Evaluation of safety and reliability parameters of supervision and control systems

Abstract

The aim of this article is the analytical evaluation of dependability and reliability indicators of vital facility supervision and control systems. Such indicators include: probability of no-failure, collective failure rate, wrong-side and right-side failure rate, average service life. The article considers systems with different redundancy rates (2-oo-2, 2-oo-3, 2-oo-2-by-2) ensuring recovery of failed equipment (channels) without interruption of operation. The paper covers such safety and reliability mechanisms as interchannel data comparison, mutual channel blocking and protection against negative failure development by mutual channel blocking. Methods . For the purpose of achieving the set goal, the article suggests a mathematical functional model based on absorbing homogenous Markovian continuous-time chains. The states of this chain reflect the number of good channels of the system, while state transition rates are identified based on the equipment failure rates of each channel and repair rates (subject to the mechanisms of interchannel data comparison and failed channel blocking). The absence of protection can be caused by such events as non-detection of failure by supervision facilities, disability of blocking mechanisms, protection tripping delay. In such case the failure of a channel (channels) causes the failure of the whole system and forces the Markovian chain into the absorbing state. The probabilities of transition into the absorbing state are divided into the probabilities of transition into state of right-side failure and state of wrong-side failure. As a failure occurrence in a situation of absent guaranteed protection against its possible negative consequences in a system that continues operating may cause undue inputs to the system’s executive mechanisms and on the assumption of the worst case scenario we deem such failure to be a wrong-side one. The used methods allow finding the probabilities of each state of the chain by solving a system of Kolmogorov-Chapman differential equations. Based on the given probabilities, the collective failure rate and average service life are identified along with the right-side and wrong-side failure rates. In order to ensure the usability of the presented methods, the authors provide approximate formulas of failure rates and approximation errors. Results . A mathematical model of operation of a multichannel microprocessor system has been developed. Formulas for calculation of system state probabilities, average service life, wrong-side and right-side failure rates have been obtained that allow evaluating the safety and fault tolerance of various systems with hot standby and in-operation operability recovery capabilities. The given formulas for calculation of system state probabilities allow increasing the number of safety and reliability indicators, if needed. The article presents the feasibility of simplified calculation of failure rates. Conclusions. The formulas given in the article can be used for evaluation of reliability, safety and longevity indicators of microprocessor-based supervision and control circuits of vital facilities (ship-borne technical facilities, trackside equipment in railway stations and open lines, fixed power facilities, etc.). In the development process they allow finding the rational system organization by means of comparative evaluation of performance of structures with various degrees of redundancy. In the context of system adaptation for application in various facilities as well as its modernization the formulas in question enable analytical calculation of the above indicators.