Extended optimal replacement policy for a system subject to non-homogeneous pure birth shocks

► We study the optimal replacement policy with general repairs. ► Use shocks occurring to a non-homogeneous pure birth process (NHPBP). ► Include two types of failures: type-I failure (minor failure) and type-II failure (catastrophic failure). ► Optimize bivariate replacement policy (n, T) under a cost structure. ► Present numerical examples.