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approach, the authors have established that the performance evaluation is more
accurate by distinguishing among different failure modes of each machine.
The remainder of this paper is organized as follows: Section 2 introduces the
problem studied with the different assumptions and notations. This is followed
by describing a transformation. In Section 4, we detail the equivalent machine
method to evaluate the system throughput. Several numerical experiments are
presented and discussed in Section 5. Finally, Section 6 summarizes the guidelines
of our contribution.
2 Problem Description and Assumptions
The production line considered in this paper consists of
K
unreliable machines or
stations separated by (
K
1) intermediate buffers (see Figure 1). The products
flow continuously in a fixed sequence from the first machine to the last one. It is
assumed that there are always available products at the input of the system and
unlimited space for material storage at the output of the last machine. In other
words, the first machine cannot be starved and the last one cannot be blocked.
The failures are operation-dependent, a machine can not fail while it is starved,
blocked or idle. All times to failure and times to repair are independent and
exponentially distributed. If no products are available in the upstream buffer
B
j−
1
the machine
M
i
will be starved and when the downstream buffer
B
j
is
full, it will be blocked.
−
Fig. 1.
A
K
-machine (
K −
1)-buffer serial production line
Each machine
M
i
has
F
i
failure modes. It can be operational, starved, blocked
or failed in a certain mode. The processing times of the different machines are
not necessarily identical.
λ
im
and
μ
im
are, respectively, the failure and repair
rate of machine
M
i
in mode
m
. We assume also that an operational machine
can fail in only one of its failure modes.
The different notations utilized in this paper are defined in Table 1.
