Analysis of a two-unit standby redundant system with three states of units

Antonín Lešanovský

Aplikace matematiky (1982)

  • Volume: 27, Issue: 3, page 192-208
  • ISSN: 0862-7940

Abstract

top
A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: I I I , I I I I I , I I I , I I I I . The repair of a unit of the type I I I can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms and mathematical expectations) are derived, e.g. time to system failure, time of non-operating period of the system and stationary-state probabilities of the couple of units of the system.

How to cite

top

Lešanovský, Antonín. "Analysis of a two-unit standby redundant system with three states of units." Aplikace matematiky 27.3 (1982): 192-208. <http://eudml.org/doc/15239>.

@article{Lešanovský1982,
abstract = {A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: $I\rightarrow II, II\rightarrow III, II\rightarrow I, III\rightarrow I$. The repair of a unit of the type $II \rightarrow I$ can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms and mathematical expectations) are derived, e.g. time to system failure, time of non-operating period of the system and stationary-state probabilities of the couple of units of the system.},
author = {Lešanovský, Antonín},
journal = {Aplikace matematiky},
keywords = {cold-standby redundant system; time to system failure; stationarystate probabilities; cold-standby redundant system; time to system failure; stationarystate probabilities},
language = {eng},
number = {3},
pages = {192-208},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Analysis of a two-unit standby redundant system with three states of units},
url = {http://eudml.org/doc/15239},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Lešanovský, Antonín
TI - Analysis of a two-unit standby redundant system with three states of units
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 3
SP - 192
EP - 208
AB - A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: $I\rightarrow II, II\rightarrow III, II\rightarrow I, III\rightarrow I$. The repair of a unit of the type $II \rightarrow I$ can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms and mathematical expectations) are derived, e.g. time to system failure, time of non-operating period of the system and stationary-state probabilities of the couple of units of the system.
LA - eng
KW - cold-standby redundant system; time to system failure; stationarystate probabilities; cold-standby redundant system; time to system failure; stationarystate probabilities
UR - http://eudml.org/doc/15239
ER -

References

top
  1. K. Arndt P. Franken, Construction of a class of stationary processes with applications in reliability, Zastosowania matematyki 16 (1979), 3, 319-393. (1979) Zbl0486.60084MR0534130
  2. R. E. Barlow F. Proschan, Mathematical theory of reliability, J. Wiley, New York-London -Sydney (1965). (1965) Zbl0132.39302MR0195566
  3. B. V. Gnedenko, Ju. K. Beljajev A. D. Solovjev, Математические методы в теории надежности, Nauka, Moskva (1965). (1965) MR0217823
  4. В. V. Gnedenko M. Dinič, Ju. Nasr, O надежности дублированной системы с восстановлением и профилактическим обслуживанием, Izv. AN SSSR, Techn. Kibernet. (1975), 1, 66-11. (1975) 
  5. B. Kopociński, Outline of renewal and reliability theory, (Polish). Państwowe wydawnictwo naukowe, Warszawa (1973). (1973) Zbl0365.60003MR0423567
  6. V. S. Koroljuk A. F. Turbin, Полумарковские процессы и их приложения, Naukova dumka, Kijev (1976). (1976) MR0420902
  7. T. Nakagawa S. Osaki, Stochastic behaviour of a two-unit standby redundant system, INFOR Canad. J. Oper. Res. and Infor. Proc. 12 (1974), 1, 66-10. (1974) Zbl0273.90019MR0433630
  8. S. Osaki, On a two-unit standby redundant system with imperfect swichover, IEEE Trans. Reliab. R-21 (1972), 1, 20-24. (1972) 
  9. S. Osaki T. Nakagawa, Bibliography for reliability and availability of stochastic systems, IEEE Trans. Reliab. R-25 (1976), 4, 284-286. (1976) Zbl0336.90023MR0403609
  10. P. R. Parthasarathy, Cost analysis for 2-unit systems, IEEE Trans. Reliab. R-28 (1979), 3, 268-269. (1979) Zbl0411.62074
  11. D. Szász, 10.1214/aop/1176995760, Ann. Prob. 5 (1977), 4, 550-559. (1977) Zbl0374.60119MR0461701DOI10.1214/aop/1176995760

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.