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A Petri net-based design inference network (PNDN) architecture is presented in this paper. The network models the logical behaviour of any design artefact developed by designers at the conceptual design level by representing the subfunctions and their inter-relationships to perform a required overall function. The theoretical framework in developing the PNDN is based on the improved theory of Petri nets and hybrid automata. The theoretical PNDN architecture was implemented in a C++ based software called the design network simulator (DNS). The logical behaviour of a design artefact is modelled through the token flow within the PNDN. The token flow model is developed both for deterministic and nondeterministic PNDN, which involves uncertainties. In this paper we present the mathematical formalism of the deterministic token flow through the PNDN. We also provide a conceptual design example in order to explain the application of our theoretical architecture for structuring the PNDN.

Context: Software reliability prediction in the early stages of development can be propitious in many ways. The combinatorial models used to predict reliability using architectures such as fault trees, binary decision diagrams, etc. have limitations in modeling complex system behavior. On the other hand, state-based models such as Markov chains suffer from the state-space explosion problem, and they need transition probability among different system states to measure reliability. These probabilities are usually assumed or are obtained from the operational profile for which the system should be used in the field. Objective: The objective of this paper is to present a method for predicting the reliability of software in industrial systems using a generalized stochastic Petri nets based approach. The key idea is to violate the assumption of state transition probabilities in the Markov chain. The state transition probabilities are calculated using Petri net transitions' throughput by performing stationary analysis under the consideration to identify and handle dead markings in the Petri net. Method: Initially, a generalized stochastic Petri net of the system under consideration is generated from the standard system's specification. Thereafter, dead markings are identified in the Petri net which are further removed to perform steady-state analysis. At last, a Markov model is generated based on the reachability graph of the Petri net, which is further used to predict the system reliability. Results: The presented method has been applied to a safety-critical system, Shut Down System-1, of a nuclear power plant, which is operational in the Canada Deuterium Uranium reactor. The predicted reliability of the system using this method is 99.99966% which has been validated using the specified system requirements. To further validate and generalize the results, sensitivity analysis is performed by varying different system parameters. Conclusions: The method discussed in this paper presents a step of performing structural analysis on the Petri net of the system under consideration to identify and handle dead markings on the Petri net. It further handles the issue of assuming transition probabilities among the system states by calculating them using Petri net transitions' throughput.

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