Technical Note—Probabilistic Analysis of a Single-Server n -unit System with ( n − 1) Warm Standbys

M. N. Gopalan
Additional contact information
M. N. Gopalan: Indian Institute of Technology, Bombay, India

Operations Research, 1975, vol. 23, issue 3, 591-598

Abstract: This paper deals with the availability and reliability of an n -unit system with ( n − 1) warm standbys and a single repair facility. The failure times of the operating unit and of a standby are assumed 1o be exponentially distributed with parameters λ 1 and λ 2 respectively. Initially, a unit is switched on and the other units are kept as warm standbys. The system breaks down when the last operating unit foils. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes, and employs the Laplace-transform technique to solve these equations. It obtains the mean down-time of the system during (0, t ) and the mean time to system failure explicitly. Finally it discusses the cases n = 2 and 3.

Date: 1975
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.23.3.591 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:23:y:1975:i:3:p:591-598

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().