"I would expect a range of structural characteristics something like 20% (or more) for body tubes made from paper that is cheaply purchased, cheaply manufactured into tube form, and subjected to a wide range of storage and handling conditions. It's not going to be like aerospace-grade aluminums or anything."
Remember, the question is not regarding the structural integrity of the tubes/structure but a pressurization model to eject the nose and parachute section.
"More variables:
--local weather conditions, incl temperature & humidity, causing the BT to shrink or swell and changing the "grip" on the shoulder of the NC"
Can be accounted for (1st order) as the difference of CTE's of the materials. More complicated models could include the tribology factors between the fibrous and polymer surfaces.
"--NC fit, incl manufacturing variation on diameter of the shoulder, surface roughness, intentionally molded surface protrusions (like those little ribs on some shoulders), unintended molded surface protrusions (mold flash), length of shoulder, and probably more"
Notches and small protrusions can have a Hertzian contact analysis done. "Random" imperfections can be handled as a probability distribution function or Monte Carlo simulation.
"--age of BT and collective number of ejection events to which it has been subjected (abused?) already"
This is probably the most challenging of the bunch. In aerospace, we basically will wear in moving parts to 10K+ cycles to understand their fatigue properties. This would probably be handled by a probability function or Monte Carlo if done at my company. It'd likely also have human factors studies attached to it to see the types of mishandling that are likely to occur.
"--number, type, size/length, and spacing of external fins which may provide some degree of reinforcement"
Again, if we're not concerned about structural failure this is not necessary. We are only concerned about "fit".
"One of the bigger variables, over which we have no control or means to estimate, is the power/weight of the blackpowder ejection charge itself. Depending on exact components (carbon from one source does not behave the same way as carbon from another source), processing (were components powdered? to dust? were they mealed, corned, etc? how many times?), and a number of other factors (what color shirt was the chemist wearing?), blackpowder batches can have a tremendous degree of variation in thermodynamic performance, calorie content, energy release rate, and a few other things. Blackpowder manufacture today is still just as much about art as it is about science."
All said and done, one could represent the nose ejection characteristics as a function of blackpowder weight and grain size. The deflagration of blackpowder in various forms/grades has been greatly studied and I do believe analytic models do exist for it. Other small factors like the color of the chemist's shirt and what he ate for breakfast are likely to come out in the wash.
Very important variables:
Parachute section volume
Amount of powder used
Important variables:
Cross-sectional area of nose cone (F=P*A)
Basic nose cone "friction" (including CTE)
Somewhat important variables:
Mass ratio of nose cone
Vent port size
BP grain size (less important in larger rockets)
External "body forces" (aerodynamic loading, inertial loading)