Most studies on optimal maintenance policies concentrate
on one-unit systems. In many practical situations, however,
systems consist of groups of identical units. By replacing
groups of failed units instead of replacing failed units
individually, cost reduction can be realised. This cost saving,
known as the economy of scale, results mostly from the quantity
discount or reduction of maintenance set-up cost per unit.
Since, in this thesis three maintenance replacement models for
multi-component system are considered: Model 1. We consider a
two-phase maintenance policy for a group of identical repairable
units. We define the time-interval (0, T] as the first phase,
and the time interval (T, T+W] as the second phase. As
individual units have two types of failures. Type I failures (
minor failures ) are removed by minimal repairs ( in both
phases ), whereas type II failures ( catastrophic failures ) are
removed by replacement ( in the first phase ) or are left idle (
in the second phase ). A group maintenance is conducted at time
T+W or upon the k-th idle, whichever comes first. Model 2. We
consider a generalized age and block replacement policies for a
multi-component system with failure interaction. The i-th
component ( 1 <= i <= N ) has two types of failures. Type I and
type II failures are age-dependent. Type I failure ( minor
failure ) is removed by a minimal repair, whereas type II
failure ( catastrophic failure ) induces a total failure of the
system ( i.e. failure of all other components in the system )
and is removed by an unplanned ( or unscheduled ) replacement of
the system. For an age replacement maintenance policy, planned
(or scheduled) replacements occur whenever an operating system
reaches age T, whereas in the block replacement case, planned
replacements occur every T units of time. We also consider the
total alpha discounted cost for each policy. Model 3. We
consider a generalized age and block replacement policies for a
multi-component system with shock type failure interaction. This
policy is similar to model 2, but the occurence of failures
comes from shocks and have two types of failures. Type I
failures and types II failures are number dependent. The aim of
this thesis is to find the optimal replacement policy which
minimizes the long-run expected cost per unit time under certain
conditions for each model.