Impact of Statistical Process Control
(SPC) on the Performance of Production
Systems
M. Colledani, T. Tolio
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
Outline of the presentation
1- Literature review
2- Problem definition
3- Isolated machine with local monitoring
4- Two machines one buffer with local monitoring
5- Two machines one buffer with remote monitoring
6- Long lines with local monitoring
7- Numerical results
8- Conclusion and future research
< Impact of SPC on System Performance >
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
1- Literature Review
- Montgomery,D.C, Introduction to Statistical Process Control, John Wiley and Sons, Inc, 1991.
- Ho C., Case K., Economic Design of Control Charts: A Literature Review for 1981-1991,
Journal of Quality Technology, 26,: 39-53,1994.
- Raz T.,” A Survey of Models for Allocating Inspection Effort in Multistage Production Systems”,
Journal of Quality Technology, 18-239-246, 1986.
- Dallery, Y.,Gershwin, S.B., “Manufacturing Flow Line Systems: A Review of Models an
Analytical Results, Queueing Systems Theory and Applications, Special Issue on Queueing
Models of Manufacturing Systems, 12(1-2). 1992.
- Gershwin S.B., Matta A. and Tolio T., Analisys of Two Machine Lines with Multiple
Failure Modes, IIE Transaction, 34(1) : 51 - 62, 2002.
- Inman R., Blumenfeld D., Huang N. and Li J..,” Designing Productivity Systems for
Quality: research opportunities from an automotive industry perspective “, IJPR, 41(9), 2003.
- Gershwin S.B., Kim J.,Integrated Quality and Quantity Modeling of a Production Line”, OR
Spectrum, 2005.
- Colosimo B.M., Semeraro Q. and Tolio T. “Designing X bar Control Charts in
Multistage Serial Manufacturing System, CIRP Journal of Manufacturing Systems, 31-6, 2002
- Tempelmeier H., Burger M, Performance Evaluation of Unbalanced Flow Lines with General
Distributed Processing Times, Failures and Imperfect Production, IIE Transactions,33,293-302, 2000.
- Helber S. Performance Anaiysis of Flow Lines with Non-Linear Flow of Material, Springer, 1999.
< Impact of SPC on System Performance >
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2- Process in Statistical control
PROCESS IN CONTROL each quality measure is in a statistical
control state.
STATISTICAL CONTROL STATE is a state where all the variations
within the observed data can be related to a set of causes not
identifiable which do not change over time (i.e. the distribution is
stable)
Example
Yt    
t
< Impact of SPC on System Performance >
 ~ IID(0,  2 )
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2- Specifications and bad parts
Even if the process is in control it can produce bad parts.
Upper Specification Limit - USL
t
Lower Specification Limit - LSL
However, if the process goes out of control the number of bad
parts produced changes (in general, infinite out of control
modes are possible).
USL
t
LSL
< Impact of SPC on System Performance >
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2- Detecting out of control states
In order to understand if the process is in control or out of control,
we can sample the produced parts (in the extreme case we can have
100% inspection). Then we measure the parts in the sample and we
perform a statistical test with the following hypotheses.
H0:
H1:
the process is in control
the process is out control
The outcome of the test is subject to two types of errors:
a error: the process is in control but the test detects an
out of control (false alarm)
b error: the process is out control but the test does not
detect it (out of control not detected)
< Impact of SPC on System Performance >
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2- Detecting out of control states
If we repeat the test many times and each test has the same a and b
errors than we can evaluate the average number of samples we have to
take in order to have an alarm (ARL = Average Run Length).
If the process is out of control
If the process is in control
t
t
ARL 0 
1
a
ARL 1 
1
1 b
For example:
a  0.0027  ARL 0  370.4
< Impact of SPC on System Performance >
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2- Detecting out of control states
If we consider a single machine in isolation and a control chart
attached to it then how many parts does the machine produce
before getting an alarm?
Let us define:
m
the sample size.
h
the number of parts produced between two samples.
If the process is in control
1
a
( h  m)
< Impact of SPC on System Performance >
If the process is out of control
1
(h  m)
1 β
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2- Inspection stations
Testing allows to draw information on the process but also on the inspected
parts.
•Inspected parts which are within the specification limits may proceed
downstream (if testing does not destroy the parts).
•Inspected parts which are outside the specification limits may be either
scrapped or reworked
Out of control
(If m=1 and h=0 than 100% inspection is
performed).
Ci ,q
iq
good
Mq
rework
scrap
Therefore the logic at an inspection station decides two things:
•control charts which send the alarms related to the out of
control conditions
•scrap/rework policies which decide the final destination of the
inspected parts
< Impact of SPC on System Performance >
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2- Some Assumptions of the Model
-The flow of material in the system is considered as discrete.
-Each machine is characterized by the same processing time, scaled to
time unit.
-Buffers have finite capacity.
-Machines can be of three types: manufacturing machines, inspection
machines or integrated machines.
-Inspection machines are perfectly accurate.
-Failures and shifts to out of control are Operation Dependent.
-Once an out of control has been detected, the time to repair it is
geometrically distributed.
-Machines can fail in different modes. We identify two classes of failures:
-f type local failures: are those for which the repairing intervention
also set the machine to the in control state;
f type local failures: are those for which the repairing intervention
reset the machine to conditions it had before the failure occurred.
< Impact of SPC on System Performance >
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3- Modelling a single machine in isolation
pi
D
Wi
i ,f i
ri.fi
false
(Ci ,q )
pi.fi
pi . f i
Di , f i
W i:
Di,fi:
Di,fi:
Ai1:
1
i
A
ri false
Wi
ri. fi
piquality
ri quality
Ai2
pi (Ci ,q )
Oi
pi. fi
ri.fi
DiO,fi i
Ai2:
pi.fi
Oi:
Quality link equations:
p ifalse (Ci , q ) 
pi (Ci , q ) 
operative in control
f type local down state
f type local down state
out of control detected
but not real
out of control detected
and real
out of control non
detected
1
1

MTTFAi (Ci , q ) ARL0 (Ci , q )[ h(Ci , q )  m(Ci , q )]
1
1

MTTD i (Ci , q ) ARL1 (Ci , q )[ h(Ci , q )  m(Ci , q )]
< Impact of SPC on System Performance >
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3- The Isolated Machine Case
Once the Markov chain has been solved and all the state probabilities have been calculated, the
performance measures for the single machine case can be derive as follows:
Total average production rate:
Ei
TOT
  (Wi )   (Oi )
Effective average production rate:
Ei
EFF
  (Wi )(1   iWi )   (Oi )(1   iOi )
System yield (fraction of conforming parts produced):
Ei
 (Wi )(1   iWi )   (Oi )(1   iOi )
Yi  TOT 
 (Wi )   (Oi )
Ei
EFF
Average production rate of parts to be scrapped:
E S   (Wi ) iWi , S   (Oi ) iO, si , S
Average production rate of parts to be reworked:
E RW   (Wi ) iWi , RW   (Oi ) iOi , RW
< Impact of SPC on System Performance >
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4- The General Case
Ci ,q
Mi
Bi
C j, j
Bq
Mq
M
scrap
RW
i,q
B
j
Bj
MK
scrap
rework
B
RW
j, j
rework
Quality has an impact on production system performance:
- Control charts allow to identify out of control states. The search for a cause for
the out of control reduces the up time of the machine.
- Scrap/rework policies allow to identify defective parts and to decide whether to
scrap or to rework them.
Total throughput
Yield
The system architecture impacts on the quality system performance:
- The presence of buffers causes a delay in the transmission of the quality signal.
Total throughput
< Impact of SPC on System Performance >
Yield
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4- Two machine one buffer with local monitoring
This system is formed by two machines M1 and M2 locally controlled by C1,1 and C2,2.
C2,2
C1,1
B
M1
p1,1 r1,1
p1, 2 r1, 2
p1, F1 r1, F1
M2
p 2,1 r2,1
p 2, 2 r 2, 2
p 2, F2 r2, F
2
Downstream
Upstream
machine M21
p1false (C1,1 )
B
p
W1
2, f 2
B
2, f 2
r
B
2, f 2
r1. f1
D1, f1
p1quality
p1. f1
p
r
r
Building
Block
evaluation
p
p
r
r
“Gershwin,
Matta,
Tolio
2002”
p (C ) r (C )
p (C ) r (C )
p1U,1(1)
U (1)
false
r1quality
D (1)
2 ,1
D (1)
2 , F2
U (1)
1,1
U (1)
1, F1
U (1)
1, F1
1,1
U (1)
false
CONVERGENCE
A
O1
B
2, f 2
r
p
D1U, f1 (1)
B
2, f 2
Markov chain solution
Stationary state
probability
distribution
< Impact of SPC on System Performance >
D (1)
false
2, 2
(1)
pUfalse
(C1,1 )
A1,U (1)
U (1)
r false
(C1,1 )
p2B, f 2
r1. f1
B2O,1f 2
2, 2
pseudo-machine MU(1)
p1. f1
r2B, f 2
D (1)
2 ,1
D (1)
2 , F2
p D (1) (C 2, 2 ) r D (1) (C 2, 2 )
Upstream
B2U, f 2 (1)
2
1
p1 (C1,1 )
D (1)
false
1,1
p U (1) (C1,1 ) r U (1) (C1,1 )
A11
r1 false
W1
p1. f1
New blocking
and starvation
probabilities
MD(1)
B
MU(1)
W U (1)
p U (1) (C1,1 )
r U (1) (C1,1 )
A2,U (1)
New failure
probabilities calculation
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4- Two machine one buffer with local monitoring
p1false (C1,1 )
B
Monitored
machine
model
p
W1
2, f 2
r2B, f 2
Blocking (starvation)
probabilities equations
A11
r1 false
B
2, f 2
W1
p1. f1
r1. f1
D1, f1
quality
1
r
p1quality
A12
p2B, f 2 
p1 (C1,1 )
O1
p1. f1
Stationary state
probability distribution
B
2, f 2
r
B2O,1f 2
 ( B j , f j (1))
 ( E (1))
r2B, f 2
f j  1,..., Fd
r2B, f 2  r jD, f j (1)
p2B, f 2
Transition probabilities
False alarm state:
 (W U (1))   (W1 )   (O1 )
 ( A (1)) U (1)
 ( A11 )
(1)
p Ufalse
(C1,1 ) 
r
(
C
)

r Ufalse(1) (C1,1 )
false
1,1
 (W U (1))
 (W1 )   (O1 )
 ( A1,U (1))   ( A11 )
r Ufalse(1) (C1,1 )  r1 false
 (A
Detected out of control state:
1,U
2 ,U
(1))   ( A )
2
1
 ( D1U, f1 (1))   ( D1, f1 )
 ( B U2 , f2 (1))   ( B2W,1f 2 )   ( B2O,1f 2 )
p
U (1)
 ( A 2,U (1)) U (1)
 ( A12 )
(C1,1 ) 
r
(
C
)

r U (1) (C1,1 )
1
,
1
U
 (W (1))
 (W1 )   (O1 )
TOT
 E2
TOT
U
2, f 2
B
B
2, f 2
(1)
r
(1)
pUfalse
(C1,1 )
A1,U (1)
U (1)
r false
(C1,1 )
p2B, f 2
p1. f1
W U (1)
p U (1) (C1,1 )
r1. f1
D1U, f1 (1)
r U (1) (C1,1 )
A2,U (1)
r U (1) (C1,1 )  r1quality
System yield:
Total average throughput:
E TOT (1)  E1
Pseudo-machine model
  (W1 )   (O1 )   (W2 )   (O2 )  E (1)
< Impact of SPC on System Performance >
Y (1)  Y1Y2 E TOT
Average buffer level:
n  n (1)
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5- Two machine one buffer with remote monitoring
C 1,2
M1
B
p 1 ,1 r1 ,1
p1, 2 r
1, 2
p 1 , F r1 , F
1
1
M2
p 2 ,1 r 2 ,1
p 2,2 r
2, 2
p 2,F r
2 2, F
Monitored machine Mi
Control chart Ci,q (i<q)
2
The approach remains the same as in the previous case, only the Markov chain is more
complicated:
Additional states:
p1false (C1,1 )
B2W,1f 2
p
O11: out of control, not detected
2
B
2, f 2
r
B
2, f 2
r1
W1
p1. f1
r1. f1
D1, f1
A11
B2O,1f 2
false
r1quality
2
1
A
p
1, 2
delay
p
p1. f1
O21: out of control, detected if the
2
1
O
p1 (C1,1 )
quality
1
state
r2B, f 2
p2B, f 2
machine was locally monitored (i=q)
A12: out of control correctly
detected by the control chart (i<q)
B
2, f 2
1
1
r
O
1
p2B, f 2
B2O,1f 2
p1,2delay represents the delay of the quality information due to the presence of the finite capacity
buffer B. It can be calculated by using the following equation:
delay 
n
1
E
< Impact of SPC on System Performance >
,2
p1delay

1
E

delay n  E
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6- Long lines with local monitoring – the approach
C1,1
M1
C 2, 2
B1
M2
Ci ,i
B2
Mi
CK ,K
Ci 1,i 1
Bi
M i 1
Bi 1
MK
By solving the two locally monitored machines systems with the presented method and
by using decomposition equations the performance of the original line can be estimated.
As for the two locally monitored machines system, the approach follows a two level
decomposition, since alternately the Markov chain representing each machine (machine
level) and each building block (buffer level) are studied .
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6- Long lines with local monitoring - failures
M U (1)
B(1)
M D (1)
M U (2)
B ( 2)
M D (2)
p1U,1(1) r1U,1 (1)
p 2D,1(1) r2D,1(1)
p U2,1(1) r2U,1(1)
p3D,1(1) r3D,1(1)
p1U, F(11) r1U, F(11)
p 2D, F(12) r2D, F(12)
p U2 , F(12) r2U, F(12)
p 3D, F(13) r3U, F(31)
U (1)
(1)
pUfalse
(C1,1 ) r false (C1,1 )
(1)
p Dfalse
(C2, 2 ) r false (C2, 2 )
(1)
pUfalse
(C2, 2 ) r false (C2, 2 )
(1)
p Dfalse
(C3,3 ) r false (C3,3 )
pU (1) (C1,1 ) r U (1) (C1,1 )
p D (1) (C2, 2 ) r D (1) (C2, 2 )
pU (1) (C2, 2 ) r U (1) (C2, 2 )
p D (1) (C3,3 ) r D (1) (C3,3 )
p3D,1(1) r3D,1(1)
p1U,1(1) r1U,1 (1)
p 3D, F(13) r3D, F(31)
p1U, F(11) r1U, F(11)
D (1)
p3D, F(13) 2 r3D, F(31) 2
D (1)
U (1)
U (1)
p1U, F(11) 2 r1, F1  2
Local failure probabilities: are simply equal to those of the correspondent machine in the original
line.
Quality linked failure probabilities: can be evaluated by using quality link equations provided.
Remote failure probabilities: can be evaluated by using the following decomposition equations.
They acts exactly in the same way as f type local failure modes for the pseudo-machines.
Upstream pseudo-machines
rjU, f j (i)  rj , f j
pUj , f j (i) 
Downstream pseudo-machines
rjD, f j (i)  rj , f j
pkD, f k (i ) 
< Impact of SPC on System Performance >
Ps j , f j (i  1)
E (i  1)
Pbk , f k (i  1)
E (i  1)
r Uj , f (i)
j  1,..., i  1, f j  1,..., F j  2
rkD, f (i )
k  i  1,... K ; f k  1,..., FK  2
j
k
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6- Long lines with local monitoring – the algorithm
C1,1
M1
C 2, 2
B1
M2
Ci ,i
B2
Mi
CK ,K
Ci 1,i 1
Bi
Bi 1
M i 1
MK
An iterative algorithm, inspired to the DDX, has been used to efficiently solve the
decomposition equations. It behaves as follows, after the initialization phase:
- Visiting all the upstream pseudo-machines for i=2,..,K-1
- Unknown failures probabilities are calculated by using decomposition equations;
- The performance of the building block l(i) are evaluated by using the two level
approach used for the two monitored machines system;
- The same steps are performed visiting all the downstream pseudo-machines for i=K-2,..,1
At the convergence, the system yield can be evaluated as:
Ysystem  Y (1)  Y (2)  ...  Y ( K  1)
i
Y (i)  Y (i)  Y (i)
U
D
Y (i ) 
U
Y
j 1
K
Y (i ) 
D
j
Y
k
k  i 1
The total and the effective average production rates:
tot
Esystem
 E (1)  E (2)  ...  E ( K  1)
< Impact of SPC on System Performance >
tot
E eff  Ysystem Esystem
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7- Numerical Results – two locally monitored machines
More than one hundred test cases with random parameters have been carried out
and compared with simulation. Some of those cases randomly selected are
reported:
Yield
E_tot
E_eff
n (1)
CASE
CT
SIM
e%
CT
SIM
e%
CT
SIM
e%
CT
SIM
1
2
3
4
5
6
7
8
9
10
1.6780
0.955
2.4
2.4138
1.9848
5.1083
1.9835
3.023
18.429
1.4289
1.6648
0.939
2.386
2.399
1.9847
5.0487
1.9844
0.034
18.632
1.4244
0.3295
0.199
0.343
0.35
0.0023
0.4969
0.0232
0.1813
0.9195
0.03
0.6562
0.1532
0.3557
0.3563
0.4067
0.4301
0.4316
0.113
0.2804
0.5368
0.6575
0.1527
0.3559
0.3567
0.4088
0.4314
0.4434
0.114
0.2809
0.537
0.1864
0.336
0.049
0.134
0.5158
0.3047
0.649
0.8546
0.152
0.0275
0.9115
0.2211
0.3755
0.3772
0.4259
0.6070
0.4612
0.4333
0.5735
0.5567
0.9132
0.2205
0.3753
0.3777
0.4280
0.6087
0.4642
0.4367
0.5743
0.5569
0.1904
0.287
0.047
0.139
0.5057
0.2687
0.6618
0.7868
0.1372
0.0287
0.7199
0.693
0.9472
0.9444
0.9550
0.7085
0.9359
0.261
0.489
0.9642
0.7199
0.6927
0.9473
0.9444
0.9551
0.7087
0.9358
0.2611
0.4891
0.9642
e % 0.0038
0.048
0.0014
0.005
0.0100
0.0361
0.011
0.0689
0.0163
0.0005
Average
<1%
<2%
System Yield
0.05
98
100
< Impact of SPC on System Performance >
Total E
0.432
97
100
Effective E
0.516
95
100
Buffer level
0.388
98
100
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7- Numerical Results – one remotely monitored
machine
Yield
E_tot
E_eff
n (1)
CASE
CT
SIM
e%
CT
SIM
e%
CT
SIM
e%
CT
SIM
Average
<1%
<2%
1
2
3
4
5
6
7
8
6.5074 2.1908 2.2900 8.0193 1.2400 2.4120 2.2066 1.3486
6.5550 2.1900 2.2679 7.8694 1.2362 2.4526 2.2119 1.3583
0.3968 0.0205 0.5525 1.2493 0.0549 0.4058 0.1317 0.1210
0.3384 0.9019 0.8995 0.9018 0.6497 0.4209 0.5395 0.2955
0.3344 0.9017 0.9008 0.9046 0.6421 0.4171 0.5386 0.2950
1.2171 0.0210 0.1444 0.3098 1.1703 0.9278 0.1622 0.1932
0.6059 0.9124 0.9139 0.9236 0.6734 0.6225 0.5725 0.3311
0.6060 0.9121 0.9137 0.9235 0.6635 0.6260 0.5735 0.3299
0.0191 0.0406 0.0216 0.0165 1.4851 0.5612 0.1701 0.3509
0.5585 0.9884 0.9842 0.9763 0.9647 0.6762 0.9423 0.8927
0.5517 0.9886 0.9858 0.9795 0.9677 0.6662 0.9391 0.8941
e % 1.2347 0.0203 0.1659 0.3264 0.3101 1.4974 0.3327 0.1565
System Yield
0.62
90
100
Total E
0.711
88
100
< Impact of SPC on System Performance >
Effective E
0.789
85
100
Buffer level
0.52
92
100
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
7- Numerical Results – K locally monitored machines
CASES
Sim.
1
An.
Err %
Sim.
2
An.
Err %
Sim.
3
An.
Err %
Sim.
4
An.
Err %
3 machine cases
10 machine cases
CAS ES
Sim.
1
An.
Err%
Sim.
2
An.
Err%
Summary of
results
E tot
0.5522
0.5559
0.67
0.8025
0.8062
0.46
E eff
0.0849
0.0854
0.58
0.4566
0.4588
0.481
Yield
0.1538
0.1538
0
0.569
0.5692
0.035
Average
<1%
<2%
E tot
0.64898
0.64605
0.45194
0.47543
0.47651
0.22737
0.5748
0.5753
0.086
0.0273
0.0271
0.732
N1
2.892
2.9
0.2
4.035
4.048
0.21
E eff
0.35825
0.35652
0.48318
0.24270
0.24265
0.02060
0.5567
0.5574
0.125
0.0269
0.0268
0.37
N2
2.604
2.618
0.35
3.650
3.648
0.033
System Yield
0.123
98
100
< Impact of SPC on System Performance >
Yield
0.55202
0.551846
0.03152
0.51049
0.509222
0.24839
0.9686
0.9687
0.01
0.9866
0.9868
0.02
N3
2.381
2.317
1.6
3.401
3.357
0.73
N4
2.184
2.179
0.125
3.188
3.189
0.016
Total E
0.672
93
100
N1
2.75398
2.75398
1.3770
3.4071
3.41109
0.0998
19.302
19.71
1.63
3.443
3.414
0.116
N5
1.997
2
0.075
2.990
2.999
0.15
N6
1.809
1.82
0.275
2.785
2.81
0.416
Effective E
0.723
92
100
N2
2.2599
2.2599
0.7390
1.2432
1.2308
0.3110
11.706
11.782
0.304
0.344
0.313
0.124
N7
1.616
1.682
1.65
2.584
2.642
0.96
N8
1.393
1.381
0.3
2.336
2.351
0.25
N9
1.106
1.099
0.175
1.951
1.951
0
Buffer level
0.799
90
100
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
7- System Behavior
h=0 - 100% insp
Effective throughput vs. N
Total Throughput and System yield vs. N
0.565
0.85
0.56
0.8
0.555
0.75
0.55
Total throughput
System Yield
0.65
EEFF
0.545
0.7
0.54
0.535
0.53
0.6
0.525
0.55
0.52
0.5
N
29
27
25
23
21
19
17
15
13
11
9
7
5
3
29
27
25
23
21
19
17
15
13
9
11
7
5
3
0.515
N
h=3
h=5
Effective throughput vs. N
Effective throughput vs. N
0.52
0.51
0.515
0.505
0.5
0.51
0.505
EEFF
EEFF
0.495
0.5
0.49
0.485
0.48
0.495
0.475
0.49
0.47
0.465
0.485
3
4
5 6
7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
N
< Impact of SPC on System Performance >
3
4 5
6 7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
N
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
8- Conclusion and Future Research
- Quality issues and productivity aspects must be jointly considered in the design
phase of production systems, since their correlation is evident.
- The proposed method, dealing with the interaction between SPC theory principles
and production system design issues, provides accurate results in the performance
analysis of such systems.
- New improvement of the method will be the integration of various scrap and
rework policies in order to identify the optimal scrap/rework parameters.
-The proposed method paves the way to the integrated analysis and solution of other
system design problem such as:
- Optimal design of control chart parameters;
- Optimal allocation of inspection devices;
- Optimal allocation of buffer space.
< Impact of SPC on System Performance >
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
Thank you for your attention.
< Impact of SPC on System Performance >
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
10- System Behavior
The behavior of systems in which the first machine is monitored by the second one
have been observed.
piquality
0.08
riqua lity
0.5
rifalse
0.94
pi
0.1
0.1
ri
0.5
0.47
 iWi
 iOi
0.03
0.9
hi(Ci,i)
0
Effective throughput vs. N
a i(Ci,i)
b i(Ci,i)
0.0027
0.6
Total Throughput and System yield vs. N
0.565
0.9
0.56
0.8
0.555
0.7
0.55
0.6
0.545
0.5
Total throughput
0.4
System Yield
0.54
0.535
N
< Impact of SPC on System Performance >
29
27
25
23
21
19
17
15
13
11
9
7
29
27
25
23
21
19
17
15
13
0
11
0.515
9
0.1
7
0.52
5
0.2
3
0.525
5
0.3
0.53
3
EEFF
mi(Ci,i)
1
N
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
< Impact of SPC on System Performance >
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione
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