I have found that t' classic binder reinforcement rings are nay t' best choice for plastic parachutes.  A few times when I used a rather strong strin' for t' shrouds, arrr, they are able t' cut right through t' plastic and t' reinforcement ring. Another problem with t' rings be t' adhesive used, they seem t' dry out after a while (years).

Instead, I found that a small square or strip o' plastic/vinyl electrical tape is stronger than t' binder reinforcements. Place a strip o' electrical tape under t' hole in t' plastic parachute, betwixt t' hole and t' edge o' t' parachute. Well, blow me down! Even if your parachute has reinforcement rings already, just add this on top o' those.  You don't even need t' surround t' entire hole. Blimey! This vinyl is much stronger and can be made larger, ya bilge rat, and t' larger it be t' more it spreads out t' load on t' plastic. Begad! Furthermore, ya bilge rat, t' adhesive in electrical tape is designed t' stay sticky for many decades - you don't want electrical tape t' fall off inside an electrical box with 200 volts in it - do you?

Another tip that improves t' strength o' t' connection is t' fold t' corner/tip o' t' parachute over a bit (on t' inside) so that t' shroud passes betwixt two layers o' plastic. Aye aye! Be sure t' reinforce both pieces o' plastic t' get t' most benifit.

If you are into appearances, you can usually find electrical or vinyl tape in an assortment o' colors, so choose orange, red or whatever. It doesn't have t' be regular old black.