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

• Autorzy: Girtler Jerzy

Identyfikatory

DOI

10.2478/pomr-2020-0035

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Gdańsk University of Technology, Faculty of Ocean Engineering & Ship Technology
• Czasopismo: Polish Maritime Research
• Rocznik: 2020
• Tom: nr 2
• Strony: 136--144
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Girtler Jerzy

• Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland

Bibliografia

• 1. Benjamin J. R., Cornell C. A.: Theory of probability, mathematical statistics, and decision theory for engineers (in Polish). WNT, Warsaw 1977.
• 2. Gercbach I. B., Kordonski CH.B.: Reliability models of technical objects (in Polish). WNT, Warsaw 1968.
• 3. Girtler J.: Physical aspect of application and usefulness of semi-Markovian processes for modeling the processes occurring in operational phase of technical objects. Polish Marit. Res. 2004 nr 3(41), vol. 11, pp. 25-30.
• 4. Girtler J.: Diagnostics as a condition for controlling the operation of marine internal combustion engines (in Polish). Studia No 28, WSM, Szczecin 1997.
• 5. Girtler J.: The semi-Markov model of energy state changes of the main marine internal combustion engine and method for evaluating its operation during ships voyage // Polish Maritime Research. - Vol. 18, nr 4, 2011, pp. 36-42.
• 6. Girtler J.: A method for evaluating theoretical and real operation of diesel engines in energy conversion formulation taking into account their operating indices // Polish Maritime Research. - Vol. 18, No. 3(70), 2011, pp. 31-36.
• 7. Girtler J.: Identification of damages of tribological associations in crankshaft and piston systems of two-stroke internal combustion engines used as main propulsion engines sea-going vessels and proposal of probabilistic description of loads as causes of these damages. Polish Maritime Research. Vol. 22, No (86), 2015, pp. 44 – 54.
• 8. Girtler J.: A concept of determining the relation between load and wear of tribological systems of ship main self-ignition engines by using probabilistic approach. Polish Maritime Research, Vol 25, No 4(100), pp. 129-137, 2018.
• 9. Girtler J.: Possibility of estimating the reliability of diesel engines by applying the theory of semi-Markov processes and making operational decisions by considering reliability of diagnosis on technical state of this sort of combustion engines. COMBUSTION ENGINES, No. 4/2015 (163), pp. 57-66.
• 10. Girtler J.: Application of semi-Markov processes for evaluation of diesel engines reliability with regards to diagnostics. Journal of Polish CIMAC, Vol. 11, No 1, pp.47-53, 2017,
• 11. Grabski F.: Theory of semi-Markov processes of technical object operation (in Polish). Zeszyty Naukowe AMW, no. 75 A, Gdynia 1982.
• 12. Grabski F.: Time of first transition of a semi-Markov process to the subset of states (in Polish). Zeszyty Naukowe AMW, Nr 3, Gdynia 1981.
• 13. Koroluk V.S., Turbin A.F: Polumarkovskije processy i ich priłożenija. Naukova Dumka, Kiev 1976.
• 14. Mine H., Osaki S.: Markovian decision processes. AEPCI, Nev York 1970.
• 15. Niewczas A.: Principles of the stochastic model of wear through friction in machine element durability issues (in Polish). Zeszyty Naukowe Politechniki Radomskiej, no 19, Radom 1989.
• 16. Piotrowski I., Witkowski K.: Operation of marine internal combustion engines (in Polish). AM, Gdynia 2002.
• 17. Rudnicki J.: Application issues of the semi-Markov reliability model. Polish Maritime Research. No 1(85)/2015, Vol. 22, pp. 55–64.
• 18. Rudnicki J.: Loads of ship main diesel engine in the aspect of practical assessment of its operation. Journal of POLISH CIMAC, Vol. 3, No 1, 2008.
• 19. Silvestrov D.S.: Polumarkovskije processy s diskretnym mnozestwom sostojanij.
• 20. Selected issues of material wear in sliding machine nodes (in Polish). Collective work edited by W. Zwierzycki. PWN, Warsaw-Poznan 1990.
• 21. Warsash Maritime Centre. The Learning Resource for Maine Engineers, Southampton Solent University, Southampton 2005.
• 22. Propulsion Trends in Tankers. MAN B&W Diesel A/S, Copenhagen 2002.
• 23. RTA Type Engines, Characteristics of Cylinder Liner and Piston Ring Wear. Service Information Bulletin No DUQ1- 02E, Diesel United Sulzer, 1991.
• 24. Girtler J, Grabski F.: Semi-Markov models of operating and technical state transitions of ship power plant machines and dangerous situations (in Polish). Interim report on the execution of the author’s research project no. 5T12C01122 financed by the State Committee for Scientific Research and entitled “Probabilistic methods for designing requiredreliability ship power plants, with special emphasis on technical diagnostics”. Prace badawcze no. 07/03/PB, Gdansk University of Technology, Faculty of Ocean Engineering and Ship Technology, Gdansk 2003.
• 25. Girtler J., Łosiewicz Z.: Analysis of properties of the diagnostic model of engine crankshaft-piston systems, adjusted to needs of rational control over the operation of these engines in the context of ship safety and protection of marine environment (in Polish). Interim report on the execution of the author’s research project No N N509 494638 financed by the Ministry of Science and Higher Education and entitled: “Decisionmaking control over the operation of crankshaft-piston systems of main propulsion engines on sea-going ships with application of technical diagnostics and taking into account safety and protection of the environment”. Prace badawcze no. 06//10/PB, Gdansk University of Technology, Faculty of Ocean Engineering and Ship Technology, Gdansk 2010.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).