Physical model and failure distribution law for electronic elements and systems

Аuthors

Avakyan A. A.^*, Kurganov A. V.^**

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

*e-mail: avakyan@niiao.com
**e-mail: kurganov@niiao.com

Abstract

A structure of an electronic circuit element is considered. It is shown that the physical failure model for a circuit element is based on two types of binary events: a conductor break and a dielectric breakdown. The physical failure model is formalized in the form of the binary failure distribution law and the binomial failure distribution law. It is proved, with the Lyapunov limit theorem, that the failure distribution law for electronic components and systems is normal. Since no failures are available on the negative part of the event time line, the failure distribution law for a circuit element is truncated normal. Some estimates of expectations and probable deviations of failures are obtained for electronic circuit elements. These estimates allow us to state that the failure probability distribution density and failure rate are equal and constant over the period up to one million hours (hundred years). Therefore, the circuit elements of electronic systems operate practically on the stationary part of failure rate. However, while the theory of redundant fail-safe systems with a great number of circuit elements is built, the application of the Poisson failure law produces relationships became less adequate to the proposed model. The results presented in the paper can be interesting for specialists in reliability theory.

Keywords:

electronics, element, probability, expectation, dispersion, random quantity, distribution law, normal law

References

1. Gnedenko B.V. Kurs teorii veroyatnostey (Course of probability theory), Moscow, Phizmatlit,1962, 472 p.
2. Gnedenko B.V., K.Belyaev Y.K., Solovyov A.D. Matematicheskiye metody v teorii nadiozhnosti ( Mathematical methods in reliability theory), Mosсow, Nauka, 1965, 524 p.

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