__How to correctly plot performance curves__

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*Y. B. Karasik, *

Thoughts Guiding Systems Corp.,

Ottawa, Canada.

e-mail:karasik@sympatico.ca

As it was pointed out in the other article, performance curves in
the performance curves database are plotted incorrectly.
They do not take into account that performance characteristics may conflict with each other.
Hence, at the same point in time it is possible to have systems with significantly different values of performance.

For example, car's fuel economy conflicts with its weight and size.
Hence, it is possible to build several cars simultaneously with very different weights and sizes, which results in very different fuel economy.
Taking into account all these cars when plotting evolution of fuel economy over time is incorrect.
One has to take into account only those cars, which have the same (or close enough) weight and size.

Thus, to correctly plot a performance characteristics vs time, one has to fix the values of other characteristics,
with which it conflicts.
Without a loss of generality we can speak about plotting vs time any characteristics, not performance only.
Suppose that characteristics *C*_{1} conflicts with *C*_{2},...,C_{k} at any instant *t*
within a time interval, over which *C*_{1} is going to be ploted.
Then to correctly plot it, one has to fix the values of *C*_{2},...,C_{k} over this interval.

In practice it is impossible as nobody builds systems with exactly the same values of
*C*_{2},...,C_{k}. But in many cases it is possible to identify systems with values
*C*_{2},...,C_{k} close enough.
For example, for any sub-compact car values of size and weight are close enough.
The same holds for compact, midsize, and large cars.

Plotting *C*_{1} vs time for not exactly the same sets of values of *C*_{2},...,C_{k}
but for sets close enough is the best what can be accomplished in practice for systems that are always produced in a fixed set of categories.

Unfortunately, there could be systems, which are mostly produced in one category, which is changing over time.
I don't have an example of such a system yet but
imagine that just large cars are produced in the 1920s, then just mid-size cars are produced in the 1930s,
then just compact cars are produced in in the 1940s, etc. For such systems, which are always produced in one changing over time category,
it is impossible to plot a performance curve.
The same holds for systems produced in several categories
if the sets of these categories change over time and different sets have no category in common.