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ReliaSoft ALTA reference: Arrhenius-Weibull and Eyring-Weibull fits of a 393/408/423 K test

ToolAccelerated Life
SourceReliaSoft (2024). "Arrhenius Relationship" and "Eyring Relationship." Accelerated Life Testing Data Analysis Reference (help.reliasoft.com). Arrhenius-Weibull and Eyring-Weibull examples.
LevelGraduate

Problem

Ten units each were run to failure at 393, 408 and 423 K. Fit a Weibull life distribution with a common shape parameter and an Arrhenius life-stress relationship by maximum likelihood; then fit the Eyring relationship to the same data and give the mean time to failure at a 323 K use temperature.

Inputs to Enter

  • Model Arrhenius (then Eyring), distribution Weibull, temperature scale K
  • 393 K: 3850, 4340, 4760, 5320, 5740, 6160, 6580, 7140, 7980, 8960 h
  • 408 K: 3300, 3720, 4080, 4560, 4920, 5280, 5640, 6120, 6840, 7680 h
  • 423 K: 2750, 3100, 3400, 3800, 4100, 4400, 4700, 5100, 5700, 6400 h
  • Use temperature 323 K for the Eyring case
Open the Accelerated Life tool

Answers

  • Arrhenius-Weibull: β = 4.2915822, B = 1,861.6186657, C = 58.9848692 (printed values reproduced to 7 digits); log-likelihood −258.1381 (scipy)
  • Characteristic life at 393 K η = C exp(B/393); acceleration 423 → 393 K = exp[B(1/393 − 1/423)]
  • Eyring-Weibull: β = 4.29186497, A = −11.08784624, B = 1,454.08635742; MTTF at 323 K = 16,610 h

Notes

Paste the three temperature blocks into the data box (one line per time, temperature first); switch the model select between Arrhenius and Eyring. The ReliaSoft data tables were read from the page images filed in References/Accelerated-Life/.

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