## ABSTRACT

Periodic testing is a method to ascertain the availability of Safety Instrumented Systems (SIS). These systems are generally passive and are activated only on demand. Testing is then required to diagnose their current state and to take the corresponding maintenance action. However, the testing procedure can provoke damage on some units of the SIS (especially the mechanical parts) and the system as a whole becomes more prone to failures. This situation is currently not well covered by standards under the so-called umbrella of imperfect testing. The decision maker must in practice come across to an optimization problem where the objective is to determine the optimal compromise between an accurate diagnostic of the current system state (high tests frequency) and the possible failures or degradation provoked by the testing procedure itself. The commonly used criteria to assess the performance of SIS are all related to the mean downtime of the SIS between two tests. The IEC 61508 provides subsequent analysis for multi-unit SIS when all the units are supposed to follow exponential lifetime distributions. It cannot be applied in this case as some parts of the system have a time varying failure rate which can increase after every test. We propose the use a of Markov process to model the degradation of the mechanical parts upon test and possible preventive maintenance after testing. Since the degradation due to tests is experienced at deterministic dates, we use the modelling framework of multiphase Markov processes to calculate the mean downtime. The paper is focused on explaining the optimization problem between the frequency of testing versus PFD_{avg} and find out the optimum frequency through simulations