Quantitative risk assessment required for safety calculations plays an important role in decision making at design, development, installation., deployment, and maintenance of systems. To mitigate against catastrophic accidents in chemical plants, a variety of protective systems, such as Safety Instrumented Systems, are implemented on processing units operating under hazardous conditions. The availability of protective systems is therefore highly critical and is dependent not only on its structural properties but also on the associated maintenance strategies. A number of models have been developed but many have been based on modelling very few protective devices, usually placed in series, and on basic configurations.
In reality, such protective systems have many redundant devices operating in parallel and requiring so many to work for the system to work, for example 2-out-of-3 pumps to manage the excess leakage of a given fluid. More often than not, a protective system does not consist of a single Unit, but several Units placed in a variety of configurations which are optimised in such a way to guaranty maximum availability. Such configurations are best represented with a corresponding fault tree which can readily include majority voting gates. There are many other complications, which make the calculations particularly complex, and which therefore require a new methodology.
For example, the unavailability of the protective system should be quantified by considering the Probability of Failure on Demand (PFD) not only for low but also for high demand rates. Additionally, the safety provided by the protective system must take into account several other factors, including differing repair rates of components, along with various periodic proof test intervals (including staggered ones which are common in many safety systems). Another complication is how to model a failed redundant component having been revealed or otherwise during a test or a demand and whether that component is repaired immediately or at the beginning of the next available opportunity. If such a repair is carried, an estimate of the risk involved in repairing the system online or offline would be critical to know. Finally, in complex protective systems consisting of many components and with the view to maximising the availability of the protective system, the availability of more than one repair crew would be another important factor to consider in the calculations.
The aim of this research is to use advanced Markov Models to solve all the above complications in complex installations, and compute the probability of failure on demand as accurately as possible. Advanced mathematical modelling and numerical analyses methods would be required to carry out the calculations, which would need to be verified using Monte Carlo simulation methods.