Is the probability of hard drive failure proportional to the time it has been running?

I want to buy some drives to backup my files. I will spend a few days backing them up and for the next months the drives will probably be unused and I will keep them just in case I need to restore from the backups. Is it okay to buy cheap refurbished hard drives then as I won't use them frequently? Are refurbished hard drives and hard drives in general that are used 10 days a year as likely to fail after e.g. 2 years as those that run constantly?