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Why the differences in hashing power and hashing accepted ?
I use 1 of those thunders and where your password is I use d=4096 and seems to run about the same as cgminer show,I also have clk speed at 348 rather than 328 it should be
I think the most likely scenario is that your miners are averaging the hashrate over a different timespan than the site is. Our reported hashrate is for the last 15 minutes, whereas if I recall correctly, cgminer reports the average hashrate since the miner was turned on. You could have just had an unlucky period of time. Do you have a high latency connection? You could be submitting many stale shares, which could also account for the disparity in hashrate.
As far as tuning, Our Thunder X6's found the best hashrate at d=2048, although d=4096 is also a good choice if you want to reduce bandwidth used. The automatic work restart testing worked the best for those miners, so I would not recommend setting a static restart interval.
With cgminer you need to use quotes or else it will assume the second password argument is another command line parameter. So use -p "d=4096 n=Zeus01" instead.