Does lifetime of tungsten incandescent lamp shorten by every turning on, directly connecting to electric grid, ie not using special device to turn it on smoothly, and how much? It was said to us in school that it shortens its lifetime.
How much it (lifetime shortening) is compared to lifetime shortening by stable ligthting? If a lamp user goes away from a lamp, planning for some time of absence, how much time of absence worth turning the lamp off and then on, for the time of absence?
When it is too long, it worths, because saved electricity is more expensive than the increase of price by having to buy new lamps more frequently (because of such behaviour). When the time is very short, it also worth, because lamp does not get cooled and do not get shock.
Do not take in account that frequent flickering causes decreased efficiency of getting light per amount of used power. (Ie if user for some reason makes frequent flickering, calculate only price of electicity and price of lamp, do not calculate amount of light produced; and it anyway produces heat efficiently and heat+light may be goal of user, anyway, consider it is ok for him since he does so).
I have found also confirmation of that the lifetime shortens in an answer on this site: https://electronics.stackexchange.com/a/214397 :
During rapid switching the filament would not cool completely before the next switch-on so it would not be stressed so much. The longer the 'off' periods the harder it is for the lamp.
My domestic experience was that lamps on dimmer switches lasted 'forever' relative to the other lamps in the house. This was due to the rotary dimmer being turned up over, say, half a second and gradually increasing the current while the element warmed up. There was no sudden inrush current.
And this question is similar to that question, but in content part of the question it is asked about 120 hz flickering. And an answer there is already accepted. And the 2 answers there do not answer about how much the lifetime shortens, ie there is no formula nor links to investigation result papers are given.