THE MECHANISM OF CONSTRUCTING AN ANALYTICAL SOLUTION FOR CALCULATING THE PROBABILITY OF NO-FAILURE OF A COLD STANDBY SYSTEM WITH HETEROGENEOUS ELEMENTS

Abstract

The task related to the calculation of the probability of no-failure (PNF) of spacecraft onboard equipment is due to the fact that with the growth of the number of types and quantity of involved elements the process of dependability calculation becomes more complex and time-consuming. In the context of design for dependability, when the process of recalculation is performed repeatedly, this drawback is critical. In order to simplify the calculations, assumptions are made. For instance, in redundant systems heterogeneous elements are used. This approach does not allow evaluating the dependability of a system that features essentially different elements. In order to reduce the time of dependability calculation of the system under consideration, as well as to increase the accuracy of the results, the paper suggests a method of analytical solution for PNF calculation. It is suggested to use the system dependability time dependence function as the main dependability indicator, while for individual elements the respective failure rate is proposed. The authors look at the problem of consideration of the complexity of such function’s construction for the cases of functional dependability calculation, when the elements of the system under consideration may not be homogeneous. For a system that includes anу number of essentially different elements with cold redundancy, a method was developed and mathematically justified that allows representing in matrix form an analytic expression for calculation of probability of no-failure (PNF). The importance of considering the performance of the facilities that ensure redundancy of functional units is demonstrated in the context of design for dependability of spacecraft. A special attention is given to systems that include a random number of essentially different elements with cold redundancy. As one of the ways of solving the above problem, the paper shows that in this case a numeric evaluation of dependability is possible using rough computation with integration and differentiation. It is proposed to evaluate the degree of approximation of such calculations as both the accuracy of the computer itself and the complexity of the system under consideration. For that purpose, serial representation of the function of probability of no-failure is used for a system after the initiation of each next element under redundancy. The resulting function is formed by grouping of summands in particular order. The potential of replacing the differentiation and integration operations is shown. Under known matrix coefficients the application of the suggested algorithm will significantly improve the accuracy and speed of PNF computation. The practical details of the task related to ensuring spacecraft operational stability under environmental effects are characterized by the importance of the factor of prompt decision-making regarding the generation of control signal aimed at ensuring homoeostasis of the onboard systems performance. The analytic expression for calculation of PNF of a system comprised of a random number of elements can be used for mapping data in computer memory as part of decision support.