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The maintenance model for a repairable system (deteriorating or improving) under N-policy using partial sum process and geometric processes are investigated in this study. In the case of a system experiencing deterioration, it is assumed that the threshold values following repair are non-decreasing and the subsequent repair times following failure follow an increasing geometric process. For an improving system, we assume that the successive threshold values are decreasing after repair, and the consecutive repair times after failure form a decreasing partial sum process. A replacement policy is adopted by which we shall replace the system by an identical new one at the time following the -th failure. Then for each of the deteriorating system and improving system, an explicit expression for the long run mean cost per unit time under policy is derived and an optimal policy for minimizing the long run mean cost per unit time is determined analytically. A numerical example is given for deteriorating system.