For exact data, every solution, , of the following system of equations maximizes the likelihood.
where:
The standard errors are the standard deviations of the estimate of the parameter. The standard errors are calculated as the square root of the appropriate diagonal element of the inverse of the Fisher information matrix.
Notation
Term
Description
Yi
retirement time for the ith system
Tij
jth failure time for the ith system
ni
number of events for the ith system
N
number of systems
Maximum likelihood (interval data)
For interval data, the maximum likelihood estimates, , satisfy the following equations:
The standard errors are the standard deviations of the estimate of the parameter. The standard errors are calculated as the square root of the appropriate diagonal element of the inverse of the Fisher information matrix.
Notation
Term
Description
Yi
retirement time for the ith system
tij
interval endpoints for the ith system
ki
number of failures for the ith system
Nij
number of failures in an interval
N
total number of systems (in each growth curve)
Conditional maximum likelihood
where:
The standard error for is:
where
with mi = ni - 1 if Yi = Tini or mi = ni otherwise
, of the following system of equations maximizes the likelihood.
, satisfy the following equations: 
is:
