In article <[EMAIL PROTECTED]>,
Till Siebert <[EMAIL PROTECTED]> wrote:
> [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
I thought of using a binomial distribution but it did not seem right to
me. I am more inclined to think it is one of those maintenance
distributions such as weibull, etc. The thing is that I am combining
two measures in one: I am combining time to repair and the frequency
of failure. Thus, if in a week the machine goes down twice and it
takes 2 hours to repair, then my total downtime is 4 hours. Then what
I am tracking is a fraction: 4hours/total production time. Who knows
what distribution this follows? Is it the binomial?
Lenin
>
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