Are there statistics showing the relationship between safety and the age of aircraft?
I could not find statistics, so I parsed the data available on https://aviation-safety.net/database. This site does have a statistics page, but it does not have an answer to your question.

I'm not a statistician so I'm sure there are much better ways to crunch and graph this data, but the raw data I found was:


The data includes 5075 crashes from the years 1919 - 2019.
The mean aircraft age is 15.58 years. This age is the age of the particular aircraft involved in the crash, not the "age" of the aircraft's type.


I did not normalize the data in any way, so take it with a grain of salt and except some skews and outliers (for example, a 75 years old DC-3 crashed earlier this year - https://aviation-safety.net/database/record.php?id=20190121-0). On the other hand, crashes in the early years will naturally skew the data, as every aircraft that crashed was new at the time of the crash.