Production quality performance in manufacturing systems processing deteriorating products

Article (PDF Available)inCIRP Annals - Manufacturing Technology 64(1) · May 2015with 80 Reads
DOI: 10.1016/j.cirp.2015.04.122
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Abstract
In several manufacturing contexts including food industry, semiconductor manufacturing, and polymers forming, the product quality deteriorates during production by prolonged exposure to the air caused by excessive lead times. Buffers increase the system throughput while also increasing the production lead time, consequently affecting the product quality. This paper proposes a theory and methodology to predict the lead time distribution in multi-stage manufacturing systems with unreliable machines. The method allows to optimally set inventory levels to achieve target production quality performance in these systems. The industrial benefits are demonstrated in a real manufacturing system producing micro-catheters for medical applications.
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Production
quality
performance
in
manufacturing
systems
processing
deteriorating
products
Marcello
Colledani
(2)
a,
*,
Andras
Horvath
b
,
Alessio
Angius
b
a
Politecnico
di
Milano,
Department
of
Mechanical
Engineering,
Via
la
Masa,
1,
20156,
Milan,
Italy
b
Universita
`di
Torino,
Department
of
Computer
Science,
Corso
Svizzera
185,
Torino,
Italy
1.
Introduction,
motivation
and
objectives
Production
quality
has
been
proposed
recently
as
an
emerging
paradigm
to
achieve
desired
service
levels
of
conforming
products
in
advanced
manufacturing
systems,
by
simultaneously
consider-
ing
quality
and
productivity
requirements
[1].
With
respect
to
this
background,
the
importance
of
an
integrated
analysis
of
production
logistics,
product
quality
and
equipment
maintenance
to
achieve
balanced
manufacturing
system
solutions
has
been
pointed
out.
This
problem
is
particularly
relevant
in
manufacturing
systems
producing
deteriorating
products.
Product
quality
and
value
deterioration
due
to
excessive
residence
times
(or
lead
times)
during
production
is
a
significant
phenomenon
in
several
technology
intensive
industries,
including automotive,
food
manufacturing,
semiconductor
and
electronics
manufacturing
and
in
polymer
forming.
For
example,
in
automotive
paint
shops
a
car
body
that
is
affected
by
prolonged
exposure
to
the
air
in
the
shop
floor
caused
by
excessive
lead
times
between
operations,
is
prone
to
particle
contamination,
leading
to
unacceptable
quality
of
the
output
of
the
painting
process.
Moreover,
food
production
is
pervaded
by
strict
requirements
on
hygiene
and
delivery
precision
requiring
a
maximum
allowed
storage
time
before
packaging.
If
the
production
lead
time
exceeds
this
limit,
the
product
has
to
be
considered
as
defective
and
cannot
be
delivered
to
the
customer.
In
these
systems,
higher
inventory
increases
the
system
throughput
but
also
increases
the
production
lead
times,
thus
increasing
the
probability
of
producing
defective
items.
Therefore,
a
relevant
trade-off
is
generated
between
production
logistics
and
quality
performance
that
requires
advanced
engineering
methods
to
be
profitably
addressed.
In
spite
of
the
relevance
of
this
phenomenon
in
industry,
the
analysis
of
production
quality
performance
under
product
deterioration
has
received
relatively
low
attention
in
the
literature.
The
manufacturing
system
is
considered
in
a
highly
aggregate
way
in
advanced
Economic
Production
Quantity
(EPQ)
models
considering
quality
deterioration
[2].
In
these
works,
the
quality
deterioration
due
to
the
parts
residence
time
along
the
stages
of
the
manufacturing
system
is
neglected.
Other
works
considered
supply
chain
coordination
mechanisms
in
presence
of
product
obsolescence
[3].
Furthermore,
production
control
policies
based
on
WIP
[4]
and
part
release
[5,6]
regulation
could
support
the
achievement
of
improved
production
quality
performance
under
product
deterioration,
although
they
do
not
provide
mechanisms
to
directly
control
production
lead
times.
The
first
model
considering
this
interaction
is
proposed
in
[7]
that
analyzed
un-buffered
systems
where
the
material
under
processing
is
scrapped
after
long
machine
failures.
Moreover,
the
performance
of
serial
lines
with
product
deterioration
is
considered
under
Bernoulli
reliability
models
of
production
stages
in
[8],
and
in
small
two-
machine
lines
in
[9].
While
all
these
works
are
important
to
shed
light
on
the
problem,
they
do
not
provide
methods
to
predict
and
control
production
lead
time
distributions
under
realistic
manufacturing
system
features.
As
a
matter
of
fact,
a
methodology
to
support
the
design
of
manufacturing
systems
under
lead
time
dependent
product
deterioration
that
integrates
quality
and
production
logistics
implications
has
never
been
proposed.
Important
questions
like
‘‘What
is
the
impact
of
buffers
on
the
production
rate
of
conforming
products
with
product
quality
deterioration?’’
remain
unsolved,
resulting
in
sub-performing
system
configurations.
To
overcome
these
limitations,
in
this
paper
an
integrated
model
of
manufacturing
systems
affected
by
product
deterioration
and
a
new
method
for
the
prediction
of
the
production
lead
time
distribution
and
the
throughput
of
conforming
products
in
these
CIRP
Annals
-
Manufacturing
Technology
64
(2015)
431–434
A
R
T
I
C
L
E
I
N
F
O
Keywords:
Manufacturing
system
Quality
Deteriorating
product
A
B
S
T
R
A
C
T
In
several
manufacturing
contexts
including
food
industry,
semiconductor
manufacturing,
and
polymers
forming,
the
product
quality
deteriorates
during
production
by
prolonged
exposure
to
the
air
caused
by
excessive
lead
times.
Buffers
increase
the
system
throughput
while
also
increasing
the
production
lead
time,
consequently
affecting
the
product
quality.
This
paper
proposes
a
theory
and
methodology
to
predict
the
lead
time
distribution
in
multi-stage
manufacturing
systems
with
unreliable
machines.
The
method
allows
to
optimally
set
inventory
levels
to
achieve
target
production
quality
performance
in
these
systems.
The
industrial
benefits
are
demonstrated
in
a
real
manufacturing
system
producing
micro-catheters
for
medical
applications.
ß
2015
CIRP.
*
Corresponding
author.
E-mail
address:
marcello.colledani@polimi.it
(M.
Colledani).
Contents
lists
available
at
ScienceDirect
CIRP
Annals
-
Manufacturing
Technology
journal
homepage:
http://ees.elsevier.com/cirp/default.asp
http://dx.doi.org/10.1016/j.cirp.2015.04.122
0007-8506/ß
2015
CIRP.
systems
are
developed
for
the
first
time.
This
approach
allows
setting
inventory
levels
to
achieve
desired
production
quality
performance
in
real
systems.
2.
System
description
The
considered
system
is
formed
by
K
manufacturing
stages
and
K
1
buffers
of
finite
capacity,
configured
in
serial
layout
(Fig.
1).
Stages
are
denoted
as
M
k
,
with
k
=
1,
.
.
.,
K,
and
buffers
are
denoted
as
B
k
,
with
k
=
1,
.
.
.,
K
1.
The
capacity
of
buffer
B
k
is
N
k
,
that
is
an
integer
number.
Finite
capacity
buffers
can
either
model
physical
conveyors
or
the
implementation
of
token-based
production
control
rules,
such
as
kanban,
regulating
the
material
flow
release
at
each
stage
[10].
Single
stage
model.
The
dynamics
of
each
stage
is
modeled
by
a
discrete-time
and
discrete-state
Markov
chain
of
general
complexi-
ty.
This
setup
allows
to
analyze
a
wide
set
of
different
stage
models
within
a
unique
framework.
For
example,
stages
with
unreliable
machines
characterized
by
generally
distributed
up
and
down
times
and
also
stages
with
non-identical
processing
times
can
be
considered
within
the
same
framework,
thus
making
the
proposed
approach
applicable
to
a
wide
set
of
real
manufacturing
systems.
In
detail,
each
stage
M
k
is
represented
by
I
k
states,
and
thus
the
state
indicator
a
k
assumes
values
in
{1,
.
.
.,
I
k
}.
The
set
containing
all
the
states
of
M
k
is
called
S
k
.
The
dynamics
of
each
stage
in
visiting
its
states
is
captured
by
the
transition
probability
matrix
l
k
,
that
is
a
square
matrix
of
size
I
k
.
Moreover,
a
quantity
reward
vector
m
k
is
considered,
with
I
k
binary
entries.
While
in
the
generic
state
i,
M
k
produces
m
k,i
parts
per
time
unit.
Therefore,
state
i
with
m
k,i
=
1
can
be
considered
as
an
operational
state
for
stage
M
k
,
while
state
i
with
m
k,i
=
0
is
a
down
state
for
stage
M
k
.
Material
flow
dynamics.
A
discrete
flow
of
parts
is
considered
in
the
system.
Stage
M
k
is
blocked
if
the
buffer
B
k
is
full.
Stage
M
k
is
starved
if
the
buffer
B
k1
is
empty.
Stage
M
K
is
never
blocked,
i.e.,
infinite
amount
of
space
is
available
to
store
finished
products.
Stage
M
1
is
never
starved,
i.e.,
unlimited
supply
of
raw
parts
is
assumed.
Operational
Dependent
Transitions
are
considered,
i.e.,
a
machine
cannot
make
transitions
to
other
states
if
it
is
starved
or
blocked.
State
transitions
take
place
at
the
beginning
of
the
time
unit
and
buffer
levels
are
updated
at
the
end
of
the
time
unit.
Part
quality
deterioration.
The
quality
of
parts
deteriorates
with
the
time
parts
spend
in
a
critical
portion
of
system,
denoted
by
two
integers,
e
and
q
with
1
e
<
q
K,
and
composed
of
those
buffers
that
are
between
stages
M
e
and
M
q
.
The
lead
time
of
a
part
is
the
time
spent
in
buffers
B
e
,
B
e+1
,
.
.
.,
B
q1
.
For
example,
for
the
system
in
Fig.
1,
e
=
2
and
q
=
4.
If
e
=
1
and
q
=
K,
then
the
time
spent
in
the
whole
system
is
considered.
The
probability
that
a
part
is
defective
at
the
end
of
the
line
is
a
non-decreasing
function
of
its
lead
time.
The
function
g(h)
indicates
the
probability
that
a
part
released
by
the
system
is
defective
given
that
it
spent
h
time
units
in
the
critical
portion
of
system.
Defective
parts
are
scrapped
at
the
end
of
the
line.
Performance
measures.
The
main
performance
measures
of
interest
are:
Average
total
production
rate
of
the
system,
denoted
by
E
Tot
,
Probability
that
the
lead
time,
LT,
is
equal
to
a
given
number
of
time
units,
h,
i.e.,
P(LT
=
h),
Average
effective
production
rate
of
conforming
parts,
E
Eff
,
which
is
given
by:
E
E
f
f
¼
E
Tot
X
1
h¼1
PðLT
¼
hÞ½1
gðhÞ
(1)
System
yield,
Y
system
,
i.e.
fraction
of
conforming
parts:
(E
Eff
/E
Tot
).
Total
average
inventory
of
the
system,
WIP.
3.
Lead
time
distribution
evaluation
In
this
section,
an
efficient
and
exact
analytical
method
to
compute
the
distribution
of
the
lead
time
in
the
critical
portion
of
the
system
is
described.
The
rationale
of
the
approach
is
explained
in
the
following.
Firstly,
the
probability
that,
at
the
moment
when
a
randomly
selected
part
enters
buffer
B
e
,
the
system
is
in
a
given
state
is
derived.
Secondly,
the
probability
that,
given
that
state
of
the
system
as
initial
condition,
the
last
part
in
buffer
B
e
crosses
the
critical
portion
of
the
system
in
h
time
units
is
analyzed.
By
taking
the
product
of
these
two
quantities
and
summing
for
all
possible
states,
the
distribution
of
the
lead
time
in
the
critical
portion
of
the
system
can
be
reconstructed.
In
the
following,
the
steps
of
this
procedure
are
briefly
described.
Starting
from
the
parameters
of
the
stages
and
according
to
the
modeling
assumptions,
a
discrete
time
Markov
chain,
denoted
by
D
1
,
can
be
determined
that
characterizes
the
overall
behavior
of
the
system.
A
state
of
D
1
is
described
by
a
vector
s
1
=
(n
1
,
n
2
,
.
.
.,
n
K1
,
a
1
,
a
2
,
.
.
.,
a
K
)
where
n
k
is
the
number
of
parts
in
buffer
B
k
and
a
k
is
the
state
of
machine
;
k
.
The
set
of
all
the
system
states
is
denoted
by
V
1
and
the
transition
probability
matrix
by
P
1
.
The
entries
of
P
1
can
be
obtained
as
shown
in
[11].
The
row
vector
of
the
steady
state
probabilities,
denoted
as
p
1
,
and
the
total
production
rate,
E
Tot
,
can
be
calculated
as
in
[11,12].
The
sub-system
including
only
that
portion
of
line
that
is
downstream
machine
M
e
is
considered
next.
This
sub-system
comprises
buffers
B
e
,
B
e+1
,
.
.
.,
B
K1
and
machines
M
e+1
,
M
e+2
,
.
.
.,
M
K
.
Machines
;
1
,
.
.
.,
;
e
are
not
considered
because,
once
a
part
is
put
in
buffer
B
e
,
these
machines
have
no
impact
on
its
lead
time.
For
this
sub-system,
a
Markov
chain,
denoted
by
D
2
,
with
initial
probability
vector
p
2
and
transition
probability
matrix
P
2
is
determined.
D
2
can
be
considerably
reduced
with
respect
to
D
1
.
A
state
of
this
model
is
given
by
a
vector
s
2
=
(n
e
,
n
e+1
,
.
.
.,
n
K1
,
a
e+1
,
a
e+2
,
.
.
.,
a
K
).
The
set
of
states
of
D
2
will
be
denoted
by
V
2
.
Note
that,
since
no
machine
feeds
parts
in
the
first
buffer
of
this
model,
all
parts
will
eventually
leave
and
the
system
will
get
empty.
In
other
words,
D
2
is
an
absorbing
Markov
chain
[12].
The
subset
of
states
in
S
2
in
which
there
are
no
parts
in
the
buffers
of
the
critical
portion
B
e
,
B
e+1
,
.
.
.,
B
q1
will
be
denoted
by
V
0
.
The
lead
time
in
the
critical
portion
of
system
can
be
expressed
as
follows:
PðLT
hÞ
¼X
s
2
2
V
2
p
2;s
2
f
ðs
2
;
hÞ
(2)
where
p
2;s
2
is
the
probability
that
a
random
part
that
enters
in
buffer
B
e
finds
the
system
in
state
s
2
and
f(s
2
,h)
is
the
probability
that
a
part
that
enters
the
critical
portion
in
state
s
2
leaves
machine
M
q
in
at
most
h
time
units.
The
first
term
in
Eq.
(2)
is
obtained
by
properly
mapping
the
states
s
1
in
D
1
into
the
states
s
2
of
the
sub-
system
in
D
2
.
For
this
reason
the
matrix
F
of
binary
entries
is
defined
that
links
the
states
in
s
1
and
s
2
if
the
states
of
all
the
stages
M
j+1
and
buffers
B
j
,
with
j
>
e,
are
the
same.
In
other
words,
the
initial
probability
of
the
state
s
2
in
D
2
,
p
2;s
2
,
has
to
be
equal
to
the
sum
of
the
probabilities
that
a
part
is
put
in
the
buffer
B
e
in
the
connected
set
of
states
s
1
in
D
1
.
Therefore:
p
2
¼p
1
Q
1
E
Tot
F
(3)
where
Q
1
is
identical
to
P
1
,
except
that
those
transitions
that
do
not
cause
the
release
of
a
part
in
buffer
B
e
are
set
to
zero.
The
second
term
in
(2)
can
be
easily
computed
as
the
distribution
of
the
first
passage
time
to
V
0
in
the
absorbing
Markov
chain
D
2
[12].
The
probability
that
the
lead
time
is
exactly
h
is
given
by
P(LT
=
h)
=
P(LT
n)
P(LT
n
1).
The
other
performance
measures
defined
in
Section
2
can
be
derived
based
on
the
lead
time
distribution
and
the
total
throughput.
Fig.
1.
Representation
of
the
analyzed
manufacturing
system.
M.
Colledani
et
al.
/
CIRP
Annals
-
Manufacturing
Technology
64
(2015)
431–434
432
4.
Numerical
results
and
system
behavior
In
the
first
experiment,
the
distribution
of
the
lead
time
in
multi-stage
manufacturing
systems
is
investigated.
A
production
line
with
five
stages
is
considered
with
parameters
reported
in
Table
1.
The
stages
correspond
to
machines
with
one
operational
state
and
one
failure
state,
with
failure
probability
p
=
1/MTTF
and
repair
probability
r
=
1/MTTR
(MTTF
is
Mean
Time
to
Failure
and
MTTR
is
Mean
Time
to
Repair).
The
machines
produce
one
part
per
time
unit
if
operational.
The
results
are
reported
in
Fig.
2.
The
following
considerations
hold:
The
distribution
of
the
lead
time
is
multi-modal
with
a
number
of
peaks
equal
to
the
number
of
production
stages,
K.
The
v-th
peak,
with
v
¼
1;
.
.
.
;
K,
is
located
in
correspondence
to
the
following
number
of
time
units,
h
v
:
h
v
¼
K
v
þX
v1
i¼1
ðN
i
1Þ
(4)
The
peaks
appear
for
the
following
reasons.
The
first
peak
corresponds
to
the
situation
where
the
system
is
empty
and
the
parts,
after
being
processed
by
stage
M
1
,
cross
the
remaining
K
1
stages,
each
one
spending
one
time
unit
for
processing.
The
v-th
peak,
with
v
¼
2;
.
.
.
;
K,
corresponds
to
the
situation
where
stage
M
v
failed
for
sufficiently
long
time
to
fill
up
all
the
upstream
buffers
and
empty
all
the
downstream
buffers.
After
the
stage
is
recovered
from
the
failure,
an
incoming
part
has
to
wait
N
i
1
time
units
in
the
upstream
buffers,
with
i
<
v,
and
1
time
unit
in
each
of
the
Kv
downstream
stages,
if
no
other
failure
occurs.
The
knowledge
of
this
behavior
can
be
exploited
to
correctly
operate
and
design
the
production
line.
In
the
second
experiment,
the
impact
of
the
buffer
size
on
the
effective
throughput,
E
Eff
,
is
investigated
for
a
simple
system
with
two
machines
and
one
buffer,
with
parameters
reported
in
Table
1.
The
quality
deterioration
function
g(h)
assumes
value
zero
for
h
=
1,
.
.
.,
h*
and
value
1
for
h
>
h*,
with
h*
=
40.
In
other
words,
if
the
parts
spend
more
than
40
time
units
in
the
system,
they
turn
into
defective.
In
the
experiment,
the
buffer
capacity
N
is
varied
from
5
to
50.
Results
are
reported
in
Fig.
3.
The
following
considerations
hold:
The
effective
throughput
curve
is
a
concave
function
presenting
a
maximum
corresponding
to
a
buffer
capacity
equal
to
25.
This
behavior
is
explained
in
the
following.
It
is
well
known
that
the
total
throughput
of
the
system
is
monotonically
increasing
with
the
buffer
size,
with
a
marginal
gain
that
reduces
while
increasing
the
buffer
size.
At
the
same
time,
if
the
first
machine
is
more
reliable
than
the
second,
while
increasing
the
buffer
size
also
the
average
lead
time
increases,
as
the
average
inventory
increases
almost
linearly.
Therefore,
the
scrap
rate
will
increase
as
a
function
of
the
buffer
size
since
the
probability
that
the
lead
time
exceeds
the
threshold
increases.
The
result
of
this
combined
effect
is
the
following.
When
the
first
phenomenon
is
more
relevant
(small
buffers),
the
effective
throughput
curve
increases
with
the
buffer
size.
When
the
second
phenomenon
is
more
relevant
(large
buffers),
the
effective
throughput
curve
starts
decreasing,
as
the
system
produces
more
parts
but
also
a
higher
fraction
of
defective
parts.
Therefore,
a
trade-off
is
generated
that
is
optimized
for
a
specific
buffer
size.
This
optimal
buffer
size
could
not
be
found
without
the
proposed
approach.
It
is
worth
to
note
that
for
N
>
h*
+1
the
curve
drops
abruptly
in
a
discontinuous
way
and
shows
a
different
slope.
This
phenome-
non
is
due
to
the
fact
that,
according
to
equation
(4),
the
lead
time
distribution
curve
in
a
two-machine
line
shows
a
probability
peak
at
level
N-1.
Therefore,
operating
a
system
with
N-1
>
h*
does
not
make
sense
in
practical
settings.
The
third
experiment
shows
the
impact
of
the
repair
probability
of
the
first
machine
on
the
effective
throughput,
for
different
buffer
sizes
in
a
line
with
two
machines
and
one
buffer.
Results
are
reported
in
Fig.
4.
The
following
considerations
hold:
For
all
the
cases,
it
is
possible
to
notice
that
faster
repair
operations
are
not
always
beneficial
in
terms
of
effective
throughput
of
the
system.
Indeed,
a
faster
repair
of
the
first
machine
increases
the
total
throughput
of
the
system
but
also
increases
the
amount
of
inventory
stored
in
the
buffer,
as
the
buffer
will
be
more
frequently
full.
This
phenomenon
increases
the
lead
time
and,
consequently,
the
scrap
rate.
This
behavior
is
more
prominent
for
large
buffers.
Indeed,
in
these
cases,
the
positive
effect
of
shorter
repair
time
on
the
total
throughput
is
less
significant
than
the
negative
effect
on
the
lead
time
increase.
This
analysis
suggests
that
improvement
actions
that
are
beneficial
on
the
total
throughput
of
the
system
(faster
repair
operations)
can
be
detrimental
on
the
effective
throughput,
if
the
products
are
perishable.
Thus,
neglecting
this
aspect
can
lead
to
sub-performing
system
configurations.
5.
Real
case
study
The
proposed
approach
has
been
applied
to
the
production
of
micro-catheters
as
high
value
medical
products
for
the
aging
society
in
the
medical
technology
sector
at
ENKI
s.r.l.
[13].
The
manufacturing
process
is
composed
of
three
main
phases:
(i)
Table
1
Data
of
the
systems
analyzed
in
the
experiments.
Exp.
no.
System
data
1Balanced
line:
l
k
¼1
p
k
p
k
r
k
1
r
k
;
m
k
¼
½1;
0
with
p
k
=
0.01
and
r
k
=
0.1,
N
1
=
N
2
=
N
3
=
N
4
=
10.
e
=
1,
q
=
K
=
5.
2
Same
machine
model
as
exp.
1
p
1
=
0.01;
r
1
=
0.05;
p
2
=
0.02;
r
2
=
0.2.
N
1
=
[5:50].
e
=
1,
q
=
K
=
2.
3
Same
machine
model
as
exp.
1
p
1
=
0.01;
r
1
=
0.25;
p
2
=
0.02;
r
2
=
[0.02:0.5].
e
=
1,
q
=
K
=
2.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
1 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Pr(LT=h)
h
Fig.
2.
Lead
time
distribution
for
a
five
machine
line.
0.7
0.72
0.74
0.76
0.78
0.8
0.82
5 10 15 20 25 30 35 40 45 50
Effective Throughput, E
Eff
Buffer size, N
Fig.
3.
Effect
of
the
buffer
size
on
the
effective
throughput.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Effective Throughput, E
Eff
r
1
N=20
N=30
N=40
N=50
Fig.
4.
Effect
of
the
repair
probability
on
the
effective
throughput.
M.
Colledani
et
al.
/
CIRP
Annals
-
Manufacturing
Technology
64
(2015)
431–434
433
material
compound
preparation
and
control,
the
(ii)
micro-
extrusion
of
the
micro-tubes
and
(iii)
final
micro-catheter
assembly.
Defects
are
mainly
geometrical,
generated
within
the
micro-extrusion
process.
The
above
defects
lead
to
extremely
high
defect
rates
(up
to
70%
in
standard
production).
During
the
phase
of
preparation
of
the
raw
material,
in
forms
of
granules,
the
moisture
level
is
measured
and
if
the
value
exceeds
a
fixed
limit,
the
granules
are
dried
to
reduce
the
moisture
level
before
the
downstream
micro-extrusion
process.
The
lead
time
between
the
drying
and
extrusion
processes
should
not
exceed
a
certain
limit
to
avoid
increase
of
the
moisture
level
by
exposure
to
the
air.
A
maximal
moisture
level
of
300
ppm
is
usually
the
accepted
limit.
Excessive
moisture
level
affects
the
material
viscosity.
This
results
in
fluctuations
of
the
material
shear
rate
and
instability
in
the
extrusion
process,
thus
affecting
the
quality
of
the
tube
section.
The
line
under
analysis
is
composed
of
three
main
stages.
Stage
M
1
is
the
compounding
stage
provides
additives
to
the
material
and
makes
the
size
of
the
pellets
homogeneous.
Stage
M
2
is
the
drying
stage,
which
reduces
the
moisture
level
of
the
material.
The
residence
time
of
the
material
in
the
dryer
depends
on
the
material
type
and
properties.
For
example,
for
PEBA
pellets
the
drying
time
is
usually
4
h.
After
the
drying
process,
the
material
is
loaded
in
the
input
hopper
of
the
extruder
at
stage
M
3
.
The
extrusion
speed
selection
is
one
of
the
key
competences
of
the
company,
directly
affecting
the
output
quality
of
the
tube.
It
is
strongly
dependent
on
the
material
type
and
tube
section
complexity,
usually
ranging
between
3
m/s
and
20
m/s.
After
the
extrusion,
each
tube
undergoes
a
set
of
very
severe
EOL
(End
of
Line)
inspections
and
non-conforming
tubes
are
scrapped.
However,
the
company’s
strategic
goal
is
to
avoid
the
generation
of
defects
by
improving
the
control
of
the
material
properties
before
the
extrusion
process.
For
this
reason,
the
lead
time
between
the
end
of
the
drying
process
and
the
feeding
of
the
granules
in
the
extruder
hoppers
must
be
limited
to
avoid
gradual
increase
in
the
humidity
on
the
granules.
After
a
deep
study
of
the
material
behavior
in
extrusion,
the
company
assessed
that
the
maximal
residence
time
of
the
material
between
these
stages
is
45
s.
Therefore,
the
main
objective
of
the
analysis
is
to
properly
design
the
in-process
buffer
included
between
the
drying
stage
and
the
extrusion
stage
in
order
to
decrease
the
fraction
of
defects
due
to
material
deterioration
in
extrusion,
thus
increasing
the
effective
production
rate
levels.
The
micro-tube
forming
line
under
the
current
configuration
has
been
modeled.
Two
types
of
tubes
have
been
considered
with
part-type
dependent
process
parameters.
The
number
of
lumens
ranges
from
4
to
26
and
the
external
diameters
ranges
from
2
mm
to
5
mm.
Time-consuming
set-up
operations
are
required
while
switching
between
part
types;
therefore
different
production
settings
have
been
considered,
one
for
each
tube
type.
The
operational
and
down
times
were
provided
by
the
company.
The
performance
of
the
system
was
evaluated
and
the
results
were
validated
through
comparison
with
historical
production
data,
showing
deviations
always
below
5%.
The
approach
proposed
in
this
paper
has
been
applied
to
design
a
different
production
control
policy
to
manage
the
available
hopper
capacity
before
the
extrusion
machine.
In
detail,
for
each
tube
type,
the
hopper
capacity
that
maximizes
the
effective
throughput
of
the
system,
under
a
constraint
on
the
maximum
hopper
capacity
currently
available
in
the
line
(1500
g),
has
been
investigated.
Results
are
reported
in
Table
2.
Similarly
to
what
was
shown
for
experiment
2
in
Section
4,
for
each
case,
the
effective
throughput
is
maximized
for
a
hopper
capacity
that
is
smaller
than
the
currently
adopted
capacity.
With
the
proposed
optimal
policy,
in
all
the
cases
only
1%
of
the
tubes
is
defective
due
to
excessive
lead
time,
against
the
6%
and
17%,
respectively,
for
each
tube
type,
in
the
current
configuration
(a
reduction
of
more
then
80%
for
both
types).
Since
defective
tubes
cannot
be
repaired
and
are
sent
to
recycling,
this
solution
entails
a
large
environmental
benefit.
Moreover,
benefits
are
achieved
in
terms
of
effective
throughput
(3.47%
and
16.8%),
while
also
reducing
the
work
in
progress
in
the
system
(50%
as
a
minimum).
This
directly
translates
into
a
reduction
of
production
costs,
thus
positively
impacting
on
the
company’s
competitiveness.
6.
Conclusions
This
paper
proposes
a
modeling
framework
and
a
methodology
to
predict
the
lead
time
distribution
in
multi-stage
manufacturing
systems.
The
lead
time
distribution
is
used
to
compute
the
system
production
quality
performance,
when
products
deteriorate.
The
theoretical
work
developed
in
this
paper
opens
the
way
for
applications
in
several
different
fields.
For
example,
supply
chain
management
approaches
can
benefit
from
the
availability
of
a
solution
to
the
problem
of
deriving
the
lead
time
distribution
in
unreliable
manufacturing
systems.
Moreover,
production
planning
approaches
that
take
into
account
the
exact
distribution
of
the
residence
time
of
parts
in
the
system
can
be
developed.
Finally,
new
production
control
policies
to
provide
a
direct
control
on
the
lead
time
can
be
elaborated
from
these
results.
Acknowledgements
The
authors
would
like
to
thank
Eng.
Moreno
Camanzi
and
Mr.
Mario
Di
Cecio
from
ENKI
s.r.l.
for
the
support
in
this
research.
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Table
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Micro-tube
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performance
under
optimized
buffer
size
(the
time
unit
is
omitted
for
confidentiality
reasons).
Tube
type
Buffer
size
(g)
E
Tot
Y
system
E
Eff
WIP
(g)
Scrap
rate
1
N
Current
=
1500
0.862
0.94
0.812
884
0.06
N
opt
=
783
0.849
0.991
0.84
448
0.009
Difference
D
%
1.5%
+5%
+3.47%
49.3%
82%
2
N
Current
=
1500
0.868
0.829
0.719
901.7
0.17
N
opt
=
591
0.85
0.991
0.842
338
0.009
Difference
D
%
2%
+19.3%
+16.8%
62.5%
93.9%
M.
Colledani
et
al.
/
CIRP
Annals
-
Manufacturing
Technology
64
(2015)
431–434
434
  • Conference Paper
    For the manufacturing system adjusted, there still is the uncertainty in the manufacturing process which is part of poor information problem with probability distribution unknown. The statistical evaluation methods depend on information with known probability distribution, which can not used to realize to evaluate the stability of the manufacturing process. Hence it is urgent to solve the problem above. Firstly, the output experimental data in the manufacturing process are selected to establish the membership function according to the fuzzy norm method. Under the given confidence level, the measurement uncertainty of the experimental data can be estimated to characterize the uncertainty of the manufacturing process. Then the relative error of the measurement uncertainty can be obtained, which can evaluate the stability of the manufacturing process. Therefore, based on the fuzzy set theory, an evaluation method for the stability of the manufacturing process using the fuzzy norm method is proposed to make up for the deficiency of the statistical methods.
  • Article
    Full-text available
    Perishable products that deteriorate before leaving the production system are common in industry. The most classic example is the food industry but several cases can be found in semiconductor manufacturing, and in polymers forming processes. These systems often require the scrapping of parts whose lead-time has exceeded a certain threshold. Previous works have considered single-product systems and have shown that the size of the buffers and actions dedicated to improve the machine availability may strongly affect the percentage of scrapped parts. In this paper, we model the dynamics of this phenomenon in a multi-product system composed of two machines that are connected through dedicated buffers. Furthermore, the model allows the use of three different policies for the mixing of products. The main contribution is a method for the calculation of the lead time distribution of each product that can be used to determine the effective throughput of the system. The relevance of the method is shown by means of numerical results that provide important insights on the problem and show counterintuitive behaviors.
  • Article
    Full-text available
    In the literature of operations management, the reliability of multistage manufacturing systems has been always modeled with uncorrelated failure processes where the reliability of each machine is assumed to be independent of any failure in the other machines. However, in real-life, machines may be subject to complex correlated failures such as increased degradation and tool wear caused by defective parts produced in preceding machines. Ignoring the correlation effect when modeling the reliability of multistage systems generally results in inaccurate estimation of the overall system reliability and inefficient operations policy accordingly. In this paper, we deal with the problem of integrated production, quality and maintenance control of production lines where machines are subject to quality and reliability operation-dependent degradation. Also, machines’ reliability is correlated with the level of incoming product quality. For illustration, we study in this paper a two-machine line model. We propose a combined mathematics and simulation-based modeling framework to jointly optimize the production, quality and maintenance control settings. The objective is to minimize the total cost incurred under a constraint on the outgoing quality. Numerical examples are given to show the effectiveness of the resolution approach and to study important aspects in multistage systems such as the allocation of inspection and maintenance efforts, the Quality-Reliability chain and the interdependence between production, quality and maintenance control settings. The results obtained demonstrate that failure correlation has a significant impact on the optimal control settings and that maintenance and quality control activities in preceding stages can play an important role in the reliability improvement of the subsequent machines.
  • Conference Paper
    Full-text available
    We present a model-based approach to performance evaluation of a collection of similar systems based on runtime observations. As a concrete example, we consider an assembly line made of sequential workstations with transfer blocking and no buffering capacity, implementing complex workflows with random choices and sequential/cyclic phases with generally distributed durations and no internal parallelism. Starting from the steady state, an inspection mechanism is subject to some degree of uncertainty in the identification of the current phase of each workstation, and is in any case unable to estimate remaining times. By relying on the positive correlation between delays at different workstations, we provide stochastic upper and lower approximations of the performance measures of interest, including the time to completion of the local workflow of each workstation and the time until when a workstation starts a new job. Experimental results show that the approximated evaluation is accurate and feasible for lines of significant complexity.
  • Article
    This paper presents an integrated model for the simultaneous production and repair activity planning of a manufacturing system whose performance output is subject to progressive deterioration. In this context, an appropriate joint control strategy is critical to reduce costs and remain competitive. The obtained control policy balances the amount of maintenance activities needed to increase the availability and reduce defects against the increase in the total cost from downtime and deterioration. The production system consists of an unreliable machine that produces one product type and where unmet demand is backlogged. The rate of defects of the machine depends on its level of deterioration, which is defined through a set of multiple operational states and the age of the machine. Additionally, an intensity control model is adapted to define the repair efficiency applied to the system, aiming to mitigate the effect of deterioration that is mainly observed on the failure intensity of the system. The solution is obtained numerically through the formulation of a Hamilton–Jacobi–Bellman equation. A numerical example is provided and an extensive sensitivity analysis is conducted to validate the obtained results.
  • Article
    Full-text available
    The ability of meeting the target production lead times is of fundamental importance in modern manufacturing systems producing perishable products, where the product quality or value deteriorates with the time parts spend in the system, and in manufacturing contexts where strict lead time constraints are imposed due to tight shipping schedules. In these settings, traditional manufacturing system engineering methods and token-based production control policies loose effectiveness as they aim at achieving target production rates while minimizing the inventory, without directly taking into account the effect on the lead time distribution. In this paper a production control policy for unreliable manufacturing systems that aims at maximizing the throughput of parts that respect a given lead time constraint is proposed for the first time. The proposed policy jointly considers the actual level of the buffer and the state of the second machine in the system and stops the part loading at the first machine if there is unacceptable risk of exceeding the lead-time constraint. The effectiveness of this new policy against the traditional kanban policy is quantified by numerical analysis. The results show that this new policy outperforms the kanban policy by providing a tighter control on the production lead time. This approach paves the way to the introduction of new lead-time oriented production control policies to maximize the effective throughput in real manufacturing systems.
  • Conference Paper
    In some kinds of manufacturing, the time a part may spend in a buffer between successive operations (such as cleaning and baking in semiconductor fabrication) is limited. Parts that wait too long must be reworked or discarded due to the risk of quality degradation. This constraint is important in several industries, especially the semiconductor industry. To study this issue, we present an analytical formulation for the part waiting time distribution in a Buzacott two-machine one-buffer transfer line. The numerical solution is tested with Little's law. Numerical experiments are provided to illustrate the accuracy of the solution as it is compared with simulation.
  • Conference Paper
    This paper presents a new decomposition method for the approximate performance evaluation of buffered multi-stage production systems where machines are modeled as generally complex discrete time Markov chains with reward. The method is based on the exact solution of smaller two-machine sub-systems, also referred as building blocks, with machines that also feature such general characteristics. A decomposition approach is developed that propagates all the possible interruptions of flow due to starvation and blocking conditions throughout the pseudo-machines of each building block. In order to deal with such general settings, new decomposition equations are developed. A new algorithm is proposed for solving these decomposition equations. The proposed method proves to be very fast and accurate over a wide range of test cases, partly reported in this paper. To prove the generality of the framework, reported cases are focused on systems with generally distributed up and down times and systems with degrading machines. This method paves the way to the analysis of a wider class of previously un-investigated systems.
  • Article
    Probability, Markov Chains, Queues, and Simulationprovides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics.The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation.Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only).Numerous examples illuminate the mathematical theoriesCarefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approachEach chapter concludes with an extensive set of exercisesProfessors: A supplementary Solutions Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to:http://press.princeton.edu/class_use/solutions.html.
  • Article
    Manufacturing companies are continuously facing the challenge of operating their manufacturing processes and systems in order to deliver the required production rates of high quality products, while minimizing the use of resources. Production quality is proposed in this paper as a new paradigm aiming at going beyond traditional six-sigma approaches. This new paradigm is extremely relevant in technology intensive and emerging strategic manufacturing sectors, such as aeronautics, automotive, energy, medical technology, micro-manufacturing, electronics and mechatronics. Traditional six-sigma techniques show strong limitations in highly changeable production contexts, characterized by small batch productions, customized, or even one-of-a-kind products, and in-line product inspections. Innovative and integrated quality, production logistics and maintenance design, management and control methods as well as advanced technological enablers have a key role to achieve the overall production quality goal. This paper revises problems, methods and tools to support this paradigm and highlights the main challenges and opportunities for manufacturing industries in this context.
  • Article
    Manufacturing systems with perishable products are widely seen in practice (e.g. food, metal processing, etc.). In such systems, the quality of a part is highly dependent on its residence time within the system. However, the behaviour and properties of these systems have not been studied systematically and, therefore, it is carried out in this paper. Specifically, we assume that the probability that each unfinished part is of good quality is a decreasing function of its residence time in the preceding buffer. Then, in the framework of serial production lines with machines having Bernoulli reliability model, we derive closed-form formulas for performance evaluation in the two-machine line case, and develop an aggregation-based procedure to approximate the performance measures in [Inline formula]-machine lines. In addition, we study monotonicity properties of these production lines using numerical experiments. A case study in an automotive stamping plant is described to illustrate the theoretical results obtained.
  • Article
    If order due dates are missed, a frequent reaction of production planners is to adapt planned lead times. How often and to what extent updates are reasonable has previously been unclear because, while trying to improve logistic target achievement, the opposite effect may be caused, which is known as the Lead Time Syndrome of Production Control. This paper investigates correlations between Lead Time Syndrome variables using a control theoretic model to gain knowledge about system transient response and the influence of the lead time updating frequency and information delay on due date reliability. These investigations lead to fundamental improvements in practice in setting planning parameters.
  • Article
    Productivity and schedule reliability are two major objectives for production areas. Companies can influence both objectives by the applied sequencing rule. While a due-date oriented sequencing rule supports the schedule reliability, a setup-time oriented sequencing rule increases productivity. Thus, a field of tension between these objectives exists in which companies have to position their production areas. To support the positioning, this paper provides a model for calculating the output lateness distribution of a production system for a setup-time oriented and a First-In-First-Out sequencing rule. Furthermore, the effect of the applied rule on productivity of production systems is analyzed.
  • Article
    An analytical method for the joint design of quality and production control parameters in unreliable multi-stage lines is proposed in this paper. Specifically, the method optimally sets the sample size, the sampling frequency and the position of the control limits of the quality control charts as well as the number of kanban cards at any production stage, by jointly considering the mutual relations between the controllers. Numerical results compare the solution of this integrated design with the configurations obtained by solving the two problems in isolation with existing techniques. They show that great benefits can be achieved by the proposed integrated design of quality and production control parameters, since it fully captures the interaction between the dynamics of the two controllers.
  • Article
    In this paper, a method is presented for information sharing in production networks with large numbers of autonomous work systems for the purpose of maintaining constant dynamic properties when the structure of physical order flows between the work systems is omni-directional and variable. It is shown that information sharing is necessary if undesirable behaviors such as oscillation or slow response are to be avoided. A method for designing the dynamic properties of such networks is presented along with a method for distributed computation and communication of information needed to locally compensate for the expected order flows from other work systems.
  • Article
    The paper discusses manufacturing enterprises’ compelling challenges that are directly stemming from generic conflicts between competition and cooperation, local autonomy and global behavior, design and emergence, planning and reactivity, uncertainty and a plethora of information. Responses in product and service design, organization of production networks, planning and management of operations, as well as production control are surveyed. As illustrated through industrial case studies, production engineering should integrate a rich body of interdisciplinary results together with contemporary information and communication technologies in order to facilitate cooperation and responsiveness that are vital in competitive, sustainable manufacturing.