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LIMITING DISTRIBUTION OF THE THREE-STATE SEMI-MARKOV MODEL OF TECHNICAL STATE TRANSITIONS OF SHIP POWER PLANT MACHINES AND ITS APPLICABILITY IN OPERATIONAL DECISION-MAKING

Abstract

The article presents the three-state semi-Markov model of the process {W(t): t > 0} of state transitions of a ship power plant machine, with the following interpretation of these states: s1 – state of full serviceability, s2 – state of partial serviceability, and s3 – state of unserviceability. These states are precisely defined for the ship main engine (ME). A hypothesis is proposed which explains the possibility of application of this model to examine models of real state transitions of ship power plant machines. Empirical data concerning ME were used for calculating limiting probabilities for the process {W(t): t > 0}. The applicability of these probabilities in decision making with the assistance of the Bayesian statistical theory is demonstrated. The probabilities were calculated using a procedure included in the computational software MATHEMATICA, taking into consideration the fact that the random variables representing state transition times of the process {W(t): t > 0} have gamma distributions. The usefulness of the Bayesian statistical theory in operational decision-making concerning ship power plants is shown using a decision dendrite which maps ME states and consequences of particular decisions, thus making it possible to choose between the following two decisions: d1 – first perform a relevant preventive service of the engine to restore its state and then perform the commissioned task within the time limit determined by the customer, and d2 – omit the preventive service and start performing the commissioned task.

Keywords:

decision, probability, ship power plant machine, semi-Markov process, ship internal combustion engine

Details

Issue
Vol. 27 No. 2(106) (2020)
Section
Latest Articles
Published
17-07-2020
DOI:
https://doi.org/10.2478/pomr-2020-0035
Licencja:
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Open Access License

This journal provides immediate open access to its content under the Creative Commons BY 4.0 license. Authors who publish with this journal retain all copyrights and agree to the terms of the CC BY 4.0 license.

 

Authors

Jerzy Girtler

Gdansk University of Technology

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