Informatics and Applications
2014, Volume 8, Issue 1, pp 21-27
ESTIMATION OF RELIABILITY OF COMPLEX SYSTEMS WITH RENEWAL BASED ON ELEMENT TEST RESULTS
Abstract
The problem of confidence estimation of reliability of complex systems with network structure with
repairable elements is considered. Estimation of reliability of a system is based on test results of its individual
elements (subsystems). Existing methods for solving this problem are designed for relatively simple series-parallel
structures consisting of elements with exponential distribution of time to failure. Solution of this problem is
suggested for the more general model of “monotone structures” with independent renewable elements, as well as
significantlymore general case of “aging” system elements (with monotonically increasing function of failure rate).
It is assumed that elements of the system are restored regardless of the state of other elements. In addition, the
solution of this problemis obtained in the natural, fromthe practical point of view, asymptotic behavior for the case
of high reliability (fast recovery) system elements.
[+] References (15)
- Gnedenko, B. V., Ju.K. Beljaev, and A.D. Solov’ev. 1965.
Matematicheskiemetody v teorii nadezhnosti [Mathematical
methods in reliability theory].Moscow: Nauka. 524 p.
- Barlow, R., and F. Proschan. 1965.Mathematical theory of
reliability. N.Y.: John Wiley&Sons. 497 p.
- Vasil’ev, N. S. 1985. Ob odnoy modeli razvitiya seti svyazi
[On one model of network development] Izvestiya
Rossiyskoy Akademii Nauk. Teoriya i Sistemy Upravleniya
[Bulletin of the Russian Academy of Sciences. Theory and
Control Systems] 6:227–234.
- Pavlov, I. V. 1988. Priblizhenno optimal’nye doveritel’nye
granitsy dlya pokazateley nadezhnosti sistem s
vosstanovleniem [Approximately optimum confidence
limits for system reliability indicators with recovery].
Izvestiya Rossiyskoy Akademii Nauk. Teoriya i Sistemy
Upravleniya [Bulletin of the Russian Academy of Sciences.
Theory and Control Systems] 3:109–116.
- Pavlov, I. V., and I.A. Ushakov. 1989. Vychislenie pokazateley
nadezhnosti dlya slozhnykh sistem s vosstanavlivaemymi
elementami [Calculation of reliability indices
for complex systems with recoverable elements]. Izvestiya
Rossiyskoy Akademii Nauk. Teoriya i Sistemy Upravleniya
[Bulletin of the Russian Academy of Sciences. Theory and
Control Systems] 6:170–176.
- Gnedenko, B. V., I. V. Pavlov, and I.A. Ushakov. 1999.
Statistical reliability engineering. N.Y.: John Wiley&Sons.
517 p.
- Konovalov, M.G. 2012. Organizatsiya raboty vychislitel’nogo
kompleksa s pomoshch’yu imitatsionnoy modeli
i adaptivnykh algoritmov [Organization of work of computer
complex using a simulation model and adaptive
algorithms]. Informatika i ee Primeneniya — Inform. Appl.
6(1):37–48.
- Pavlov, I. V. 2012. Raschet i optimizatsiya nekotorykh
kharakteristik dlya modeli vychislitel’nogo kompleksa
[Calculation and optimization of some characteristics of
the model computer complex]. Informatika i ee Primeneniya
— Inform. Appl. 6(2):59–62.
- Barlow, R., and F. Proschan. 1966. Tolerance and confidence
limits for classes of distributions based on failure
rate. Ann.Math. Stat. 37(6):1184–1195.
- Pavlov, I. V. 1977. Doveritel’nye granitsy v klasse raspredeleniy
s vozrastayushchey funktsiey intensivnosti otkazov
[Confidence limits in the class of distributions with
increasing failure rate function]. Izvestiya Rossiyskoy
Akademii Nauk. Teoriya i Sistemy Upravleniya [Bulletin
of the Russian Academy of Sciences. Theory and Control
Systems] 6:72–84.
- Lloyd, D., and M. Lipow. 1962. Reliability management,
methods andmathematics.N.J.: Prentice-Hall, Englewood
Cliffs. 684 p.
- Beljaev, Ju.K. 1967. Doveritel’nye intervaly dlya funktsiy
ot mnogikh neizvestnykh parametrov [Confidence intervals
for functions of many unknown parameters]. Dokl.
AN SSSR 196(4):755–758.
- Beljaev, Ju.K., T.N. Dugina, and E. V. Chepurin. 1967.
Vychislenie nizhney doveritel’noy otsenki dlya veroyatnosti
bezotkaznoy raboty slozhnykh sistem [Calculation
of the lower confidence estimates for the probability
of failure-free operation of complex systems]. Izvestiya
Rossiyskoy Akademii Nauk. Teoriya i Sistemy Upravleniya
[Bulletin of the Russian Academy of Sciences. Theory and
Control Systems] 2:52–59.
- Pavlov, I. V. 1981. O korrektnosti fidutsial’nogo podkhoda
pri postroenii doveritel’nykh granits dlya pokazateley
nadezhnosti slozhnykh sistem [On the correctness of the
fiducial approach when constructing confidence limits for
the indicators of reliability of complex systems]. Izvestiya
Rossiyskoy Akademii Nauk. Teoriya i Sistemy Upravleniya
[Bulletin of the Russian Academy of Sciences. Theory and
Control Systems] 5:46–52.
- Pavlov, I. V. 1981. O fidutsial’nompodhode pri vychislenii
doveritel’nykh granits dlya funktsiymnogikh neizvestnykh
parametrov [On fiducial approach in calculating confidence
limits for functions of many unknown parameters].
Dokl. RAN 258(6):1314–1317.
[+] About this article
Title
ESTIMATION OF RELIABILITY OF COMPLEX SYSTEMS WITH RENEWAL BASED ON ELEMENT TEST RESULTS
Journal
Informatics and Applications
2014, Volume 8, Issue 1, pp 21-27
Cover Date
2014-03-31
DOI
10.14357/19922264140103
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
complex systems; network structures; reliability; time to failure; renewal time; resource function; failure
rate function
Authors
I. V. Pavlov
Author Affiliations
Bauman Moscow State Technical University, 5, 2nd Baumanskaya Str., Moscow 105005, Russian Federation
|