Modelling framework for performance analysis of SIS subject to degradation due to proof tests

Abstract

Safety Instrumented Systems (SIS) assure safety of equipment/process by performing the safety functions in demand situations. In low-demand mode of operation, final elements of SIS mostly remain idle and safety performance is measured by probability of failure on demand on average (PFDavg). In this mode, SIS are not continuously monitored but subjected to periodic tests (namely proof tests) to ascertain availability for demand situations. Sometimes, proof tests don’t reveal all undetected dangerous failures and may even deteriorate mechanical components by introducing additional stress. To model such degradation phenomena, we propose a framework (based on multiphase Markov process) by adding discrete degraded states between the working and the failed states. The impact of tests is modelled by increasing the transition rates between degraded states. The amplitude increase depends on the current system state at testing time. Then, analytical formulas are developed for the evaluation of the time-dependent PFD under various maintenance policies. Later, a case study on Down hole safety valves (DHSV) is presented to find an optimum test frequency. The optimization problem arises due to the following trade-off: high frequency testing will ensure high availability of DHSV for demand situation, but the stress generated will accelerate degradation to resultant failure.