Abstract
With the aim of solving the reliability modeling and calculation of multivariate stochastic degradation systems, two stochastic degradation models based on the bivariate Wiener process are proposed, in which two performance characteristics are composited to one variable. Two different failure modes including the defect-based failure and the duration-based failure are considered. The explicit expressions of the system reliability are derived in the cases that the performance characteristics are not composited or the performance characteristics are composited according to the linear combination of the degradation measurements. An algorithm based on the Monte Carlo simulation is proposed to simulate the degradation process, in which the performance characteristics are composited in arbitrary forms, and the correctness of the analytical results is also verified. Finally, some numerical examples are presented to illustrate the present reliability assessment method。
Highlights
董庆来1, 王伟伟1, 司书宾2 (1.延安大学 数学与计算机科学学院, 陕西 延安 716000; 2.西北工业大学 机电学院, 陕西 西安 710072)
Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes[ J]
Competitive failure analysis of a stochastic degradation system based on performance characteristics fusion
Summary
董庆来1, 王伟伟1, 司书宾2 (1.延安大学 数学与计算机科学学院, 陕西 延安 716000; 2.西北工业大学 机电学院, 陕西 西安 710072) 首先,假设持续时间失效阈值为常数。 注意到 Γ1 = min{ γ1,γ2} 以及 γi = inf{ t ≥ 0: Xi( t) ≥ Di1} , i = 1,2,通过对一个性能指标达到失 效阈值的时刻及另一个未达到失效阈值的性能指标 在该时刻的数值取条件,得到 函数 fτ(t) 和分布函数 Fτ(t) 的随机变量,并考虑以 下 2 种情形:一种情形是分布在[0, + ∞ ) 上的随机 述 2 个性能指标的退化过程,并假设它们是相互独 立的。 下面,利用算法 1 给出 2 个性能指标相关时采 用函数 H( x1,x2) =| x1 - x2 | 描述系统退化程度情形 下的系统可靠度曲线。 假设 τ = 0,L1 = 0.1,即只考 虑单阶段退化过程。 为了得到 2 个性能指标之间的 相关性对系统可靠度的影响, 分别令 ρ1 = - 0.8, - 0.5,0,0.5 和 0.8,将可靠度曲线画在同一个图中, 如图 5 所示。 其余参数取值与图 2 相同。 从图 5 可 以发现,在其余参数值相同的情形下, 相关系数 ρ1 的值越大,系统的可靠度越高。 因此,2 个性能指标 的退化过程是正相关(或负相关) 时,如果假设它们 彼此独立,则会低估(或高估) 系统可靠度。
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