Reliability of fault tolerant control system with Markovian parameters

Fault tolerant control system with Markovian parameters (FTCSMP), as a model of active fault tolerant control system (AFTCS), was used to analyze the system stability in several papers. However, little research was on the reliability of FTCSMP. FTCSMP model was used to evaluate the reliability of redundant sensors monitored by fault detection and isolation (FDI). In this model, two homogeneous Markov stochastic processes with different state spaces were defined: One represented system components failures and the other represented the decisions of the FDI process. Based on Markov theory, the reliability and safety of the sensor/FDI unit were studied. When system fault process and FDI process of FTCSMP were both birth and death process, fault detection delay was divided into two kinds; effective and ineffective. The influence of both kinds of delay to the unit reliability and safety was analyzed. A numerical example of dual redundant inertial navigation system was given to show the usefulness of the proposed theoretical results.