Aim.The paper analyzes the functional survivability of structurally complex technical systems. This approach is the evolution of the structural survivability paradigm, when the system/element failure criterion is binary. The paper shows that given a wide variety of probabilistic scenarios of adverse effects (AE) on a system, an invariant model kernel is identified that is responsible for the interpretation of functional redundancy. The aim is to identify the proportion of retained operable states within the acceptable computational time, when the fixed number u of elements is disabled as the result of AE. In this case the analysis of survival law is conducted at the confluence of functional redundancy analysis and probabilistic AE models of arbitrarily wide variety. 

Methods. A technical system is considered a controllable cybernetic system equipped with specialized survival facilities (SF). System survivability analysis uses logic and probabilistic methods, as well as the results of the combinatorial theory of random allocation. It is assumed that: a) AE are localized and single (one effect affects exactly one element); b) each of the system’s elements has a binary logic (operability – failure) and zero resilience, i.e. destruction after one effect is guaranteed. Subsequently this assumption is generalized for the case of r-fold AE and L-resilient element. 

Results. The paper reconstructs a number of variants of the destruction law and survivability functions of technical systems. It is identified that those distributions are based on prime and generalized Morgan numbers, as well as Stirling numbers of the second kind that can be recovered using the simplest recurrence formulas. While the assumptions of the mathematical model are generalized for the case of nr-fold AE and L-resilient elements, the generalized Morgan numbers involved in the estimation of the destruction law are identified using the random allocation theory by means of n-fold differentiation of the generating polynomial. In this case it does not appear to be possible to establish a recursive relation between the generalized Morgan numbers. It is shown that under homogeneous assumptions regarding the survivability model (equally resilient system elements, equally probable AEs) in the correlation kernel for the system survivability function, regardless of the destruction law, is the functional redundancy vector F(u, e), where u is the number of affected elements, e is the system’s limiting efficiency criterion, below which its functional failure is diagnosed, F(u, e) is the number of system states operable in terms of e under u failures (destructions) of its elements. 

Conclusions. Point models of survivability are an excellent tool of express analysis of structurally complex systems and tentative estimation of survivability functions. The most simple assumptions of structural survivability can be generalized in cases when the system’s operability logic is not binary, yet is associated with the level of system operation efficiency. In this case we must speak of functional survivability. The PNP computational complexity of the survivability evaluation problem does not allow solving it by means of a simple enumeration of the system states and AE variants. Ways must be found of avoiding simple enumeration, e.g. by using conversion of the system operability function and its decomposition by means of generalized logical and probabilistic methods.

The paper develops theoretical models of dependability of commercial aviation (CA) flight crews based on the resource method of designing organizational social objects. The aim was to provide an objective description of flight crew activity. Formal models of crew composition were constructed. Definitions of dependability of intense profession members are presented using the example of CA crews. The competitive environment of the open global air transportation market is leveled against the standardization of airline activities and primary object of aviation, i.e. CA pilot and flight crew. Air disasters of the last few decades highlight the primary causes, i.e. professional properties deficiency in pilots and excessive workload of flight crews in CA operations. This situation is caused by not only the pressure of the business environment, but also by the critical insufficiency of scientifically grounded methods of managing flight operations in terms of the human component. The paper developed theoretical models of dependability of flight crews based on classical logic and resource method of designing organizational social objects of the transportation industry (airline). The essence of the problem. In commonly known literature there still is no theoretical framework, formal models that could be used for calculation and management of dependability of activities. Crew resources are researched in terms of dependability and efficiency. In general, crew dependability is understood as the sum of dependabilities of crew members for the completion of the assigned tasks. The dependability depends on the composition of specialized skills and individual qualifications of the crew members. The efficiency is the result of three components: communications, decisions, delegation. These interactions can be formal and informal. The scientific substantiation and definition of the parameters of the crew’s assignment in terms of the estimated dependability and efficiency parameters are the solution of the problem. Problem formalization. In order to formalize the problem of objective description of flight crew activity, the crew may be considered as a class of individuals. The logic of classes (sets) uses the class-forming operator C, for “class”, predicate of inclusion of individuals into class Î, a binary predicate, predicate of inclusion of a class into a class. In order for a class to exist it suffices for it to be formed out of the range of values of term t. Class generation principles are expressed in the following axioms: Each element of a class can be chosen regardless of the class formation, the independence principle. A class of individuals exists (does not exist) if it is formed (not formed) in accordance with the definition of class formation and formation axioms. Subsequent statement of the problem must be directed in detail, specific solutions for the development of models suitable for calculation and management of flight operation. Thus, the development of the theoretical essence of the composition and size of crew is a relevant problem and can be solved based on classical logic, managerial control theory, information theory.

Aim. Railway transportation is affected by a whole range of transportation incidents, both related to rolling stock, i. e. vehicle-to-vehicle collisions, derailments, broken cast parts of bogies, etc. , and infrastructure, i. e. broken rail, fires at railway stations and terminals, broken catenary, etc. Among the above incidents, collisions at level crossings are the most likely to cause a public response, as collisions between trains and road vehicles often cause multiple deaths that are reported in national media, which entails significant reputational damage for JSC RZD. Additionally, collisions often cause derailment of vehicles, which may cause deaths and major environmental disasters, if dangerous chemical products are transported. Beside the reputational damage, collisions at level crossings cause significant expenditure related to the repair of damaged infrastructure and rolling stock, as well as damage caused by trains idling due to maintenance machines operation at the location of incident. That brings up the issue of optimal allocation of investment to facilities preventing unauthorized movement of road vehicles across level crossings (hereinafter referred to as protection systems). This problem is of relevance, as replacing level crossings with tunnels and viaducts is not going fast and does not imply the eventual elimination of all level crossing. Hence is the requirement for rational allocation of funds to the installation of protection systems over the extensive railway network. Given the above, the aim of this paper is to develop decision-making guidelines for the reduction of the number of transportation incidents in terms of statistical criteria, i. e. quantile and probabilistic.

 Methods. The paper uses methods of deterministic equivalent, of equivalent transformations, of the probability theory, of optimization.

 Results. The problem of maximizing the probability of no incidents is reduced to integer linear programming. For the problem of minimizing the maximum number of incidents guaranteed at the given level of dependability, a suboptimal solution of the initial problem of quantile optimization is suggested that is obtained by solving the integer linear programming problem through the replacement of binomially distributed random values with Poisson values. 

Conclusions. The examined models not only allow developing an optimal strategy with guaranteed characteristics, but also demonstrate the sufficiency or insufficiency of the investment funds allocated to the improvement of level crossing safety. Decision-making must be ruled by the quantile criterion, as the probability of not a single incident occurring may seem to be high, yet the probability of one, two, three or more incidents occurring may be unacceptable. The quantile criterion does not have this disadvantage and allows evaluating the number of transportation incidents guaranteed at the specified level of dependability.

Цель. Оценка показателей надежности на машиностроительном предприятии осуществляется при проектировании изделий и по данным из эксплуатации. На этапе проектирования широко применяются автоматизированные программные комплексы, которые используют различные методы расчета показателей надежности: деревья отказов, цепи Маркова и др. Исходные данные для такого типа расчета основаны на анализе конструкции изделия и характеристиках его узлов и элементов. Совершенно иным образом осуществляется анализ показателей надежности в эксплуатации. Обработка информации об отказах происходит по рекламациям, поступающим от заказчиков и эксплуатирующих организаций, в сервисные службы предприятий-изготовителей. Суммарное количество отказов по всем видам изделий должно оцениваться службой или подразделением надежности в регламентированный срок. Данная процедура обработки данных об отказах необходима для расчета показателей безотказности и ремонтопригодности. По результатам полученных числовых характеристик производится сравнение с установленными в технической документации значениями. На основе данного сопоставления делается вывод о соответствии или несоответствии конкретного изделия заданным требованиям надежности. Значения показателей надежности в технической документации вводятся на основе испытаний на надежность опытных образцов. Однако в виду различия условий проведения испытаний, процедур фиксации их результатов и единиц измерения, значения показателей надежности, устанавливаемые в технической документации и получаемые в процессе эксплуатации, несравнимы. В вагоностроении наработка подвижного состава чаще всего измеряется в километрах пробега. Однако функционирование большого количества компонентов вагонов оценивается в циклах, часах и т.д. Именно в этих единицах измерения в большинстве случаев происходит формирование значений показателей надежности по итогам испытаний опытных изделий. В процессе оценки показателя безотказности для дверей прислонно-сдвижного типа, устанавливаемых на электропоезда пригородного сообщения, возникла необходимость аппроксимирующего перевода наработки, выраженной в циклах открытия/закрытия, в наработку, выраженную в километрах пробега. Вследствие возникшей проблемы было принято решение о построении математической модели, наилучшим образом отображающей зависимость двух разноименных величин. Чаще всего математические модели строятся и верифицируются на основе исходных наблюдений рассматриваемого показателя и объясняющих факторов. В данном случае исходными данными являются один фактор (циклы открытия/закрытия) и показатель (километры пробега), следовательно, можем использовать модель парной линейной регрессии. 

Результаты. Проведен анализ взаимосвязи циклов открытия/закрытия прислонно-сдвижной двери и километров пробега электропоезда пригородного сообщения. На основе этого получена модель парной линейной регрессии. Проведена верификация, по результатам которой, можно сделать заключение о репрезентативности полученных результатов.

 Выводы. Предоставленная методика расчета обобщающего контролируемого показателя надежности (средней наработки на отказ) на примере дверей прислонно-сдвижного типа показывает, что модель парной линейной регрессии может быть использована для перевода средней наработки на отказ из циклов в километры пробега, необходимого для оценки показателей надежности в эксплуатации.