Minimizing costs while meeting safety requirements: Modeling deterministic (imperfect) staggered tests using standard Markov models for SIL calculations

In industry, potentially hazardous (technical) structures are equipped with safety systems in order to protect people, the environment, and assets from the consequences of accidents by reducing the probability of incidents occurring. Not only companies but also society will want to know what the effect of these safety measures is: society in terms of “likelihood of undesired events” and companies in addition in terms of “value for money,” the expected benefits per dollar or euro invested that these systems provide. As a compromise between demands from society (the safer the better) and industry (but against what cost), in many countries government has decided to impose standards to industry with respect to safety requirements. These standards use the average probability of failure on demand as the main performance indicator for these systems, and require, for the societal reason given before, that this probability remain below a certain value depending on a given risk. The main factor commonly used in industry to “fine-tune” the average probability of failure on demand for a given system configuration in order to comply with these standards against financial risk for the company is “optimizing” the test strategy (interval, coverage, and procedure). In industry, meeting the criterion on the average probability of failure on demand is often demonstrated by using well accepted mathematical models such as Markov models from literature and adapting them for the actual situation. This paper shows the implications and potential pitfalls when using this commonly used practical approach for a situation where the test strategy is changed. Adapting an existing Markov model can lead to unexpected results, and this paper will demonstrate that a different model has to be developed. In addition, the authors propose an approach that can be applied in industry without suffering from the problems mentioned above.