Применение марковских процессов для анализа и управления эксплуатационной технологичностью летательного аппарата

The process of aircraft operation involves constant effects of various factors on its components leading to accidental or systematic changes in their technical condition. Markov processes are a particular case of stochastic processes, which take place during aeronautical equipment operation. The relationship of the reliability characteristics with the cost recovery of the objects allows us to apply the analytic apparatus of Markov processes for the analysis and optimization of maintainability factors. The article describes two methods of the analysis and control of object maintainability based on stationary and non-stationary Markov chains. The model of a stationary Markov chain is used for the equipment with constant in time intensity of the events. For the objects with time-varying events intensity, a non-stationary Markov chain is used. In order to reduce the number of the mathematical operations for the analysis of aeronautical engineering maintainability by using non-stationary Markov processes an algorithm for their optimization is presented. The suggested methods of the analysis by means of Markov chains allow to execute comparative assessments of expected maintenance and repair costs for one or several one-type objects taking into account their original conditions and operation time. The process of maintainability control using Markov chains includes search of the optimal strategy of maintenance and repair considering each state of an object under which maintenance costs will be minimal. The given approbation of the analysis methods and maintainability control using Markov processes for an object under control allowed to build a predictive-controlled model in which the expected costs for its maintenance and repair are calculated as well as the required number of spare parts for each specified operating time interval. The possibility of using the mathematical apparatus of Markov processes for a large number of objects with different reliability factors distribution is shown. The software implementation of the described methods as well as the usage of tabular adapted software will contribute to reducing the complexity of the calculations and improving data visualization.Процесс эксплуатации летательного аппарата сопровождается постоянным воздействием различных факторов на его компоненты, приводящие к случайным или систематическим изменениям их технического состояния. Марковские процессы являются частным случаем случайных процессов, которые имеют место в процессе эксплуатации объектов авиационной техники. Очевидная связь характеристик безотказности объектов с затратами на их восстановление позволяют применить аналитический аппарат марковских процессов для анализа и управления эксплуатационной технологичностью летательных аппаратов. В статье описываются методы анализа и управления эксплуатационной технологичностью объектов, основанных на стационарных и нестационарных марковских цепях. Модель стационарной марковской цепи используется для объектов, у которых интенсивность событий постоянна во времени. Для объектов с переменной во времени интенсивностью событий используется нестационарная марковская цепь. С целью сокращения вычислительных объемов, необходимых для выполнения анализа эксплуатационной технологичности объектов авиационной техники с помощью нестационарных марковских процессов, представлен алгоритм их оптимизации. Предложенные методы анализа с помощью марковских цепей позволяют провести сравнительные оценки ожидаемых затрат на техническое обслуживание и ремонт одного или нескольких однотипных объектов с учётом их начальных состояний и времени эксплуатации. Процесс управления эксплуатационной технологичностью с использованием марковских цепей заключается в поиске оптимальной при каждом состоянии объекта стратегии технического обслуживания и ремонта (варианта действий), при которой затраты на его техническую эксплуатацию будут минимальными. Проведённая апробация методов анализа и управления эксплуатационной технологичностью с использованием марковских процессов для объекта, подконтрольного в эксплуатации, позволила построить прогнозно-управляемую модель, в которой рассчитаны ожидаемые затраты на его техническое обслуживание и ремонт, а также необходимое количество запасных частей на каждый заданный интервал наработки. Показана возможность использования математического аппарата марковских процессов для большого количества объектов с различными законами распределения характеристик надёжности. Программная реализация описанных методов, а также использование программного обеспечения, адаптированного к табличной среде, будут способствовать снижению трудоёмкости расчётов и более наглядному представлению получаемых данных

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Application of Markov processes for analysis and control of aircraft maintainability

The process of aircraft operation involves constant effects of various factors on its components leading to accidental or systematic changes in their technical condition. Markov processes are a particular case of stochastic processes, which take place during aeronautical equipment operation. The relationship of the reliability characteristics with the cost recovery of the objects allows us to apply the analytic apparatus of Markov processes for the analysis and optimization of maintainability factors. The article describes two methods of the analysis and control of object maintainability based on stationary and non-stationary Markov chains. The model of a stationary Markov chain is used for the equipment with constant in time intensity of the events. For the objects with time-varying events intensity, a non-stationary Markov chain is used. In order to reduce the number of the mathematical operations for the analysis of aeronautical engineering maintainability by using non-stationary Markov processes an algorithm for their optimization is presented. The suggested methods of the analysis by means of Markov chains allow to execute comparative assessments of expected maintenance and repair costs for one or several one-type objects taking into account their original conditions and operation time. The process of maintainability control using Markov chains includes search of the optimal strategy of maintenance and repair considering each state of an object under which maintenance costs will be minimal. The given approbation of the analysis methods and maintainability control using Markov processes for an object under control allowed to build a predictive-controlled model in which the expected costs for its maintenance and repair are calculated as well as the required number of spare parts for each specified operating time interval. The possibility of using the mathematical apparatus of Markov processes for a large number of objects with different reliability factors distribution is shown. The software implementation of the described methods as well as the usage of tabular adapted software will contribute to reducing the complexity of the calculations and improving data visualization