RE: The Poisson process and Lognormal action time.
This kind of problem arises a lot in the actuarial literature (a
process for the number of claims and a process for the claim size),
and the Poisson and the lognormal have been used in this context - it
might be worth your while to look there for results.
Glen
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This is a very general and important event process. It is also used to
describe
the general failure-repair process that occurs at any repair shop. The
Poisson
is a good approximation of the arrival times of equipment to be repaired,
and
the log-normal is a good approximation of the time it takes to repair it.
>From an operations standpoint, the downtime is approximated by the
exponential
distribution (occurrence) and a log-normal repair time, which includes
diagnosis,
replacement and validation.
In the Air Force (1982-1995) where the reliability and maintainability of
equipment has to be
characterized, the means are determined and used in a form called
availability.
We never got beyond the use of availability. They never got into the
distribution and confidence interval aspects.
As a general approximation, the log-normal distribution approximates human
reaction times to events.
DAHeiser
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