Hollander M, Peña E A
Department of Statistics, Florida State University, Tallahassee 32306, USA.
Lifetime Data Anal. 1995;1(4):377-401. doi: 10.1007/BF00985451.
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.
对可靠性系统的随机建模的动态方法进行了进一步探索。这种建模方法特别适用于负载共享、软件可靠性和多变量失效时间模型，其中组件的失效特性受其使用程度、负载量或所经历应力程度的影响。该方法纳入了这样一种直观概念：当一个连贯系统中的一组组件在某一时刻失效时，会从一个结构函数“跳跃”到另一个结构函数，后者支配其余正常运行组件的剩余寿命，并且由于组件寿命本质上受它们所构成的结构函数影响，那么在这样的失效时刻，其余组件寿命的随机结构也应有一个跳跃。对于这种动态建模的系统，研究了其跳跃时间的随机特性。这些跳跃时间的特性使我们能够获得系统寿命的特性。特别是，对于马尔可夫动态模型，针对一般连贯系统、并联系统和串并联系统，获得了跳跃时间精确分布函数的具体表达式。我们推导了一个新的分布函数族，它描述了动态建模系统跳跃时间的分布。
