Abstract
The paper considers theoretical explanation and construction of some mathematical models of a transportation mean operational process in reference to maintenance optimal periodicity. The important finding is that the objectively existing engineering transportation means maintenance optimal periodicity is determined in the different from the probabilistic methods way. There is a scientifically proven explanation for the mentioned above periodicity optimization with the help of the specially introduced hybrid-optional effectiveness functions distribution. The developed doctrine uses the entropy paradigm conditional extremization approach. This contribution allows obtaining the wanted optimal periodicities sidestepping the related states probabilities determination and their further extremization. The essential breakthrough of the developed doctrine is that the optional objective effectiveness functions, in such a case, are the corresponding combinations of the intensities of the studied system’s possible transitions from state to state, which relates with the set of the considered operational options. Corresponding limit solutions for the zero-to-zero ratio indeterminate forms are analyzed. Theoretical speculations are illustrated with the example calculation experiments. The necessary diagrams are plotted.
Highlights
Operation of any transportation mean requires periodical maintenance and repair. As it has been considered in references Dhillon (2006), Nakagawa (2005), and Smith (2005), issues of reliability, risks, maintainability, and maintenance ought to be taken into account by engineers
Instead of the classical probabilistic approach represented with the procedure of equations (1)–(9) we propose to apply the multi-optional effectiveness hybrid functions entropy conditional optimization doctrine developed hereinafter
The other difference is the consideration of the system’s possible partial restoration. In those cases when the parameters of the general models, similar to portrayed in Figure 1, and described with expressions (1)–(9), have some certain other specific values, the probability of the state “2”, Eq (9), may have the extremum. In such cases the optimal maintenance periodicities are determined in the framework of the proposed and developed multi-optional conditional optimality doctrine, likewise (10)–(19), too
Summary
Operation of any transportation mean requires periodical maintenance and repair. As it has been considered in references Dhillon (2006), Nakagawa (2005), and Smith (2005), issues of reliability, risks, maintainability, and maintenance ought to be taken into account by engineers. It is worth mentioning the problems of aircraft noise assessment, prediction, and control (Zaporozhets, Tokarev, & Attenborough, 2011); estimation of quality parameters in the radio flight support operational system (Solomentsev, Zaliskyi, & Zuiev, 2016); synergy of piloted, remotely piloted and unmanned air systems in single air navigation space (Chepizenko, Kharchenko, & Pavlova, 2013); consequences of shallow flows of liquid on the airport runways and automobile roads (Beljatynskij, Prentkovskis, & Krivenko, 2010) 2) multi-optional hybrid functions of a special kind, which are composed for discovering some sought after optimal (in a certain respect) values with taking into account the uncertainty of the functions “multi-optionality” (Goncharenko, 2016, 2017a, 2017b, 2018a, 2018c)
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