An optimal replacement policy for a system with finite spares

This paper develops a new replacement policy for a system with multiple spare units. An optimal replacement period is determined by maximizing the mean time to failure of the system. We show that there exists a finite and unique optimal replacement period T
k
for units with strictly increasing failure rates. We also proof that the optimal replacement period for a system with spares is decreasing in k, Furthermore, an algorithm is presented to get the optimal replacement period and a numerical example is given to illustrate the result. with strictly