Algorithm for reliability analysis of phased-mission systems

The purpose of this paper is to describe an efficient Boolean algebraic algorithm that provides exact solution to the unreliability of a multi-phase mission system where the configurations are described through fault trees. The algorithm extends and improves the Boolean method originally proposed by Somani and Trivedi. By using the Boolean algebraic method, we provide an efficient modeling approach which avoids the state space explosion and the mapping problems that are encountered by the Markov chain approach. To calculate the exact solution of the phased-mission system with deterministic phase durations, we introduce the sum of disjoint phase products (SDPP) formula, which is a phased-extension of the sum of disjoint products (SDP) formula. Computationally, the algorithm is quite efficient because it calls an SDP generation algorithm in the early stage of the SDPP computation. In this way, the phase products generated in the early stage of the SDPP formula are guaranteed to be disjoint. Consequently, the number of the intermediate phase products is greatly reduced. In this paper, we also consider the transient analysis of the phased-mission system. Special care is needed to account for the possible latent failures at the mission phase change times. If there are more stringent success criteria just after a mission phase change time, an unreliability jump would occur at that time. Finally, the algorithm has been implemented in the software package SHARPE. With SHARPE, the complexities of the phased-mission system is made transparent to the potential users. The user can conveniently specify a phased-mission model at a high level (through fault trees) and analyze the system quantitatively.