Re: time series with binary data

On 13 Nov 2005 23:22:39 -0800, "gauger" <ulrich.gauger@xxxxxxxxx>
wrote:

> Hello NG,
>
> I am reflecting the following problem:
>
> Given a set of machines. These machines are assessed each day (say for
> 90 days) as working (= 1) or not (=0).
> Hence I get series of length 90 consisting of 0s and 1s.
>
> For these series I want to calculate a kind of index with the following
> properties:
>
> a machine that works every day gets the index 1,
> a machine that never works gets the index 0.
>
> (These are the easiest cases).
>
> Furthermore, a machine that works every second day is much better than
> a machine that works for 45 days correctly and for the other 45 days
> not at all.
> Furthermore I want to specify (in advance) a "critical value" for the
> longest period of "non-working" that is accceptable (say four days). A
> machine that exceeds this number is bad. But not as bad as a machine
> that only every third day...
>
> Has anybody any idea?

See Bob's post for the general picture. Where are the costs?

You seem to want to count intervals of "down-time"
in a non-linear way -- penalizing a sum that is made up
of fewer, larger numbers. That suggests that you could
compute the *square* of the down-times, and total them.
Of course, other transformations could be checked, to see
what gives the sort of equivalency that you want, between
number of intervals and their lengths.

Between 0 and 1? - The biggest sum of squared times
happens with 90 days "down", or "3600". It would be a
fairly natural number to take the square root of that sum
of intervals-squared, if you wanted a numerical index with
a "dimension", namely, with a maximum of 90 days.

To put that between 0 and 1, divide it by 90.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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