Arrhenius Accelerated Life Calculator

Purpose and model boundary

This model projects an entered test-condition life scale to a use temperature with an Arrhenius acceleration relationship. It then evaluates exponential or two-parameter Weibull mission reliability. It evaluates user-supplied life-model parameters; it does not select an activation energy, fit a distribution, or establish that the same failure mechanism applies at both temperatures.

Inputs and units

The user chooses exponential or Weibull life and a consistent time unit. Required inputs are activation energy ΔH in electron-volts, test and use temperatures in degrees Celsius, test-condition scale life, test exposure, and use-condition mission time. Weibull mode also uses shape β; exponential mode uses β = 1 internally.

Governing relationships

Temperatures are converted with T_K = T_C + 273.15. Using the Boltzmann constant k = 8.617333262145 × 10^-5 eV/K, the workbook calculates:

ln(AF) = (ΔH / k) × (1 / T_use,K - 1 / T_test,K)

AF = exp(ln(AF))

η_use = η_test × AF

equivalent use exposure = test exposure × AF

For mission time t, with β = 1 for the exponential model:

R(t) = exp[-(t / η_use)^β]

F(t) = 1 - R(t)

B10 = η_use × [-ln(0.9)]^(1/β)

median = η_use × [ln(2)]^(1/β)

The workbook evaluates these expressions in logarithmic form where necessary and clips extreme mission exponents to stable probability endpoints. The chart reports log10(AF) over temperature; it is equation-derived sensitivity, not measured data.

Calculation sequence

1. Validate selections, active Weibull shape, temperatures above absolute zero, life scale, exposure, and mission time.
2. Calculate ln(AF) and reject acceleration, life-scale, or exposure exponents outside the workbook's supported log range.
3. Convert the valid log factor into acceleration, projected scale life, and equivalent use exposure.
4. Evaluate mission survival, failure probability, B10, and median life.
5. Evaluate Model_Status in the exact order shown below.

Outputs and interpretation

Headline outputs are acceleration factor, projected use-condition scale life, and mission reliability. Supporting values expose the logarithmic factor, equivalent use exposure, failure probability, B10, and median life. A large acceleration factor is a consequence of the entered assumptions, not independent evidence that the extrapolation is credible.

Validation and status logic

This precedence is taken from the workbook Validation!B20 formula. Invalid states return protected zero numeric outputs and must not be interpreted as physical zeroes.

Assumptions and limitations

• The same dominant failure mechanism and life distribution apply at test and use conditions.
• Temperature is the relevant accelerating stress; humidity, voltage, cycling, interactions, and changing mechanisms are outside scope.
• True acceleration changes distribution scale while Weibull shape remains unchanged.
• Activation energy is a user-supplied engineering assumption; no material or mechanism lookup table is included.
• The workbook evaluates parameters and does not fit them, test goodness of fit, or quantify parameter uncertainty.
• Long extrapolations can be extremely sensitive to small temperature or activation-energy errors.

Restrictions and non-computing states

Both Celsius temperatures must be strictly above absolute zero. Scale life and Weibull shape must be positive and all active values must stay within the published limits. The workbook also rejects individually valid values whose combined logarithmic exponent would overflow its supported numeric range.

Errors and warnings

NOT VALID blocks interpretation. CHECK leaves arithmetic available but identifies a non-accelerating temperature direction or zero activation energy. A connection or calculation-service failure is not an Arrhenius finding.

The equations, logarithmic safeguards, active-input rules, named outputs, and status precedence were verified directly against the delivered workbook, its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

• NIST/SEMATECH e-Handbook — Arrhenius acceleration — Arrhenius acceleration-factor equation and applicability.
• NIST — Physical acceleration relationships — Scale-life projection and unchanged Weibull shape under true acceleration.
• NIST SI Units — Temperature — Exact Celsius-to-kelvin offset.
• NIST/CODATA fundamental constants — Boltzmann constant in electron-volts per kelvin.