What is the life span of Arduino nano ?
Flash memory can degrade with time and the program can become corrupted or lost - however:
Reliability Qualification results show that the projected data retention failure rate is much less than 1 PPM over 20 years at 85°C or 100 years at 25°C.
Wet electrolytic capacitors dry out over time. When resurrecting old hardware the first thing you do is replace all the electrolytic capacitors. Depending on how much you de-rate them they could last a few years, or tens of years, before they need replacing. If possible avoid them and use MLCC and tantalum instead since they never dry out.
The biggest problem of any kind of industrial installation is that of the environment. Corrosion from airborne contaminates (water, etc) will destroy the PCB (oxidise the copper of the tracks, etc) long before the components have worn out. Proper sealing, and even "potting" in extreme environments, is essential for longevity.
Another important thing to remember is to factor in a certain number of failures over the intended lifetime of the product. If you find you will be needing to replace portions of a unit on a semi-regular basis then make those portions easy to replace. For instance, it may be more cost effective to routinely replace a board after 5 years rather than have to replace the entire unit every 8 years because the board that has failed is impossible to replace (e.g., it's potted).
As others have mentioned you shouldn't be using an Arduino of any form in a product. Instead you will be designing (or paying someone to design) a dedicated PCB. During that design phase extra steps can be taken to make the board more rugged - such as wider tracks and thicker copper that will take longer to corrode; increased clearances that will take longer for corroded copper to bridge; components chosen to have a suitable MTBF, etc.
Many components have a "service life" or "lifetime" quoted. This is especially important for components such as electrolytic capacitors. For instance, the EEUFR1C471 from Panasonic (to pick one at random) is quoted as 6000 hours at 105°C. 105°C is the maximum temperature you can run it at, so the quoted service life is a minimum at worst case parameters. 6000 hours is, of course, just 250 days (about 8 months or so) - but of course that is worst case, and the minimum guaranteed time (they guarantee that it will run for at least 6000 hours at 105°C). Run it at a lower temperature and you get longer life out of it.