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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