Application of Markov processes for analysis and control of aircraft maintainability

Abstract

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.

Assessment of trends in chloroform content in drinking water of infiltration water intake

“…Thus, according to the results of the totality of conducted studies, it can be considered that linear regression models, in general, reflect the deterioration of drinking water quality by such indicator as the content of CFs. The application of Markov chains allows us to obtain data on changes in drinking water quality in the short and medium term [7][8][9][10][11][12], to reveal that for the forecast period (1 -4 months) there is a marked increase in the rate of accumulation of CFs, which ultimately increases the risk of deterioration of drinking water quality.…”

“…Markov processes are a convenient mathematical tool for studying objects of different nature in order to predict the dynamics of their changes in the medium and short-term periods [9][10][11][12]. A particular case of Markov processes are Markov chains, for which it is assumed that in each period of time the system can be in one of a finite or countable set of states, and the transition from one state to another (including itself) occurs at discrete moments of time.…”