Here is a great article from EarthSky.org about the upcoming changes to the tornado warning system in Missouri and Kansas. I tend to agree with the author, and others I've talked to, that I'm not sold that this will be a positive change. I feel like there is still enough ignorance about the difference between a watch and a warning, that three tiers of warnings may just confuse people more.
I agree a change is needed, the Joplin MO tornado proves that. Many people there flat out ignored the warning and the first siren, but took interest when the second tornado siren sounded. I feel that the biggest issue here is you can't care more about someone's safety than they do and affect it. I'm not so sure a "tornado warning" versus a "particularly dangerous situation tornado warning" is going to do any better reaching the target group.
I think my cynicism comes from the complacency a good percentage of the public has about severe weather, and their lack of accountability for personal safety. I hope I'm wrong, and this turns out to be a great improvement.
The bottom line is this: If there is a tornado warning for your area, there is a higher probability you will die if you don't do something to protect yourself. Also, it's not the tornado siren's job to keep you safe. It's your job to keep you safe. If you don't own a NOAA All Hazards Radio, you aren't doing enough to protect you and those around you.
Be safe.