With the rapid advances of computer-based technology in missioncritical domains such as aerospace, military, and power industries, critical systems exhibit more complex, dependent, and dynamic behaviours. Such dynamic system behaviours cannot be fully captured by existing reliability modelling tools. In this paper, we introduce a new reliability modelling tool, called dynamic reliability block diagrams (DRBD), to model dynamic relationships between system components. Due to the complexity of DRBD models that involve dynamic conceptual modelling constructs, such as a state dependency (SDEP) block, design errors, which are subtle and difficult to detect, can be easily introduced during the modelling process. To formally verify and validate the correctness of a DRBD model, we propose a Petri net based approach by converting DRBD constructs into coloured Petri nets (CPN). We use a case study to illustrate how to convert a DRBD model into CPN, and how to use an existing Petri net tool to analyse and verify dynamic system behavioural properties. Our case study and experimental results show that DRBD models are a powerful tool for system reliability modelling, and our proposed verification approach can effectively ensure the correct design of DRBD models for complex and large-scale computer-based systems. Key Words Reliability modelling, dynamic reliability block diagram (DRBD), coloured Petri net (CPN), formal verification, model checking 1.

With the rapid advances of computer-based technology in mission-critical domains such as aerospace, military, and power industries, critical systems exhibit more complex, dependent, and dynamic behaviors. Such dynamic system behaviors cannot be fully captured by existing reliability modelling tools. In this paper, we introduce a new reliability modelling tool, called dynamic reliability block diagrams (DRBD), to model dynamic relationships between system components. Due to the complexity of DRBD models that involve dynamic conceptual modelling constructs, such as a state dependency (SDEP) block, design errors, which are subtle and difficult to detect, can be easily introduced during the modelling process. In order to formally verify and validate the correctness of a DRBD model, we propose a Petri net based approach by converting DRBD constructs into colored Petri nets (CPN). We use a case study to illustrate how to convert a DRBD model into colored Petri nets, and how to use an existing Petri net tool to analyze

Abstract—Computer system reliability is conventionally modeled and analyzed using techniques such as fault tree analysis (FTA) and reliability block diagrams (RBD), which provide static representations of system reliability properties. A recent extension to RBD, called dynamic reliability block diagrams (DRBD), defines a framework for modeling dynamic reliability behavior of computer-based systems. However, analyzing a DRBD model in order to locate and identify design errors, such as a deadlock error or faulty state, is not trivial when done manually. A feasible approach to verifying it is to develop its formal model, and then analyze it using programmatic methods. In this paper, we first define a reliability markup language (RML) that can be used to formally describe DRBD models. Then we present an algorithm that automatically converts a DRBD model into a colored Petri net (CPN). We use a case study to illustrate the effectiveness of our approach and demonstrate how system properties of a DRBD model can be verified using an existing Petri net tool. Our formal modeling approach is compositional, thus it provides a potential solution to automated verification of DRBD models. Index Terms—System reliability, reliability block diagram (RBD), extensible markup language (XML), colored Petri net (CPN), time Petri net, formal modeling and analysis, automated verification, deadlock detection. API BNF