Computer-Assisted Markov Failure Modeling of Process Control Systems

Process control systems (PCS) are systems with control loops and continuous state dynamic variables such as pressure, temperature, and liquid level. Existing computer-assisted failure modeling schemes for PCS are based on a static description of system operation (eg, by digraphs, signal-flow-based graphs). This paper presents a dynamic approach to the failure modeling of PCS. The givens for the methodology are: 1) a set of first order differential equations with feedback describing the interaction between system variables, 2) failure and repair rates for the control units constituting the PCS. The methodology is based on the discrete state space-discrete time representation of PCS dynamics. Probabilistic system behavior is simulated by a Markov chain. An algorithm is developed for the mechanized construction of the transition matrix. Input preparation for the algorithm is illustrated by examples. Useful features of the methodology are: 1) failure model accuracy can be verified or improved by a change in the input data for mechanized model construction, 2) effect of changes in system parameters on PCS failure characteristics can be quantified. These features are demonstrated on a simple level-control system. The limitations of the methodology are discussed.