Stationarity of failure flow for electronic elements and systems

Аuthors

Avakyan A. A.

Research institute of aircraft equipment, 18, Tupolev St., Zhukovsky, Moscow Region, 140182, Russia

e-mail: avakyan@niiao.com

Abstract

It is shown theoretically that the failure flow for electronic elements and systems is not a Poisson one. In order to the failure flow being a strictly Poisson flow, the probability of a binary event must tend to zero, with the number of elements approaching infinity, that dis-agrees with the physical model of a failure. At the same time, multiple statistical data for electronic element and system failures obtained with rigorous calculation methods, con-firms the Poisson character of their failure flow. The paper discloses and gives a strict ex-planation for this contradiction between the practice and the theory. The contradiction oc-curs because the operational time is less than the mean failure time for a circuit element by a factor with value from ten thousand to hundred thousand. Over such a long interval related to the maximum value both the failure distribution density function and the failure rate function have in practice the same values and they are stationary during the entire operating life. The proven theorem declares that the failure rate for a system, which consists of the infinite number of absolutely reliable elements (element reliability characteristics and their quantity tend to infinity), tends to a constant value. The theorem shows that it is not reasonable to improve system reliability for a system with a great number of elements by improving the reliability of system elements. The results obtained in the paper will be in-teresting for researchers in reliability theory.

Keywords:

failure flow, Poisson flow, limit, theory, practice,, circuit element, probability, distribution law, normal law, exponential law

References

1. Avakyan A.A. Materialy mezhdunarodnogo simpoziuma «Nadiozhnost i kachestvo,» Penza, 2012, pp. 477-480.
2. Gnedenko B.V., K.Belyaev Y.K., Solovyov A.D. Matematicheskiye metody v teorii nadiozhnosti (Mathematical methods in reliability theory), Moscow, Nauka, 1965, 524 p.
3. Gnedenko B.V. Kurs teorii veroyatnostey (Course of probability theory), Moscow, Phizmatlit,1962, 472 p.
4.  Cramer H. Matematicheskie metody statistiki (Mathemtical methods of statistics), Moscow, Mir, 1973, 496 p.

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