Methods and formulas for planning values in Accelerated Life Test Plan

Intercept and slope specified

When the scale σ (or Weibull shape β), the intercept (β₀), and the slope are specified (β₁), the standardized intercept is calculated as follows:

The standardized slope is calculated as follows:

Term	Description
σ	specified value for the scale
β	specified value for the Weibull shape
	specified value for the intercept
β₁	specified value for the slope
γ₀	standardized intercept
γ₁	standardized slope

When the scale (or Weibull shape), the slope, and a percentile are specified, the standardized slope and intercept are calculated as follows.

where

for location-scale models (normal, logistic and smallest extreme value)

for log-location-scale models (Weibull, exponential, lognormal and loglogistic)

Term	Description
σ	specified planning value for the scale
β	specified planning value for the Weibull shape
β₀	intercept
β₁	specified planning value of the slope
t	specified planning value of a percentile
Φ^-1(p)	inverse CDF of the chosen distribution
p	proportion of failures at stress level x
x	stress level

When the scale (or Weibull shape), the intercept, and a percentile are specified, the standardized slope and intercept are calculated as follows:

for location-scale models (normal, logistic and smallest extreme value)

for log-location-scale models (Weibull, exponential, lognormal and loglogistic)

Term	Description
σ	specified planning value for the scale
β	specified planning value for the Weibull shape
β₀	specified planning value of the intercept
β₁	slope
t	specified planning value of a percentile
Φ^-1(p)	inverse CDF of the chosen distribution
p	proportion of failures at stress level x
x	stress level

When the scale (or Weibull shape) and two percentiles are specified, the standardized slope and intercept are calculated as follows.

where:

for location-scale models (normal, logistic and smallest extreme value) and

for log-location-scale models (Weibull, exponential, lognormal, loglogistic)

Term	Description
σ	specified planning value for the scale
β	specified planning value for the Weibull shape
β₀	intercept
β₁	slope
t₁	specified planning value for a percentile
t₂	specified planning value for a percentile
Φ^-1(p)	standard inverse cdf of the chosen distribution
p₁	proportion of failures at stress level x₁
p₂	proportion of failures at stress level x₂
x₁	stress level
x₂	stress level