Components in S1 fail according to some general distribution
(the failure rate of the components is an arbitrary function of
time) while in S2 the components have constant failure rates, i.e.
the time between failures for a S2-component is exponentially
distributed. A failed component has to wait for the repair facility,
the waiting time has some general distribution (each component
has a distribution of its own). All the repair time distributions in
the system are also governed by general probability laws.
Operational behaviour of the system is studied under
certain conditions: the type of redundancy is specified to be in
parallel and the policy to be followed in the system repair is
closely fixed. A method based on supplementary variables and
Laplace transforms is developed to formulate a mathematical
model for the system. The supplementary variable technique is
used to obtain the modelšs partial differential-difference equations,
the state equations, which describe the behaviour of the system.
With the help of Laplace transforms both transient and steady-
state solutions for these state equations are found. From these
solutions reliability indices are drawn for the system.
Furthermore it is indicated that the steady-state solutions are
independent of the type of waiting time and repair time
distributions; in these solutions only the expected values of these
distributions appear. It is also shown that the steady state is
achieved under quite general conditions and that the solutions for
the steady state can be found without any exact knowledge about
the distributions of the system.
(Turun Kauppakorkeakoulu 1975. Tutkielmia.
Proceedings of The Turku School of Economics and Business
Administration, Series A II - 1:1975, 385-399).