Performance evaluation of fault tolerant control systems using Markov and semi-Markov models

Most reconfigurable control designs are based on the availability of valid information concerning failure. However, since perturbations from various sources in or outside the control system can affect the fault diagnosis results, the information obtained by the fault detection and identification (FDI) subsystem is rarely perfect. The objective of this study is to develop a quantitative measure to evaluate the reliability and performance of fault tolerant control systems (FTCS), which include FDI and redundancy management (RM) techniques, without the availability of perfect FDI information.; The occurrence of the component failures and FDI and RM decisions of a FTCS is a random process. The FTCS behavior due to component failures and FDI/RM processes can be modeled as a Markov or semi-Markov chain. To each state of this chain, it is further assumed that an incremental performance value can be assigned. The probability distribution of the performance accumulated over a mission is then used to indicate the system performance. The probability distribution of the cumulative performance is evaluated by performance transform method.; Relative to previous literature, this study: (1) Extends the concept of the performance transform method to semi-Markov models. (2) Analyzes the decision process of combined sequential probability ratio tests (SPRT) by using Monte Carlo simulations. (3) Reduces the convolution sums for the semi-Markov chains to more practical recursive forms when holding time mass functions are of the appropriate form. A simple FTCS example is presented to illustrate the above methods.