Metallurgical and Materials Transactions A

, Volume 35, Issue 5, pp 1471–1476

Temperature-dependent variability in lifetime prediction of thermally activated systems


  • R. Raj
    • Department of Mechanical Engineeringthe University of Colorado
  • I. E. Raj
    • Department of Mechanical Engineeringthe University of Colorado
  • D. M. Frangopol
    • Department of Civil Architectural and Environmental Engineeringthe University of Colorado
  • J. S. Kong
    • Dept. of Civil and Environmental Eng.Korea University

DOI: 10.1007/s11661-004-0255-9

Cite this article as:
Raj, R., Raj, I.E., Frangopol, D.M. et al. Metall and Mat Trans A (2004) 35: 1471. doi:10.1007/s11661-004-0255-9


The lifetime of high-temperature systems is often controlled by thermally activated mechanisms such as diffusion. The variability in the lifetime of such systems is analyzed when the operating temperature varies according to a normal (Gaussian) distribution. Linear approximation analysis is employed to obtain simple closed form results for the probability density function (pdf) for the lifetime. The Gaussian variation in temperature is shown to transform to a log-normal distribution for the lifetime. The standard deviation of the log-normal distribution can be predicted from the activation energy, the peak temperature, and the standard deviation of the temperature distribution. Higher activation energy and lower operating temperature increase the variability of the lifetime. This approximate result is compared with the exact transformation. Lifetime experiments with incandescent tungsten lamps are compared to the theoretical prediction.

Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2004