ESTIMATION OF FAULT DETECTION AND DIAGNOSTIC TESTS’ LENGTH FOR CONTACTS

Popkov Kirill Andreevich, Postgraduate student, Lomonosov Moscow State University (1 Leninskie Gory street, Moscow, Russia), kirill-formulist@mail.ru

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Background. The article considers problems of operability checking and identification of condition of the N contacts by means of experiments based on arrangement of two-pole circuits, made from these contacts, with subsequent ”testing” of these circuits, i. e. finding Boolean functions realized by the circuits constructed. Random constant faults of contacts are permitted; at the same time, it is assumed that not more than k contacts are faulty, where k is a given natural number that does not rank over N. It is necessary to minimize a number of contact circuits required for operability checking and identification of condition of all contacts.
Materials and methods. The author used the method of “locking” of contact circuits with such faults of the contacts, under which each of the circuits realizes a Boolean constant.
Results. The lower bounds k/[sqrt(N)] and k/(N-k) were obtained for the number of circuits mentioned. In the cases k=N-1 and k=N the exact values of this number were found.
Conclusions. For operability checking and identification of condition of contacts it is impossible to manage with circuits, the number of which is less than some fixed numbers depending on N and k.

contact, fault, contact circuit, fault detection test, diagnostic test.

1. Gavrilov M. A. Teoriya releyno-kontaktnykh skhem [Theory of relay-contact networks]. Moscow; Leningrad 1950, 304 p.
2. Kolduell S. Logicheskiy sintez releynykh ustroystv [Logic synthesis of relay devices]. Moscow 1962, 440 p.
3. Lupanov O. B. Asimptoticheskie otsenki slozhnosti upravlyayushchikh sistem [Asymptotic estimation of control system complexity]. Moscow: Izd-vo MGU, 1984, 138 p.
4. Popkov K. A. Diskretnaya matematika [Discrete mathematics]. 2013, vol. 25, no. 4, pp. 30–40.