ABSTRACT
In Fig. 1 the Reliability Block Diagram (RBD) of a small exemplary network is presented; e1 and e6
1 INTRODUCTION
The current paper is a continuation of Malinowski (2013), where a series-parallel-reducible system characterized by its capacity defined as a function of component capacities was considered. Its subject is a flow network via which a commodity (water, gas, electric power, etc.) is delivered from inflow to outflow points. The paper can be classified as a contribution to the field of reliability of flow networks regarded as multi-state repairable systems. Multi-state systems with binary or multistate components have been studied with increasing interest during the recent decades. A broad overview of multi-state reliability models and methods used for their analysis, along with the comprehensive survey of relevant literature can be found in Lisnianski et al. (2010) and Lisnianski & Levitin (2003). Methods of computing failure/ repair frequencies, intensities, and availabilities of multi-state systems are investigated in Chang et al. (2004), Druault-Vicard & Tanguy (2006), and Korczak (2007). As far as series-parallel flow networks are concerned, the literature on this subject is rather scarce, however some interesting results, related to the topic of this paper, can be found in Klinz & Woeginger (2004) and Krumke & Zeck (2013).
