Random shutdown since El Capitan install

Since installing El Capitan, my 27-inch late 2009 iMac with 2.8 GHz Intel Core i7 and 16GHz RAM has been going to a gray screen and shutting down at random times. So far I've been able to restart it, but it's very disconcerting since there is no advance warning. I've tried resetting the SMC and NVRAM, as well as starting in safe mode and reinstalling the OS all to no avail. It keeps doing the same thing. I've searched for anyone with similar problems in the support community with no luck. Does anyone have any ideas or suggestions? Thanks very much for any help you can offer.