# average event time if event did not occur to everyone

How to determine the average or expected time duration of an event to a group statistically correct, if this event has not happened to everybody yet?

One could consider only those to whom the event occurent and simply to statistics for this sub-group, however then it is neglected that there is the complementary sub-group which provides reason to shift the expected event occurence time to the right.

Example: In a group of people owning a smartphone, we want to find out for each brand, when on average the display breaks. Of course, there are people who posess a mobile phone that did not get damaged (yet?). Shall we include this sub-group as well, and how?

Sample data:

Person | display broke after x years
1      | 1.0
2      | 1.5
3      | 2.0
4      | never and has the phone for 0.5 years
5      | never and has the phone for 3.0 years


Only considering the first 3 persons who suffered a phone damage, we might think, the expected lifetime is 1.5 years, however there is a person (nr 5) who has his phone for 3 years and no problem occured (yet?). Shall we even consider person nr 4 that supports the thesis that the phone will at least last for 0.5 years?