  This manuscript studies the preventive replacement policy for a series or
parallel system consisting of n independent or dependent heterogeneous
components. Firstly, for the age replacement policy, Some sufficient conditions
for the existence and uniqueness of the optimal replacement time for both the
series and parallel systems are provided. By introducing deviation costs, the
expected cost rate of the system is optimized, and the optimal replacement time
of the system is extended. Secondly, the periodic replacement policy for series
and parallel systems is considered in the dependent case, and a sufficient
condition for the existence and uniqueness of the optimal number of periods is
provided. Some numerical examples are given to illustrate and discuss the above
preventive replacement policies.
