# 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:

### Notation

TermDescription
σspecified value for the scale
βspecified value for the Weibull shape
specified value for the intercept
β1specified value for the slope
γ0standardized intercept
γ1standardized slope

## Percentile and slope specified

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)

### Notation

TermDescription
σspecified planning value for the scale
βspecified planning value for the Weibull shape
β0 intercept
β1specified planning value of the slope
tspecified planning value of a percentile
Φ-1(p)inverse CDF of the chosen distribution
pproportion of failures at stress level x
xstress level

## Percentile and intercept specified

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)

### Notation

TermDescription
σspecified planning value for the scale
βspecified planning value for the Weibull shape
β0specified planning value of the intercept
β1slope
tspecified planning value of a percentile
Φ-1(p)inverse CDF of the chosen distribution
pproportion of failures at stress level x
xstress level

## Two percentiles specified

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)

### Notation

TermDescription
σspecified planning value for the scale
βspecified planning value for the Weibull shape
β0intercept
β1slope
t1specified planning value for a percentile
t2specified planning value for a percentile
Φ-1(p)standard inverse cdf of the chosen distribution
p1proportion of failures at stress level x1
p2proportion of failures at stress level x2
x1stress level
x2stress level
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