After repair or replacement the operation continues. Expected number of replacements in a specified period helps to estimate costs, plan inventories etc., also some times the probability of more than a given number of failures n to occur over a period of the time will be of major interest.
As for the assumptions we have:

• Repaired to as-good-as new condition.
• MTTF and MTBF.
• The time between the n^th and (n+1)^th failure is calculated from the probability that the (n+1)^th failure will occur between t and t+dt given that the n^th failure occurred at t_n.