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Built-in control and diagnostic hardware capacity determination method based on the radioelectronic equipment probabilistic model

DOI 10.18127/j19998465-201902-01


S.V. Ignatiev – Dr.Sc.(Eng.), Professor, Head of Department, Yaroslavl Higher Military School of Air Defense
A.A. Klemin – Ph.D.(Eng.), Associate Professor, Senior Lecturer, Yaroslavl Higher Military School of Air Defense
O.V. Trushina – Deputy Head of Department of Department, JSC «A.L. Mints Radiotechnical Institute» (Moscow)
A.A. Yakovlev – Lecturer, Yaroslavl Higher Military School of Air Defense
A.S. Logovskiy – Ph.D.(Phys.-Math.), Main Product Engineer, Director of STC, JSC «A.L. Mints Radiotechnical Institute» (Moscow)

The article discusses the method of justifying and calculation the radio-electronic equipment (REE) built-in control and diagnostic hardware (BCDH) capacity based on a REE probabilistic model. One of the ways to improve the stationary availability factor is to reduce the mean restoration time (increase in the restoration rate). In turn, the reduction of the restoration time is possible by reducing the failure detection time and failure localization time. This problem is solved including the use of built-in control and diagnostic hardware (BCDH) in radio-electronic equipment (REE). The increase in the number of BCDH elements leads to an increase in the stationary availability factor of the REE functional part. However, the REE with BCDH stationary availability factor decreases due to an increase in failure intensity of the control and diagnostic part.
The REE probabilistic model is proposed to solve this contradiction. The model makes assumptions. The failure intensity and restoration intensity are considered as the simplest, the restoration time and the operating time between failures – distributed according to the exponential distribution. In this case, the process taking place in the physical system can be considered as Markov process.
Probabilistic models, for REE with BCDH and without BCDH, are constructed, for which the Erlang differential equation system is compiled. For the Markov process in the steady state, the differential equation system is transformed into an algebraic equation system. The solution of this equation system gives expressions for the probability limits of the states of REE with BCDH and without BCDH. On the basis of the obtained expressions, the influence of the failure intensity and the restoration intensity on the stationary availability factor of REE with BCDH and without it is considered. The conditions necessary to fulfill the requirements for the stationary availability factor and for the effect from the use of BCDH are determined. The charts of the obtained dependences are analyzed in order to determine the maximum number of BCDH elements. Because REE and BCDH are usually built on the elements of the same type and operated under the same conditions, it is assumed that their failure intensities are proportional to the number of non-restorable elements. The concept of the equipment capacity, as the number of non-restorable elements, is introduced. The resulting ratio of failure intensities allows to go to the ratio of the REE capacity and BCDH capacity and to determine the maximum BCDH capacity, which does not lead to a decrease in the stationary availability factor of the REE system with BCDH in general.
The proposed method for determining the BCDH capacity can be applied at the development stage of REE or at the stage of finalization when REE characteristics are reduced to the dependability requirements after appropriate testing.
On the basis of the obtained mathematical expressions, a software product is created that will allow you to calculate the required number of BCDH elements.

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