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I don't think the duration of the silence should scale with MR, it doesn't sound like much but you can easily hit 200 MR, giving him the ability to lock enemy champions down to 3 second windows of ability use. Shrapnel bomb, silenced 3 seconds. 6 seconds later, blam 1 enemy silenced 3 seconds, 6 seconds later, SB is back up Blam! silenced 3 seconds. A flat 1.5 seconds with the can't efffect for 6 seconds would probably be sufficiant to generate the disruption your intending him to have. Have the MR contribute to bonus damage if you'd like him to benefit off of that build.
Also since your building up a lot of MR from how it seems he's structured, consider changin the bonus damage on his passive shots to (+.15 bonus AD) Apart from a Maw of Malmortius there's no damage + MR items, so it'll give him a more viable scale to work with, insinuating he's meant to be a MR/Damage build. It does however provide him with a straight damage build which wouldn't work well with an MR build style.
In a pure damage build (300 bonus physical damage) he's generating an additional 45 damage for the dot per shot. I'd also consider making it a set amount of damage over 3 seconds. His end passive at your base with this new ratio over 3 seconds would be 135 damage/3 seconds = 45 dps on top of his auto attacks vs your complete origional write up at my ratio which would be 135 dps for 3 seconds = 405 damage over 3 seconds on top of his auto attacks which are hitting for about 400 damage apiece at this point on a pure damage build.
I really like the thought of a dedicated MR damager, there really isn't one. I know he's not really going to hit 300 damage and 200+ MR, so he's got options but I think altering the passive damage per shot would solidify that he's supposed to build MR primarily, with some damage on the side.
I think his R might work a bit better as a 5 seconds shield flat, that absorbes up to X/X/X (+ MR) damage done to and inside it. Scaling the MR at .25 isn't going to contribute much given the enormous base value of the shield itself. Making it a bubble that absorbs damage makes it great at absorbing a lot of focus shot damage or general teamfight AoE's. It could also straight up block targeted projectiles like Caitlyn's Ultimate.