Reliability and maintainability characteristics in semi-Markov models

• Autorzy: Grabski F.
• Języki publikacji: EN

Abstrakty

EN

The characteristics of semi-Markov process we can translate on the reliability characteristics in the semi-Markov reliability model. The cumulative distribution functions of the first passage time from the given states to subset of states, expected values and second moments corresponding to them which are considered in this paper allow to define reliability function of the system. The equations for many reliability characteristics and parameters are here presented.

Słowa kluczowe

EN

semi-Markov model; reliability characteristics

• Wydawca: Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Journal of Polish Safety and Reliability Association
• Rocznik: 2016
• Tom: Vol. 7, No. 1
• Strony: 79--86
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Grabski F.

• Naval University, Gdynia, Poland

Bibliografia

• [1] Barlow, RE. & Proshan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinchart and Winston, Inc.
• [2] Cinlar, E. (1969). Markov renewal theory. Adv. Appl. Probab 2, 1, 123-187.
• [3] Feller, W. (1964). On semi-Markov processes. Proc. Nat. Acad. Sci. USA. 51, 4, 653-659.
• [4] Grabski, F. (1982). Theory of Semi-Markov Operation Processes. ZN AMW, Gdynia. 75A. (in Polish).
• [5] Grabski, F. (2002). Semi-Markov models of reliability and operation. IBS PAN. Warsaw. (in Polish).
• [6] Grabski, F. (2014). Semi-Markov Processes: Applications in Systems Reliability and Maintenance. Elsevier; Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Sydney.
• [7] Korolyuk, VS. & Turbin, A. F. (1976). SemiMarkov processes and their applications. Naukova Dumka, Kiev. (in Russian).
• [8] Korolyuk, V. S. & Turbin A. F. (1982). Markov Renewal Processes in Problems of Systems Reliability. Naukova Dumka, Kiev. (in Russian).
• [9] Lev′y, P. (1954). Proceesus semi-markoviens. Proc. Int. Cong. Math. Amsterdam, 416-426.
• [10] Limnios, N. & Oprisan, G. (2001). Semi-Markov Processes and Reliability. Birkhauser, Boston.
• [11] Pyke, R. (1961). Markov renewal processes: definitions and preliminary properties. Ann. of Math. Statist. 32, 1231-1242.
• [12] Pyke, R. (1961). Markov renewal processes with finitely many states. Ann. of Math. Statist. 32, 1243-1259.
• [13] Pyke, R. & Schaufele, R. (1964). Limit theorems for Markov renewal processes. Ann. of Math. Statist 32, 1746-1764.
• [14] Silvestrov, DC. (1980). Semi-Markov processes with a discrete state space. Sovetskoe Radio, Moskow. (in Russian).
• [15] Smith, WL. (1955). Regenerative stochastic processes. Proc.Roy.Soc. London. A, 232, 6-31.
• [16] Takács, L. (1954). Some investigations concerning recurrent stochastic processes of a certain type. Magyar Tud. Akad. Mat. Kutato Int. Kzl 3, 115-128.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).