A discussion on “A bivariate optimal replacement policy for a repairable system”

In this short paper, a bivariate optimal replacement policy for a repairable system with a geometric process maintenance model is discussed. Zhang Zhang, Y.L., 1994. A bivariate optimal replacement policy for a repairable system. Journal of Applied Probability 31, 1123–1127] and Sheu Sheu, S.H., 1999. Extended optimal replacement model for deteriorating systems. European Journal of Operational Research 112, 503–516] obtained different expression of the long-run average cost per unit time (i.e. average cost rate) of the system respectively. We show that both of their results are correct, therefore, Sheu’s comment (1999) on the result of Zhang (1994) is wrong.