Lets look at one case, not scientific, just my observation, where I have a
compact fluorescent above the staircase. This fixture is only turn on about
5 seconds most of the time which is just enough for me to go up or down the
staircase and once or twice we leave it on for about a minute or two but its
switched perhaps 20 times in a day and burn out is around 6 month but not
longer than a year and that seems to be the case for the last 10 years. This
comes out to about 10.5 to 21 hours which is ridiculously short burn time.
With the same duty cycle my incandescent lamp will last 2-3 years. In other
words it will take 2 to 6 compacts by the time one incandescent lamp is burn
out and you don't even have to do the math for this situation. I do it
because I have converted to compacts and have cases of this stuff and we
have no more 60W incandescent lamps in the house. I also have similar short
burn life for the circle-lines in the bathrooms but those lamps run about
$10 per pop. (The ones in the bathrooms are switched a lot but no more than
10 minutes on at any time.) In my area we can't even dispose the
fluorescents in the regular trashcan so it requires extra handling and
energy to recycle both the lamp and the electronics. As suggested I'll look
into the "cold cathode" CFLs.If you have duty cycles as short as five seconds and you turn your
lights on and off an average of twenty times a day, you should stick
with a halogen or incandescent bulb. Cold cathode CFLs are another
option but as Don points out, these lamps are currently available only
at the lower end of the wattage scale. A 5-watt TCP CC-CFL produces
just 230 lumens or about the same amount of light as a standard
25-watt incandescent. In a six bulb bathroom vanity light that may
not be a problem but for a single socket stairwell fixture it would be
a rather poor choice.

Cheers,
Paul

I can see that others have been down this road. I also have a small
"under the counter" light that fails regularly too. The bulbs last for
maybe 6 months at most. They are the T F8 style bulbs. I think they are
9 or 10 inches. I am going to replace the lights completely and go with
what I had before. They may not have been energy savers, but they sure
lasted for years before I had to change them. That alone is going to
save me a lot of money at the rate I am currently spending on bulbs,
ballasts, etc.

Thanks everyone for all the great advice. I appreciate it. Great group!