More on evaluating the probability of failure on demand and probability of false operation of monitoring and control systems of NPP power generating units

Abstract

Aim. This paper aims to build a methodology for identifying the probability of failure on demand of a monitoring and control system of a high operational risk facility. The method is based on Markov chains. The initial assumptions for the model are the possibility of explicit (detectable) and hidden (undetectable) failures in the control and safety system. As it is known [1], in case of a manifested system failure, remedial measures are taken. In the course of a recovery operation, the controlled facility is disabled, therefore, during this period no operation demand may occur. In the event of a hidden failure of a control system, the system may receive operation signal that will be missed. The constructed model may produce a non-stationary and stationary solution. In the non-stationary case, the obtained system of Kolmogorov differential equations is solved numerically, while in the stationary case, an analytical solution of the resulting system of algebraic equations is found. In addition, the paper examines the effect of the model parameters on the final estimated characteristics.  Methods. Markov models are used for describing the examined technical system. The final probabilities were obtained using a developed system of Kolmogorov equations. A stationary solution was obtained for the system of Kolmogorov equations. Classical methods of the probability theory and mathematical dependability theory were used. A numerical solution to the system of differential equations was found using a 4th order Runge-Kutta method.  Conclusions. The obtained stationary solutions conservatively estimate the probability of failure on demand and the probability of false operation.