🚀 go-pugleaf

We have purchased a simplified model of a complex kinetic chemical reaction.
This model uses as inputs data from an industrial scale process (and the data
from that process has all the usual errors associated with real-life data:
noise, drift, bias, etc).

The model produces six outputs (concentrations) that can be directly compared
to composition analyses from the plant (which are also subject to all sorts
of errors).  There is one tuning parameter (that has a semi-theoretical basis)
for the model that adjusts the production of one key component (and indirectly
all the other concentrations - there are a total of 19 predicted compositions).

The problem is when we tune the model to match the plant's production of the
key component at one set of (historical) operating conditions, it cannot 
accurately predict even the key component's concentration at other sets of
operating conditions.

Naturally, we think that the model has been oversimplified to the point of 
unusability, while the view of the company that developed the model is that
our plant data is too noisy.  Their suggested approach is to use an average
of the plant data inputs to develop an average tuning parameter value and use
that.  Their justification for this is that the variation in the predicted 
compositions from the model with an "average" tuning parameter should be less 
than the variation in the plant's measured compositions.  (Even if the
variations do turn out this way, I don't think it would take a model with a 
theoretical basis to get this sort of behavior!)

We can analyze the variation in a large set of plant data.  We can also tune 
the model to match the key component concentration for every point in the set
of data.  If we then define a function which is the sum of the differences 
between the six plant concentrations and the six predicted ones, we would know
the variation in the defined function, the variation in the tuning parameter
and the variation in the plant data inputs to the model.  

What we would like to say, based on the above information is something like:
                                                                          	
"Ah hah!  Since the variation in the tuning parameter is larger (or has a 
larger effect on the defined function) than any of the variations in the plant
data, obviously the model is not valid!"

Is there any way to reach this conclusion in a valid statistical way? 
Especially given the fact that we do not know the theoretical relationships 
between the plant data inputs to the model and the model outputs?

Any help will be *most* appreciated (and might contribute to my job security!).
Please reply here or to to james_cox@Kodak.COM (which may or may not actually
get to me.)