Number of faults a system can withstand without repairs
  We consider the following scheduling problem. A system is composed of $n$ processors drawn from a pool of $N$. The processors can become faulty while in operation and faulty processors never recover. A report is issued whenever a fault occurs. This report states only the existence of a fault, but does not indicate its location. Based on this report, the scheduler can reconfigure the system and choose another set of $n$ processors. The system operates satisfactorily as long as at most $f$ of the $n$ selected processors are faulty. We exhibit a scheduling strategy allowing the system to operate satisfactorily until approximately $(N/n)f$ faults are reported in the worst case. Our precise bound is tight. 
Michel Goemans, Nancy Lynch, Isaac Saias