Accession Number : AD0652681
Title : AN APPLICATION OF SPECTRAL THEORY AND A GENERALIZED BIRTH AND DEATH PROCESS TO A RELIABILITY PROBLEM,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Gross,Alan J. ; Persico,Donald J.
Report Date : MAY 1967
Pagination or Media Count : 23
Abstract : The authors consider a system of electrical generating units that must produce a constant amount of power for a specified length of time T regardless of the number of units operating at any time t, where 0 < or = t < or = T. Such a system is called a load-sharing system, because whenever a component fails the remaining operating components share equally among themselves the power increase required of the operating components in order to sustain the power output of the system. In addition to the N operating units we assume there are x units in an active standby capacity for the system. If an operating or on-line unit should fail and a standby unit is available, the standby unit is switched instantaneously (with a certain probability) into operation. We also assume there is a repair facility which is available for the system. Thus, whenever a unit fails, be it an operating or standby unit, the failed unit enters the repair facility. The authors develop and solve in this paper the system of differential equations which describes the operation of the system and whose solution enables us to calculate the reliability of the system at any point in time.
Descriptors : (*RELIABILITY(ELECTRONICS), DIFFERENTIAL EQUATIONS), (*FAILURE(ELECTRONICS), *MATHEMATICAL MODELS), MAINTENANCE, PROBABILITY, PROGRAMMING LANGUAGES, REAL NUMBERS, COMPUTER PROGRAMS, MATRICES(MATHEMATICS), SERIES(MATHEMATICS), CONVERGENCE, SWITCHING CIRCUITS
Subject Categories : Electrical and Electronic Equipment
Mfg & Industrial Eng & Control of Product Sys
Distribution Statement : APPROVED FOR PUBLIC RELEASE