[EMAIL PROTECTED] wrote:
> We track a metric that consists of the fraction of hours that a machine
> was not running during a week. The numerator is the number of hours
> not running and the denominator is the number of hours running plus the
> hours not running. This is a weekly metric. I wish to calculate
> control limits on this metric such that I can pinpoint if in a
> particular week the machine is out of control. What is the
> distribution of this statistic so that I can calculate the lower and
> upper limits? or should I just estimate the distribution with
> historical data and calculate the limits from there? What do you
> recommend.
Fractions are B distributed, at least if you have a small sample number.
You can calculate a confidence interval around a long time mean and
compare the measure of a week with it and so decide whether its fraction
of non-running time is exorbitantly high or low (outside the CI). Such a
decision would be mathematically exact I think. Maybe it is also possible
to replace B with an approximately similar N which
is easier to handle; that depends on whether the number of hours in a week
is hight enough and, I�m not sure now, whether such an approximation is
useful at all (depends on similarity of N and high sample number B).
Bye, Till
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