Application of probability distributions mixture of safety indicator in risk assessment problems

  • Lidiya N. AleksandrovskayaEmail author
  • Anna E. Ardalionova
  • Ljubisa Papic
Original Article


The main indicator of quality functioning of the aircraft pilotage system is flight safety. Thereby, in accordance with acceptable risk concept, demands with safety indicators are being determined in probability form and circumferential acceptable risk values could be very small order of magnitude 10−6–10−8. Such demands for the precision characteristics of vertical echeloning and automatic landing of civil aircrafts are valid during flights in all weather conditions. At certification of aircrafts these demands should be confirmed. Thereto, the only possible way of demand confirmation with such small risks is statistical mathematical modeling in the wast range of disturbing factors. Mathematical modeling is inseparable part of aircraft piloting system development and it is accepted as legitimate at corresponding verification, which enables the guarantee for adequate aircraft movement modeling. The most complete information about aircraft movement probability characteristics is contained within laws of their probability distributions. In classical mathematical statistics papers there is no investigations of very small and very big probabilities. Therefore for solving the safety problems, connected with needs for investigation “tail” (last) distribution parts, necessary to develop a new methods. One of them is presented into this paper. For problems of statistical modeling of aircraft movement in the wast range of disturbing factors the typical appearance of “breach”—distribution law alteration of analyzed parameters. The cause of the “breach” is realization of unlikely extreme values of disturbed random factors and their mixtures at large quantities of modeling, which reconduct corresponding systems in areas of nonlinearity. It is mentioned that the effect of “breach” is characteristical not only for problems of aircraft piloting but also for the wast range of problems in different practice applied areas—ecology, quality management (Six Sigma methodology) and other.


Risk Safety indicator Precision characteristics of aircraft Requirement confirmation Probabilities distribution laws mixture Minimum squares method 



  1. Aleksandrovskaya LN, Kirilin AV, Zavalashin IV, Ardalionova AE (2014a) The concept of acceptable risk: problems and solutions. Commun Depend Qual Manag 17(2):27–38Google Scholar
  2. Aleksandrovskaya LN, Kerber OB, Ardalionova AE, Kirilin AV (2014b) Methods of express analysis safety indicators aircraft automatic landing at stage of mathematical modeling. Commun Depend Qual Manag 17(2):53–65Google Scholar
  3. David HA, Nagaraja HN (2003) Order statistics, 3rd edn. New York, Wiley-InterscienceCrossRefGoogle Scholar
  4. Himmelblau DM (1972) Appliad nonlinear programming. McGraw-Hill Inc., New YorkGoogle Scholar
  5. Korolev VYu, Benning VE, Shorgin SYa (2011) Mathematical foundation of risk theory. Fizmatlit, Moscow (in Russian) Google Scholar
  6. Kryukov SP, Bordunov SD, Aleksandrovskaya LN, Aronov IZ, Zakharevich AP, Kuznetsov AG, Kushel’man VYa (2007) Methods of risk analysis and assessment in tasks of safety management of complex technical systems. Corporation Aerokosmicheskoe Oborudovanie, St. Petersburg (in Russian) Google Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  • Lidiya N. Aleksandrovskaya
    • 1
    Email author
  • Anna E. Ardalionova
    • 2
  • Ljubisa Papic
    • 3
    • 4
  1. 1.Faculty Flight Vehicles TestsMoscow Aviation Institute (National Research University)MoscowRussia
  2. 2.Public stock company Moscow Institute of Electromechanics and AutomaticsMoscowRussia
  3. 3.Faculty of Technical SciencesCacakSerbia
  4. 4.DQM Research CenterCacakSerbia

Personalised recommendations