Among the diversity and various degrees of significance of the factors that affect an object’s failure flow, there is one, i.e. its “ageing,” that causes changes in the number of failures per time unit that makes it non-stationary (in terms of dependability). In this context, the elaboration of service procedures is of high importance, especially with regards to long lifecycle objects.

Methods of identifying dependability indicators of stationary objects are known and widely used in practice. Nevertheless, as regards non-stationary objects there are practically no generally accepted approaches to the identification of their dependability indicators that would be convenient for engineering calculations. Meanwhile, the analysis of publications dedicated to this subject given in this paper shows the relevance and potential demand for such methods in various technical matters.

The aim of this paper is in the development of an analytical model of evaluation of dependability indicators of non-stationary objects. The main concept of the proposed approach consists in substituting the real non-stationary object with a virtual analogue, of which the failure flow is stationary, i.e. a formal stationarization (in terms of dependability) of the object occurs, which legitimizes the use of well-developed methods of solving stationary tasks by extending them to the cases of non-stationary objects. The approach is rough. The main problem is identifying the value of the constant failure flow rate of the fake object expressed through the time-dependent parameters of the “ageing” characteristic of the real (non-stationary) object that in this paper is deemed to be known. In order to increase the generality of consideration, the definition of equivalent failure rate (or associated mean time to failure) in this paper is given for three cases: 1) The real object “ages”, i.e. its failure rate is an increasing function of time. Two approaches are suggested to the identification of the equivalent failure rate: a) based on the condition of equality of the mean times to failure of both objects (real and fake); b) based on the condition of equality of the dependability functions of the objects to the predefined prediction time. For some laws of “ageing” the task has been solved analytically in closed form. Using the numerical example, the comparative accuracy of the approaches has been evaluated. 2) The object is characterized by a piecewise constant failure rate that is typical to systems and devices that operate in “open” environments (with seasonal changes in failure rate). Both exact and approximate (in linear approximation) expressions for the dependability function and mean time to failure for such object have been obtained. 3) The object’s failure rate dependance is a piecewise constant non-periodical time function. Such model is sufficiently universal as after time discretization and piecewise constant approximation with a given accuracy many analytical time dependencies of failure rate can be reduced to it. Method-wise, the task is solved similarly to item 2), i.e. the non-periodic process is treated as a periodic one with an infinitely long period. Under the condition of reasonable practicality of object operation (e.g. for economic reasons) defined in this paper, expressions for the dependability function and mean time to failure have been obtained. The findings of the paper may be useful in solving the dependability-related tasks for non-stationary technical objects. 

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.

The aim of this paper is to develop a model that would enable a standardized representation of malicious software’s structure, functions and to get a quantitative estimation of the fault tolerance of information and telecommunication networks affected by malicious software. The paper shows the relevance and importance of the malicious software models and evaluation of the fault tolerance of information and telecommunication networks affected by malicious software. Malicious software refers to software systems able to covertly deploy, establish unauthorized virtual data communication channel, self-propagate, self-modify, conduct unauthorized collection of information on the network and information technology interference against it. The structural and functional model of malicious software developed in this paper is composed of the following set of diagrams and function descriptions: structures of covert deployment and malicious software installation using electronic mail, structural and functional diagram of the main module of malicious software and covert deployment modules, structural and functional diagram of malicious software while implementing malicious functions, malicious software certificate. The diagrams detail the standard functions, operating procedures and information interaction of malicious software modules of the external and internal networks via an unauthorized virtual data communication channel. Primary malicious software modules are considered through the example of the Careto targeted computer attack. The model of fault tolerance of information and telecommunication networks affected by malicious software is described by indicators that characterize the ability of the networks and information security facilities to maintain and recover specified probabilistic and temporal characteristics over the period of malicious software activity. The following indicators are considered: probability that information and telecommunication networks and information security facilities maintain the specified probabilistic and temporal characteristics over the period of malicious software activity, probability that information and telecommunication networks and information security facilities recover the probabilistic and temporal characteristics after the effects of malicious software activity, factor of operation availability of information and telecommunication networks to perform the specified probabilistic and temporal characteristics under malicious software activity at an arbitrary moment in time, mathematical expectation of the duration of malicious software activity, mathematical expectation of the recovery time of the probabilistic and temporal characteristics of information and telecommunication networks and information security facilities. It is assumed that the values of the parameters required for the calculation of the indicators of the fault tolerance model of information and telecommunication networks were obtained as the result of a testbed simulation of the networks affected by malicious software. In the conclusion it is noted that the developed models enable the identification of the general structure of covert deployment and installation of attacking malicious software using electronic mail, structural and functional diagram of the main module of malicious software and covert deployment modules, structural and functional diagram of malicious software while implementing malicious functions, malicious software certificate, as well as evaluate the fault-tolerance of information and telecommunication networks and information security facilities affected by malicious software, quantify the probabilistic and temporal fault tolerance, recoverability and availability characteristics of networks.