A study on some system safety with geometric process repairs

Abstract

A 3-state Markov model is used to model some safety-critical systems, when the system states can be divided into three kinds of categories: Operating States, Failed-Safe States & Failed-Unsafe States. These models are used to estimate the system safety and security. Based on these models, a new model is built when the system fails, different defect states have different measures. For Failed-Safe States, the repair process is adopted and for the other failed states is not. The repeatedly repairs have some influences on the operating times, repair times and the coverage to different failed states. Geometric Process is employed to describe this repair process and get some indexes of the system safety.Operational State at time t Probability that the system is in the Failed-Safe State at time t Probability that the system is in the Failed-Unsafe State Probability vector for the Markov model at time t Transition rate matrix of the Markov process Safety function at time J: