Skip to main content
SpringerLink
Log in

Variation Coefficient and Some Distribution Laws in the Context of Cutting Tools and Other Technical Objects Reliability Modeling

  • Conference paper
  • First Online:
Book cover Advances in Design, Simulation and Manufacturing (DSMIE 2019)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

Abstract

In the paper some practice of the usage of three distribution laws: Gauss, Gamma, and Weibull for reliability modeling of technical objects in general and metal cutting tools in particular are analyzed and arranged. Selection of distribution law and estimation of its parameters based on empirical data are the main tasks in reliability simulation. It is stressed that selection of the above-mentioned laws should be made taking into account the process mechanism; otherwise, it leads to some false conclusions such as equivalence of Gamma and Weibull distribution. Mentioned distribution laws and their usage are analyzed from the position of physical interpretation. The conditions are shown when the above-mentioned distribution laws are similar. The simplified dependence that connects the shape parameter of Weibull distribution and variation coefficient is obtained and confirmed statistically. The variation coefficient defines the shape parameters for both Gamma and Weibull distributions uniquely and reflects the mechanism of the process. The variation coefficient and failure rate in addition to formal criteria are shown to be the main indicators for the distribution law selection.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Katsev, P.G.: Statistic Methods of Cutting Tools Research. Mashinostroyeniye, Moscow (1974). (in Russian)

    Google Scholar 

  2. Ostreykovskiy, V.A.: Theory of Reliability. Vyschaya Shkola, Moscow (2003). (in Russian)

    Google Scholar 

  3. Barrlow, R., Proschan, F.: Mathematical Theory of reliability. Sovetscoye radio, Moscow (1969). (in Russian)

    Google Scholar 

  4. Gamma distribution fitting: NCSS Statistical Software. https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Gamma_Distribution_Fitting.pdf. Accessed 17 Nov 2017

  5. Akram, M., Hayat, A.: Comparison of Estimators of the Weibull Distribution. Financial Econometrics Series. Deakin University, Geelong (2013)

    MATH  Google Scholar 

  6. Nielsen, M.A.: Parameter estimation for the two-parameter Weibull distribution. In: All Theses and Dissertations, p. 2509. Brigham Young University, Provo (2011)

    Google Scholar 

  7. Abernethy, R.B., Breneman, J.E., Medlin, C.H., Reinman, G.L.: Weibull Analysis Handbook. Pratt & Whitney Aircraft, West Palm Beach, FL (1983)

    Book  Google Scholar 

  8. Yudina, A.V.: Statistics. Educational materials of VGUES. https://abc.vvsu.ru/books/pr_stat1/page0010.asp#xex24. Accessed 17 Nov 2017. (in Russian)

  9. Bulashev, S.V.: Statistic for Traders. Sputnic+, Moscow (2003). (in Russian)

    Google Scholar 

  10. Mironenco, E.V., Vasylieva, L.V.: Research of the machining stability influence at cutting tool operation regulations in the conditions or multi-criteria optimization. In: Bulletin of SevNTU. Mashinopryladobuduvannya ta transport: zb. nauk. pr., vol. 107, pp. 151–154. SevNTU, Sevastopol (2010). (in Russian)

    Google Scholar 

  11. Varma, B.S., Kumar, S.S., Madhu, S.: Reliability of ZTA ceramic cutting tools while machining carbon steels. CMR J. Eng. Technol. 1(2), 1–18 (2016)

    Google Scholar 

  12. Dreval, A.V., Litvinenko, A.E.: Scientific works of “Tool equipment and technologies” department of MSTU n.a. N.E. Bauman for improving efficiensy of cutting tools operation. Science and education. http://technomag.bmstu.ru/doc/48836.html. Accessed 18 Nov 2017. (in Russian)

Download references

Author information

Authors and Affiliations

  1. Zaporizhzhya National Technical University, 64 Zhukovskogo St., Zaporizhzhya, 69063, Ukraine

    Mykhaylo Frolov

Authors
  1. Mykhaylo Frolov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mykhaylo Frolov .

Editor information

Editors and Affiliations

  1. Department of Manufacturing Engineering, Machines and Tools, Sumy State University, Sumy, Ukraine

    Vitalii Ivanov

  2. Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, China

    Yiming Rong

  3. Department of Manufacturing and Production Engineering, Poznan University of Technology, Poznan, Poland

    Justyna Trojanowska

  4. Leibniz Institute for Agricultural Engineering and Bioeconomy, Potsdam, Brandenburg, Germany

    Joachim Venus

  5. Department of Processes and Equipment of Chemical and Petroleum-Refineries, Sumy State University, Sumy, Ukraine

    Oleksandr Liaposhchenko

  6. Faculty of Manufacturing Technologies with a seat in Presov, Technical University of Kosice, Prešov, Slovakia

    Jozef Zajac

  7. Department of General Mechanics and Machine Dynamics, Sumy State University, Sumy, Ukraine

    Ivan Pavlenko

  8. Faculty of Mechanical Engineering, University of West Bohemia, Pilsen, Czech Republic

    Milan Edl

  9. Department of Information and Communication Traffic, University of Zagreb, Zagreb, Croatia

    Dragan Perakovic

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Frolov, M. (2019). Variation Coefficient and Some Distribution Laws in the Context of Cutting Tools and Other Technical Objects Reliability Modeling. In: Ivanov, V., et al. Advances in Design, Simulation and Manufacturing. DSMIE 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-93587-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-93587-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93586-7

  • Online ISBN: 978-3-319-93587-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation