Abstract
ABSTRACT The article presents possible application of the theory of semi-Markov processes in creating the eight-state model of the process of appearance of the propulsion systems ability and inability states on sea-going vessels performing transportation tasks in a relatively long operating time t (t → ∞). The model has been proved to be able to be successfully used for determining the reliability of the abovementioned systems. The probability of faultless operation in time t was assumed the measure of system reliability. Operating situations of sea-going vessels were characterised, with special attention being paid to the fact that the loads of propulsion system components of these vessels are of random nature. These loads lead to damages which for this reason were also considered random events. It was also assumed that the damages provoke the appearance of states of inability of particular ship propulsion system components which means that these states are random events as well. The states of ability of a given ship propulsion system have been assumed to exist when all components of this system are in the state of ability. In case when at least one component is in the state of inability, the entire system is in the state of inability. Conditions were formulated for the reliability model of an arbitrary system to be able to be worked out in the form of the semi-Markov process. The need for the use of technical diagnostics in reliability examination of sea-going ship propulsion systems was indicated. In conclusions, certain qualities of the article were highlighted which are, in author’s opinion, of highest importance in reliability examination of sea-going ship propulsion systems.
Highlights
Sea-going ships perform transportation tasks in remarkably different weather and sea conditions, which generally depend on: wind force and direction, sea undulation level, speed and direction of sea currents, level of underwater hull section overgrowing with algae and crustaceans, ship over-icing, and type of the water region in which the ship sails while performing the transportation task [9, 10, 19]
The semi-Markov model of changes of the technical state of an arbitrary propulsion system provides opportunities for determining its reliability taking into account both preventive services oriented on protecting against damages, and those forced by the damages
The use of the semi-Markov process, instead of the Markov process, as the model of reliability state changes of propulsion systems working on sea-going ships in a given time results from the fact that we have to expect that the random variable T(ij) which represents the time interval when the system is in state si given that the state is sj, and the random variable Ti which is the time interval when the system is in state si(i = 0, 1, 2, ..., 7) independently on what the state is, have arbitrary concentrated distributions in set R+ = [0, +∞)
Summary
Sea-going ships perform transportation tasks in remarkably different weather and sea conditions, which generally depend on: wind force and direction, sea undulation level (height, length and direction of waves), speed and direction of sea currents, level of underwater hull section overgrowing with algae and crustaceans, ship over-icing, and type of the water region in which the ship sails while performing the transportation task [9, 10, 19]. If it can be loaded only within a limited range, for instance along an external main engine characteristic hnom = idem or ht = idem (Fig. 3), and, simultaneously, with the power much smaller than Nen or Net, we have to assume that the propulsion system is in the state of inability This conclusion results from the fact that when the system is loaded within a limited range, for instance along the line segment A-D of the controller characteristic (Fig. 3), the generated thrust force T (Fig. 2) and its component TN (being the driving force) are not large enough to balance, in storm conditions, the force Rx which is the total hull resistance at ship’s speed v. This model is necessary for determining the reliability of the analysed propulsion systems
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