Reliability and Availability Analysis of Mechanical Systems Using Stochastic Petri Net Modeling Based on Decomposition Approach

Reliability and availability assessment of a complex system in a single model, considering binary states of individual components, using Markov technique is difficult due to state space explosion problem. Inclusion of various types of dependencies in the model further aggravates it. To overcome this, Stochastic Petri net (SPN) modeling based on decomposition is proposed for reliability and availability assessment of mechanical systems. The decomposition is based on three aspects of the system: Hierarchical level, basic structure and dependency. The model is demonstrated at three hierarchical levels. Individual component (level '3') SPN model is developed assuming Weibull failure distribution, while the individual subsystem (level '2') SPN model is developed considering the arrangement of components within the subsystem. The individual model at level '2' is reduced to an equivalent single net model and its equivalent transition rate is derived from its basic structure assuming the independence of components. This along with the dependencies (e.g. repair, standby redundancy) are included in the system model (level '1'). The repair distribution in this model is assumed exponential. Reachable markings are generated for the system model to obtain the reduced state space of Semi-Markov model for assessment of reliability and availability of the system. The steps of the proposed methodology are suggested and these are illustrated for a pumping system, with two pumps; one in standby.