Acceleration Factor Calculators

Calculate acceleration factors using industry-standard reliability models

Arrhenius Model

Used for temperature acceleration in reliability testing. Models the relationship between temperature and failure rate.

Formula:

AF = exp[(Ea/k) × (1/Tuse - 1/Ttest)]

Activation Energy (Ea)(eV)

Typical range: 0.3-1.5 eV for electronic components

Use Temperature(°C)

Test Temperature(°C)

Coffin-Manson Model

Used for thermal cycling fatigue. Models the relationship between temperature range and fatigue life.

Formula:

AF = (ΔT_test/ΔT_use)^C

Test Temperature Range (ΔT_test)(°C)

Use Temperature Range (ΔT_use)(°C)

Coffin-Manson Coefficient (C)

Typical range: 2-5 for electronic components

Norris-Landzberg Model

Plastic strain range model accounting for thermal cycling frequency, temperature range, and maximum temperature effects. Used for solder joint fatigue analysis.

Formula:

AF = (f_field / f_test)^-m × (ΔT_field / ΔT_test)^-n × e^(E_a / k × (1 / T_max,field - 1 / T_max,test))

Frequency Factors

Field Frequency (f_field)(cycles/unit time)

Thermal cycling frequency in field conditions

Test Frequency (f_test)(cycles/unit time)

Thermal cycling frequency in test conditions

Frequency Exponent (m)

Typically 1/3 (0.333) for SnPb eutectic solder

Temperature Range Factors

Field Temperature Range (ΔT_field)(°C)

Temperature range in field conditions

Test Temperature Range (ΔT_test)(°C)

Temperature range in test conditions

Temperature Range Exponent (n)

Typically 1.9 for SnPb eutectic solder

Maximum Temperature Factors

Field Maximum Temperature (T_max,field)(°C)

Maximum temperature in field conditions

Test Maximum Temperature (T_max,test)(°C)

Maximum temperature in test conditions

Activation Energy (E_a)(eV)

Activation energy. For E_a/k = 1414, E_a ≈ 0.122 eV

Peck's Model

A form of Eyring model accounting for relative humidity and temperature effects. Combines an inverse power law for humidity with the Arrhenius equation for temperature.

Formula:

AF = (RH_u / RH_t)^-n × exp[(E_a / k) × (1/T_u - 1/T_t)]

Humidity Factors

Use Humidity (RH_u)(%)

Relative humidity under use conditions

Test Humidity (RH_t)(%)

Relative humidity under test conditions

Humidity Exponent (n)

Typically 2.7 (Peck's paper) or 3 (Wayne Condra's discussion)

Temperature Factors

Use Temperature (T_u)(°C)

Temperature under use conditions

Test Temperature (T_t)(°C)

Temperature under test conditions

Activation Energy (E_a)(eV)

Typically 0.79 eV (Peck's paper) or 0.9 eV (Wayne Condra's discussion)

About Acceleration Factors

Acceleration factors are used to relate failure rates or lifetimes under test conditions to those under use conditions. They allow engineers to:

Reduce test time by using accelerated stress conditions
Predict product reliability under normal operating conditions
Compare different stress conditions and their effects
Design appropriate test plans for reliability validation