Aircraft Operation Depending Upon the Uncertainty of Maintenance Alternatives

Abstract

The paper considers the theoretical explanation and construction of some mathematical models of the aircraft operational process in reference to maintenance organizations preferred by aviation experts and aircraft operators. The uncertainty of such operational multi-alternativeness is evaluated on the basis of subjective entropy of preferences demonstrated by aircraft operators and aviation experts. When applying the maximum principle of subjective entropy, the optimal distributions of the preferences are obtained. The proposed concept allows finding the optimal distribution of the aircraft fleet according to the available maintenance alternatives. To optimize the above mentioned distribution, one may take into account the possible development and improvement of maintenance organizations and so called “shadow” components. The paper also discusses a significant approach that helps to evaluate the effectiveness of organizations functioning in the area of aviation. This evaluation can be carried out at both global and continental levels as well as state, operator, and airline levels. The respective modeling has been performed and is illustrated with diagrams.

Aeronautical and Aerospace Material and Structural Damages to Failures: Theoretical Concepts

“…This is a radically different ideology from that of subjective analysis [1,5], where it is postulated that an individual's subjective optimal distribution of her/his preference functions accordingly with the achievable set of alternatives that she/he has taken into consideration, that is, SEMP.…”

“…With the use of the supposed multioptional optimality, likewise in subjective analysis [1,5] conditional optimality of the individual's subjective preference distribution with extremizing subjective entropy, that is, applying the doctrine analogous to the SEMP concept, we have the right to write down the postulated functional in view of [2][3][4]:…”

“…where h i F i are specific hybrid optional effectiveness functions of the option effectiveness functions: F i and h i F i are similar to the preference functions of [1,5], however, in this problem setting the assumed specific hybrid optional effectiveness functions h i F i are not related with anybody's preferences or choice; x is unknown, an uncertain multiplier of the Lagrange type; t p * is the system's (see Figure 1) and the system's described process intrinsic parameter, suspected to be an optimal (in such a problem setting, t p * , which is accepted by an assumption optimal value of maintenance periodicity, is going to deliver the maximal value to the probability P 1 t of the damaged but still not fractured (failure) state "1" of a material, [2][3][4]); γ is the normalizing coefficient (function). The solution t p * of the objective functional in (1) is obtained on the basis of the necessary conditions for the extremum existence of the functional in (1):…”

“…The doctrine proposed in this paper uses a similar mathematical apparatus; however, an original objective [2][3][4] versus subjective theoretical concept is described, applied, and discussed in [1,5] for finding certain extremal values of reliability measures (probabilities). In those cases, studied in the works of [1,5], the use of SEMP is essential for optimal decision making.…”

“…In those cases, studied in the works of [1,5], the use of SEMP is essential for optimal decision making.…”