It sounds from the wording of your description you are not certain twisting is the failure mode. When you find a product where the stylet will not fit inside, can you cut open the catheter, and can you tell by visual examination whether twisting of the braided tube has occurred? If it is impossible to tell by visual examination, would it be permissible to mark a straight line on the braided tubes before assembly, then when you cut open samples, you can judge on the straightness of the line inside the assembly. To draw a conclusion about correlation, you should cut open both tubes which fit a stylet and tubes which do not, and be sure there is a statistical distinction on the straightness of the lines between two groups.
I don't have any experience with braided tube. But I have worked with twisting failures arising from wire that was wound on a spool. If there is any memory in the material, where it does not want to lie flat when unspooled, you might find different behavior between the outside of the spool versus the small-radius inside turns of the spool. If your material is never spooled, well then never mind. It was just a thought. Many times, a problem appears random, but that situation is a consequence of our ignorance of how a factor is important, so no one pays attention to it and we have no data to guide our thinking. While problem-solving, I usually concentrate on discontinuities in the process, that is where you are more likely to recognize differences that catch your attention, like switching from an almost empty spool to the next full spool. Of course. if the lengths of tube are pre-cut and randomized before you get them, any valuable clues you might glean from spooling become invisible to you.
My next suggestion depends on how long is your assembly process and whether this is a 10% problem or a 1:1000 or 1:1,000,000. You only do this test once you have proven that twisting is a causal factor and you can reliably assess twisting. On a one-time experimental study, follow parts through the assembly process. At each step in the sequence, remove a part from the line and test whether the stylet can be inserted. If so, return the tested part to the assembly line. I can understand if you do not want to ship any parts handled in this experimental study since this extra handling is a deviation from your established process, so the assemblies with extra handling can be marked as scrap and sorted out at the end of the sequence. If the sequence is long, too long to study stepwise, then go to the middle step of the sequence and test with the stylet. If you find failures at the end of the sequence, but you don't find any failures at the midway point, the twisting phenomenon is happening downstream of the midway point. You have now eliminated half of the list of potential causes. Do that again, until you can isolate where in the sequence the phenomenon is occurring. If you can isolate the location where it happens, that knowledge might provide clues on how it is happening.
