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

Aplikace matematiky (1982)

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

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## Abstract

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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: $I\to II,II\to III,II\to I,III\to I$. The repair of a unit of the type $II\to I$ 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

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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

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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) MR0403609
10. P. R. Parthasarathy, Cost analysis for 2-unit systems, IEEE Trans. Reliab. R-28 (1979), 3, 268-269. (1979) Zbl0411.62074
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