Research Reports from the Department of Operations

Document Type

Report

Publication Date

2-1-1970

Abstract

Reliability characteristics such as long-run availability and the time to system failure (TSF) of a system consisting of a single unit in use backed by (N-1) spares and C repair facilities have been obtained when failures of the unit in use as well as spares in storage occur with constant failure rates λ1 and λ2, respectively, and the repair time of these units follows an exponential distribution with parameter μ. The long-run availability has been derived using known results of birth and death processes. Making use of the property that the TSF period followed by a system down (SDT) period forms a renewal process, the expected TSF within a renewal period has been obtained. For the system having a single repair facility, the ratio of the expected TSF to the expected repair time has been numerically evaluated for different values of failure intensities ρ1 and ρ2 of the units in use and in storage, and for various values of N, the total number of units in the system. The initial number of units to be provided has also been shown graphically for 90, 95, and 99 percent availability of the system.

Keywords

Operations research, Reliability (Engineering)--Mathematical models, System analysis--Mathematical models, Renewal theory, Failure time data analysis, Distribution (Probability theory)

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 175

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

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