A dynamic approach to the stochastic modelling of reliability systems is further explored. This modelling approach is particularly appropriate for load-sharing, software reliability, and multivariate failure-time models, where component failure characteristics are affected by their degree of use, amount of load, or extent of stresses experienced. This approach incorporates the intuitive notion that when a set of components in a coherent system fail at a certain time, there is a 'jump' from one structure function to another which governs the residual lifetimes of the remaining functioning components, and since the component lifetimes are intrinsically affected by the structure function which they constitute, then at such a failure time there should also be a jump in the stochastic structure of the lifetimes of the remaining components. For such dynamically-modelled systems, the stochastic characteristics of their jump times are studied. These properties of the jump times allow us to obtain the properties of the lifetime of the system. In particular, for a Markov dynamic model, specific expressions for the exact distribution function of the jump times are obtained for a general coherent system, a parallel system, and a series-parallel system. We derive a new family of distribution functions which describes the distributions of the jump times for a dynamically-modelled system.

译文

进一步探索了可靠性系统随机建模的动态方法。这种建模方法特别适用于负载分担,软件可靠性和多变量故障时间模型,其中组件故障特征受其使用程度,负载量或所经历的应力程度的影响。这种方法结合了一个直观的概念,即当相干系统中的一组组件在某个时间发生故障时,从一个结构函数到另一个结构函数的 “跳跃”,这控制了其余功能组件的剩余寿命,并且由于组件寿命受到它们构成的结构函数的内在影响,然后,在这样的故障时间,其余组件的寿命的随机结构也应该发生跳跃。对于此类动态建模系统,研究了其跳跃时间的随机特征。跳跃时间的这些属性使我们能够获得系统寿命的属性。特别是,对于马尔可夫动态模型,对于一般相干系统,并行系统和串并联系统,可以获得跳跃时间的精确分布函数的特定表达式。我们推导了一个新的分布函数族,该函数描述了动态建模系统的跳跃时间分布。

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