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Throughput Evaluation of Buffered Unreliable
Production Lines with Machines Having
Multiple Failure Modes
Yassine Ouazene, Alice Yalaoui, Hicham Chehade, and Farouk Yalaoui
Laboratoire d'Optimisation des Systemes Industriels (UMR-STMR-CNRS 6279)
Universite de Technologie de Troyes, 12 rue Marie Curie, CS 42060
10004 TROYES, France
{
yassine.ouazene,alice.yalaoui,hicham.chehade,farouk.yalaoui
}
@utt.fr
Abstract.
This paper presents an analytical method to evaluate the
system throughput of buffered serial production lines. The machines are
unreliable and each machine can have more than one failure and repair
modes. The flow of parts through the production line is considered as a
continuous flow of material. The proposed method is composed of two
main steps. The first one consists of transforming each machine into a
single failure and repair mode machine based on a well-known aggrega-
tion technique. In the second step, the system throughput is evaluated
using an approximate approach called Equivalent Machine Method. This
method is based on the analysis of the different states of each buffer us-
ing birth-death Markov processes. For each buffer, the birth and death
ratios are defined taking into account the probabilities of blockage and
starvation of its related upstream and downstream machines. Then, each
original machine is defined by its equivalent production rate considering
its processing rate, its availability and the influence of the buffers lim-
itations and the other machines. The system throughput is defined as
the bottleneck between the equivalent production rates. This method
considers both homogeneous and non-homogeneous production lines.
A comparative study based on different test instances is presented and
discussed. The obtained results prove the effectiveness and the accuracy
of the proposed method comparing with both simulation and aggregation
methods.
Keywords:
Manufacturing Systems, Performance Evaluation, Through-
put Analysis, Equivalent Machine Method, Multiple Failure Modes.
1 Introduction
An accurate estimation of a production or transfer line performance is necessary
for the optimization of its design and utilization. A system performance can be
expressed using many measures such as: machines availability, work in process
and throughput. This last performance measure can be defined as the number
