Abstract
In this paper, we consider the problem of optimal
design of the multi-state parallel-series system. The
system has n subsystems connected in series and
each subsystem has a number of components
connected in parallel. The system and each
component may be in states 0, 1,. . ., M. The state of
a subsystem is equal to the state of the best
component in the subsystem. The state of the system
is equal to the state of the worst subsystem. The
state distribution of each component is known, that
is, the probability for the component to be in each
possible state is given. The state distribution of the
system is a function of the state distributions of the
components. When the system is in state i (01 i I
M), the utility of the system is represented by g Our
objective is to find the number of components that
each subsystem should have in order to maximize
the expectation of the system utility.