncertainty theory
discrete time
multi-state system
reliability indexes
