Re: Some Paradox on Confidence Interval on Population Parameter!

On the other hand, if what you are really trying to measure is the
theoretical long-term average failure rate, then each day is only a
sample.
Yi is NOT a population parameter in that case, because the
"population"
parameter would be the average Yi measured over the entire population
of
days, whatever that happened to be. If you assume that the underlying
failure rate is not changing over time (at least, not over the time
that you
are collecting data), and that failures on one day do not depend upon
failures on any other day, then you might assume that the number of
failures
in any given day follows a Poisson distribution, and what you are
really
trying to estimate is the Poisson parameter lambda for the daily
number of
failures. You certainly have an appropriate confidence interval in
that
case, which will depend upon how many days you have measured.>>

This sounds quite appropriate. So Yi is no longer population
parameter. It becomes a daily sample point. Hence there is an
assumption that there exist a population parameter F which we dont
know and is the TRUE failure rate.

So the whole thing becomes like that of a control chart, where Yi are
individuals observations plotted. Say we have past 100 days Yi, using
this we can construct the upper control limits.

Lets say now we continue plotting from day 101 and so on,
1. How do we know there is indeed a SHIFT in the failure rate?
2. Do we need to update the control limits after every 100 days?

Thank you!

.

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