One stage in reliability and probability analysis of systems safety is the assessment of the importance of the elements or ranking of the elements according to the degree to which they influence the systems reliability and safety. Existing methods (according to Birnbaum, criticality, Barlow and Proshan, Wessel and Fussel, Butler) [1, 2] are based on a Boolean model of systems reliability (structure functions, structure schemes, fault tree, and event tree), for which the assumption that at each moment in time the state of the system (functional or malfunction) depends only on the state of the element at that time is important. Using the terminology of the theory of finite automata, Boolean models describe only systems with no memory or combination systems. The reliability indicators of combination systems at a given moment in time are functions of the reliability indicators of the elements at that time.There exits, however, a quite large class of systems whose state depends on the sequence of faults and restorations of the elements in the time period from the start of operation up to the instantaneous moment (systems with periodic control, preventive maintenance, and so on). By analogy to finite automata, it is natural to term such systems sequential. Boolean models and the methods based on them for assessing the importance of elements are inapplicable for reliability analysis of such systems, since it is impossible to construct a Boolean function that describes the dependence of the indicator of operability of the system at some moment in time on the indicators of the operability of elements at the same time, because Boolean functions describe only systems with no memory [2][3][4]. The reliability indicators for sequential systems at a fixed moment in time are functionals and not functions of the distribution of the production of the elements up to the fault and the moment of restoration of the elements.The simplest example of a sequential system is a system that includes the protected object and the safety system. In [5, 6] such systems are called protected object -safety system systems, and methods for analyzing their reliability taking into account the technical maintenance are proposed there.In the present paper we assume that this system functions in the time interval [a, b], and the protected object and the safety system are not restored. If the protected object malfunctions before the safety system, then the operable safety system shuts down the entire system. If, however, the protected object malfunctions after the safety system and before the time b, then a catastrophe occurs (final, extremely undesirable event with uncorrectable consequences). The time interval [a, b] can be, for example, the time interval between two successive checks of the operability of the safety system. Let Fo.p(t) and Fs.s(t) be the distribution functions of the operation time of the protected object and the safety system before failure, respectively, and the failures of each system are independent. Then the probability that ...

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Damage in the form of fatigue cracks can arise and corrosion processes can be initiated in the material of a structural element under prolonged simultaneous exposure to variable stresses of different nature. In this connection, it is necessary to construct an adequate mathematical model of the reliability that would make it possible to determine the lifespan of the structure during operation. Accurate values of the lifespan indicators of a part are impossible to obtain in the case of multidimensional loads. For this reason, it is of practical interest to obtain estimates of these indicators, which is the subject of discussion in this article.Damage in the form of fatigue cracks can appear and corrosion processes can be initiated in the material of a structural element under prolonged simultaneous action of variable stresses of different nature. These processes are irreversible, and ultimately result in failure of the element [1]. Thus, the pipelines in a nuclear power plant operate under simultaneous exposure to corrosive media, high pressure and temperature, pressure and temperature pulsations, liquid and vapor flows, radiation, mechanical impacts, and so forth [2]. In practice, most operating objects are subjected to several destructive factors. Thus, in most practical situations multidimensional cyclic loads act on a part.Since the character of each action of periodic loads on a part is random in general, it is desirable to use a stochastic approach to obtaining the lifespan indicators of a part operating under cyclic perturbations. In addition, the part itself is manufactured with a definite accuracy, which is also of a random nature. This makes it necessary to develop reliability-probabilistic computational methods which would be able to answer any questions concerning the lifespan of a system during operation.Accurate values describing the functioning of a system can be obtained only for certain distribution laws for an applied load, even in the case of one-dimensional perturbations [3]. In the case of multidimensional loads, accurate lifespan indicators cannot be obtained even for the simplest load distribution laws, so that it is of practical interest to estimate them. A method for obtaining the lower (pessimistic) estimate of the probability P(t, x) of failure-free operation under conditions of discrete degradation of a part is described in [5]; this method is based on inferences from the Hausdorff estimator [4]. In the present article this method is extended to the case where a multidimensional cyclic load acts on a part.Formulation of the Problem. Consider a part on which act n independent fluxes of periodic perturbations. Let the time intervals between adjacent load cycles of type i τ i1 , τ i2 , τ i3 , ..., τ ik be independent and have the same distribution function F i (t) = F ij (t) = P(τ ij ≤ t), i = 1, 2, 3, 4, ..., n and j = 1, 2, 3, ..., k, with the possible exception of F i1 (t) = P(τ i1 ≤ t) ≠ F i (t).Similarly, we shall assume that each perturbation of the type i changes the damage accumulat...

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An analysis of statistical data of diagnostic measurements of two parameters determining the performance of the RBMK-1000 SHADR-8A flowmeters – the minimum value of the negative amplitude half-wave at the transistor flow measuring unit (TIBR) input and the mean-square deviation over the flowmeter ball rotation period – made it possible to develop a mathematical model of the flowmeter parametric reliability. This mathematical model is a random process, which is a superposition of two delayed renewal processes. Studying the flowmeter operational reliability model provides an exponential estimate of the probability that the parameters determining the flowmeter performance will not exceed the specified levels. Using the Bernoulli scheme and the probability-estimating relationship for the flowmeter performance parameters, it is possible to calculate the probability of failure-free operation of both a single reactor quadrant and the coolant flow measurement system. In addition, it becomes possible to estimate the quadrant failure rate. Important for practice is the possibility of predicting the number of failed flowmeters depending on the system operation time. An indicator of the system reliability can be the average number of failed flowmeters, the relation for which is given in the paper. All the research results were obtained without any additional assumptions about the random values distribution laws. The obtained results can be easily generalized for the cases when the vector dimension of the determining parameters is greater than two. The use of the results of this study is illustrated by calculated quantitative values of the flowmeter parametric reliability indicators and the coolant flow measurement system.