Skip to main content
SpringerLink
Log in

Linear Mathematical Theory of Accelerated Life Testing

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Problems of accelerated life testing are formulated and the basic definitions are given. The notion of the so-called acceleration function is introduced. Using this notion, we define the integral time distribution function of no-failure operation of a piece of equipment. The linearity criterion is formulated for the acceleration function. Using the obtained relation, which is a generalization of the Palmgren–Miner rule, we work out the accelerated testing method for determining the reliability with the load increasing continuously or stepwise.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Effects of Voltage Deviation on Electronic Tubes, Bull. GEA 5636, General Electric, New York (1959).

  2. J. Kimmel, “Accelerated life testing of paper dielectric capacitors,” in: Proc. 4th Natl. Symp. on Reliability and Quality Control (1958), pp. 120–134.

  3. Kh. B. Kordonski, “Forced tests of the reliability of machines and devices,” Standardizatsiya, 7, 21–24 (1964).

    Google Scholar 

  4. Yu. V. Linnik, Least Square Method and the Foundations of the Mathematical-Statistical Theory of Observation Data Processing [in Russian], Fizmatlit, Moscow (1958).

    Google Scholar 

  5. M. A. Miner, “Cumulative damage in fatique,” J. Appl. Mech., 12 (1945); Trans. Am. Soc. Mech. Eng., 67, A159–A164.

  6. O. M. Namicheishvili, “On one property of the wear function,” Proc. Tbilisi State Univ. Ser. Phys. Sci., 133, 277–280 (1969).

    Google Scholar 

  7. O. M. Namicheishvili and A. N. Lavrov, “On some properties of the reliability margin,” Bull. USSR Acad. Sci. Eng. Cybern., No. 2, 112–116 (1968).

    Google Scholar 

  8. New Departure Handbook, New Departure Division General Motors Corporation, Bristol Connecticut, USA (1952).

  9. A. G. Palmgren, “Die Lebensdauer von Kugellagern,” Z. Vereines Dtsch. Ing. (ZVDI) 68, No. 14, 339–341 (1924).

    Google Scholar 

  10. Probability and Mathematical Statistics [in Russian] (Yu. V. Prokhorov, ed.), Bolshaya Rossiskaya Entsiklopediya, Moscow (2003).

  11. Reference Data for Radio Engineers, Int. Telephone Telegraph Corp., New York (1956).

  12. N. M. Sedyakin, “On one physical principle of reliability theory,” Bull. USSR Acad. Sci. Eng. Cybern., No. 3, 80–87 (1966).

    Google Scholar 

  13. Ya. B. Shor, Statistical Methods of Analysis and Control of Quality and Reliability [in Russian], Sov. Radio, Moscow (1962).

  14. H. Sturges, “The choice of a class-interval,” J. Am. Stat. Assoc., 21, 65–66 (1926).

    Article  Google Scholar 

  15. Traité de fiabilité par Maurice Schwob et Guy Peyrache, Masson&Cie, Paris (1969).

  16. W. A. Weibull, “Statistical representation of fatique failures in solids,” Göteborg (1949.

Download references

Author information

Authors and Affiliations

  1. Georgian Technical University, Tbilisi, Georgia

    A. Prangishvili

Authors
  1. O. Namicheishvili
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Prangishvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Prangishvili.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 94, Proceedings of the International Conference “Lie Groups, Differential Equations, and Geometry,” June 10–22, 2013, Batumi, Georgia, Part 1, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Namicheishvili, O., Prangishvili, A. Linear Mathematical Theory of Accelerated Life Testing. J Math Sci 216, 580–585 (2016). https://doi.org/10.1007/s10958-016-2918-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-2918-7

Search

Navigation