Reliability modeling of three-state systems with multiple types of components

In this paper, a system consisting of three states: perfect functioning, partial functioning, and down is considered. The system is assumed to be composed of several non-identical groups of binary components. The reliability of the system states under various assumptions on the component lifetimes is investigated. For this purpose, first, a new concept of bivariate survival signature (BSS) is introduced. Then, under the assumption that the component lifetimes of each type are exchangeable dependent, representations for the joint reliability function of the state lifetimes are obtained based on the notion of BSS. In the particular case, three-state systems composed of two types of different modules such as general-series (parallel) systems and systems with component-wise redundancy are investigated. Several examples are presented to illustrate the theoretical results.

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01