Those who took a course on logics at university know that from a false statement anything follows. Michael Slocum et al. probably don't. Otherwise, they would not be so proud of their "improvements" [1] to the following formula of ideality:
Ideality = (the sum of useful functions)/(the sum of harmful functions + cost) (1)
Indeed, who told them that this formula is true ? No Altshuller book contains it. Moreover, Altshuller never discussed "the degree of ideality". He only spoke about ideal machine, ideal final result, etc. He never proposed a measure of deviation of the real machines from the ideal ones. This did not seem to interest him. Or may be he felt that a measure of ideality would not be as useful as the notion of ideal machine.
However, somebody in Russia devised such a formula and brought it to America as a "portion" of TRIZ (Tsourikov ? Zlotin ? or somebody else ? I could not find the source^{1}). The formula is pretty idiotic but it is not a legitimate language in science. That is why, it suffices to say that it is simply false.
Indeed, what does "the sum of useful functions" mean ? Are useful functions numbers which can be added up ? Should not one first define the measure of usefulness of a useful function before speaking about "the sum of useful functions" ? Similarly, should not one first define the measure of harmfulness of a harmful function before speaking about "the sum of harmful functions" ? The anonymous authors of the "formula" of ideality did not address these issues.
Moreover, they tacitly assumed that the numbers of both useful and harmful functions are finite. That all such functions can be revealed and enumerated. May be it is true for useful functions. But you can never know all harmful functions that system has. There could be hidden harmful functions undiscovered for long time. And at no point in time you can be sure that discovered all harmful functions and no surprises will happen in the future.
In addition, I have a gut feeling that if the aforementioned measures are ever consistently defined, they will have to have some dimension (as mechanical forces have the dimension of Newtons and electrical currents have the dimension of Ampers). I am not sure that usefulness of useful functions can be measured in the same units as harmfulness of harmful functions. They might be measured in different ones. Say, the usefulness of useful functions could be measured in Zlotins, whereas the harmfulness of harmful functions could be measured in Tsourikovs. Then, the above formula of ideality would measure it in (Zlotins/Tsourikovs), which is, obviously, wrong. Because the degree of ideality (as any degree of anything) has to be dimensionless.
In short, there are many indications that the above formula of ideality is false. And from false anything follows, including the formula of Michael Slocum et al. [1].
The fact that it also has no meaning can be shown as follows. Consider the main relationship of the axiomatic design [2]:
{ 

} 

[ 

]  { 

} 
where FR1, FR2, FR3 are functional requirements, and DP1, DP2, DP3 are design parameters.
All these variables and coefficients may have different dimensions. Indeed, consider, for example, a faucet that mixes cold and hot water. In this case FR1 is the range of water flow that faucet can provide. (Hence it is measured in litres/sec.) FR2 is the range of water temperature that faucet can provide (which is measured in degrees of Celcius). FR3 is nothing in this case.
Analogously, DP1 is the range of possible angles of the handle that controls the cold water flow. DP2 is the range of possible angles of the hot water handle. Both are measured in angular degrees. Hence, A11 and A12 have dimension of litres / (sec · angular degree). But A21 and A22 have dimension of Celcius degree/ angular degree.
Thus, expression A11 + A22 + A33 has as much sense as ( 2 apples + 5 oranges + 3 peaches). Nevertheless, this is precisely what Sir Michael et al. propose as the numerator of the formula of ideality [1] ! The proposed denumerator is no less ridiculous.
To say that anything follows from false is to say not the whole truth. The whole truth is that from false one can derive both true and false conclusions. It is up to a person to decide which way to go. Mr. Slocum et al. opted to derive false from false ! It does not reflect well on their reputation.
R E F E R E N C E S:
1. Michael Slocum, Catherine Lundberg, Katrina Walter, "Reangularity, Semangularity, and Ideality",
The June 2003 issue of the TRIZjournal.
2. Nam Pyo Suh, "The Principles of Design", (Oxford University Press, 1990).
Addendum
^{1} After this article was published I learned that the formula was proposed by Zlotin and the idea of measuring the degree of ideality was imposed on Altshuller in the 1980s, who resisted it. An argument on the issue that took place in Petrozavodsk between Altshuller on one side and Zlotin, Litvin, etc. on the other was taped. From the tape it is clear that Zlotin & Co. were taking Altshuller for a dumb when he resisted the idea of the specific ideality promoted by Zlotin & Co. and the idea of measuring ideality on the whole. In fact he was just wiser than his opponets.