Modeling Functional Architectures Using Markov Chains

Systems Engineering has evolved interdisciplinary, collaborative approaches to product and process development to manage the development of increasingly complex systems. Architecture definition is a key part of the Systems Engineering process. This research focuses on the functional architectures used to describe the decomposition, definition, and allocation of system functions and behavior. Existing state-based modeling of system behavior readily captures subsystem inputs and outputs, making Discrete Time Markov Chain analysis straightforward. However, this is not yet the case for functional modeling and analysis which describes a top-down decomposition of system functional and performance requirements, the logical sequencing of functions, the relative timing and duration of functions, and the inputs and outputs that trigger the execution of functions.Thus, a new method is needed to further leverage the information captured during functional architecting that relates to functional flow, timing, and data & message exchanges. Using a simplified avionics example, this new method is demonstrated and results in the creation of experiment data tables summarizing the execution of the functional chain under various input conditions. Markov chain analysis is then used to analyze the resulting sequence of functional states and transition probabilities. This aids system architects in analyzing system behavior to influence system design, testing, and operation even with increasing system complexity.