Given a system (S) that accepts a tuple of parameters ($\alpha, \beta, \gamma \dots$ etc). These parameters affect the performance of S in a different way. For instance, decreasing $\alpha$ would improve performance of S at some rate, whereas decreasing $\beta$ has a reversed effect. How can one define a performance metric that captures the effects of all parameters in a simple, clear and correct manner.
If the system exists in reality, hence measurements can be taken arbitrarily, what approach one can use to achieve an accurate metric?
I give an example to clarify the question:
Suppose I have a sorting algorithm (A). Performance of A depends on the number of input numbers, precision of the numbers (32, 64, ...) bit, or whether they are partially sorted or not (assuming this can be quantified somehow). Let's limit ourselves to only these 3 factors. If we say A sorts 1000 numbers in 1 millisecond. This doesn't say anything about precision nor entropy of the input. How can we come up with a standard, metric, or unit to describe the performance of A using preferably a single number with a single unit so that they capture all the factors mentioned above.
