The reliability and availability of the systems

Malfunction of the ballast water treatment systems on board ships is a criterion that has never been reported or included in any research, but could prove to be the most important factor in ballast water treatment system performance. Performance reliability of certain ballast water treatment systems on board ships have indicators which should be observed, followed and analysed over a longer period of system exploitation. Reliability is the ability of the system for operational work without interruption (Pham 2000). Predictions of potential failures caused by software or hardware errors, as well as potential failures in mechanical part performance, can only be predicted once findings from the experience in handling technologically-similar systems on board ships are found. External factors on ships are one of the most important factors, because the dynamics of movements are constantly under external influences. Likewise, operator reliability and exposure to high temperatures are also very important in assessing the reliability of the proposed system (Siewiorek and Swarz 1982).

The reliability of these types of devices can be shown as an exponential function of the time interval if the time interval is considered to be the useful lifespan of the device. For electronic systems such as sophisticated devices for the on-board ballast water treatment of ships, the failure density function has a form of an exponential distribution, so the failure frequency function is the same by definition (Turban et al. 2003):

In the Eq. (6), we can see that the failure frequency function has a constant value (λ). As such, the equation for the reliability function R(t) (exponential law of reliability) has the form of:

The computing subsystem of some of the ballast water treatment systems on board ships can be found in three states: proper function, procedural failure and non-procedural failure (Shooman 2002). Computing subsystem reliability depends on the probability of proper function and failures in a specified time. The probability of a computing subsystem of certain ballast water treatment systems on board ships going from a state of proper function to a state of non-procedural failure is:

where P_i.o probability of non-procedural state, P_c probability of proper functioning state, μ frequency of repairs, F redundancy failure detection ratio, Δt time lag/time interval, λ malfunction index.

The Malfunction index is the relation between malfunctioning components and operational components:

where P_c is the number of components which remained operational after a specified time, and P_f is the number of components which malfunctioned after the specified time of functioning.

Redundancy is a characteristic of the quality of the computing system that ensures failure avoidance when one part of the system fails. This is generally ensured through the use of additional software, through the reliability of the two redundant systems working in parallel and with a known malfunction index for these types of devices in predefined ship conditions.

It can be assumed that the computing part of the subsystem in the system with two parallel subsystems, one of which is redundant, will be regularly maintained by the operator and through the self-diagnosis function for error removal. In this way, the possibility of malfunction of some ballast water treatment systems on board ships is reduced.