Never Stops
Computerized Repairable Inventory Management with
Reliability Growth and System Installations Increase
Jin Tongdan, Ph.D.
Teradyne, Inc., Boston
When: May 8, 2006
Where: Texas A&M International University
What are Repairable Systems/Products
1. System can be fixed during its lifetime
2. Capital intensive and long lifetime
3. Diagnostic tools, maintenance and utilization
4. PM and reliability growth metrics
Challenge Yourself, Drive Product Growth
G
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IN
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es
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m
ico
nd
uc
to
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nd
us
try
Outlines
• ATE and Semiconductor Industry Overview
• ATE Reliability Growth Model
• Defective Module Repair Time Estimate
• Repairable Inventory Service Controller
• Conclusions
Worldwide ATE Market Trend
Source: www.altera.com
World population=6 billion
Who are the Players in ATE
Teradyne
30%
Advantest
11%
Agilent
19%
Credence
6%
LTX
7%
YEW
12%
NPTest
10%
Other
5.6%
© 2004 Prime Research Group
Reproduction prohibited
Lowering the cost of capacity
Semiconductor Manufacturing Process
Source: From Young Soon Song et. al. “Semiconductor electronics design project”.
Semiconductor Manufacturing Process
Fundamental Processing Steps
1.Silicon Manufacturing
a) Czochralski method.
b) Wafer Manufacturing
c) Crystal structure
2.Photolithography
a) Photoresists
b) Photomask and Reticles
c) Patterning
Source:
From Young Soon Song et. al. “Semiconductor electronics design project”.
Semiconductor Manufacturing Process (cnt’d)
3.Oxide Growth & Removal
a) Oxide Growth & Deposition
b) Oxide Removal
c) Other effects
d) Local Oxidation
4. Diffusion & Ion Implantation
a) Diffusion
b) Other effects
ATE Semitest Market Segments
Broadband
Wireless / RF
Computing
Mass Storage
Datacom
Consumer
Disk Drive
Read Channels
Disk Drive SOC
SERDES/SONET
10/100/1000BaseT
Infiniband
CODECs
Microcontrollers
Printhead drivers
Battery management
Servo/motor drivers
Automotive control
Smart Power
Smart cards
Baseband
processors
Cable Modem
xDSL
Set-top box
Converters
DVD R/W
Microprocessor
Chipsets
Graphics
Network
Processors
HSM
Mobile/Cordless Phone
WLAN, Bluetooth
Pagers/PDA Rx/TX
GPS Systems
Digital Satellite Rx
Cable Tuners
Automatic Test Equipment
ATE Cost: 1~3 million US$
PCB Module: 30,00 ~ 100,000 US$
Useful Lifetime: 5 to 10 years
System MTBF: 1,500 to 3,000 hours
Module MTBF: 40,000-60,00 hours
Mainframe Testhaed DIB Cover Dock Ctrl PCB ModuleInstrumentations:
•
High-speed digital
•
Analog
•
DC
•
Memory
ATE Operation Principle
Source: www.maxim-ic.com
Square waves
or arbitrary analog wave
Square waves or
Two Factors for Repairable Inventory
1.System and instrument reliability growth
- failure intensity rate reduced per system
2. Expansion of the system installations
Bathtub Failure Rate Curve
Source: http://www.weibull.com
fa
u
lt
s
p
er
u
n
it
t
im
e
MTBF and Installations Impact Field Returns
Failure Returns Per Week with Different Sytem Installation Rate and MTBF
0
10
20
30
40
50
60
70
1
3
5
7
9
1
1
1
3
1
5
1
7
1
9
2
1
2
3
2
5
2
7
2
9
3
1
3
3
3
5
3
7
3
9
4
1
4
3
4
5
4
7
4
9
5
1
Week No.
F
ai
lu
re
s
P
er
W
ee
k
Install 10 sys/wk, MTBF=1500
Install 10 sys/wk, MTBF=2500
Install 5 sys/wk, MTBF=1500
Failures=58
Failures=39
Failures=25
Benefit of High MTBF to Inventory
1. High MTBF means customer satisfaction
2. More than 31 million$ holding cost (1500 vs 2500 hrs)
3. Less repair facility and logistic costs
Existing Research Work
1.
Zamperini, M., Freimer, M. “A Simulation Analysis of the
Vari-Metrics Repairable Inventory Optimization Procedure for the U.S.
Coastal Guard”,
Proceedings of 2005 Winter Simulation Conference
.
2.
Guide, V., Srivastava, R., “Invited review for repairable inventory
theory: models and applications”,
European Journal of Operations
Research
, vol. 102, 1997
3.
Kim, J. et. al.,”Optimal algorithm to determine the spare inventory level
for a repairable-item inventory system”,
Computers Operations
Research
, vol. 23, 1996
4.
Jung, W., “Recoverable inventory systems with time-varying demand”,
Production and Inventory Management Journal
, vol. 34, 1993
5.
Wasserman, G., Lamberson, L., “Spares Provisioning Under Reliability
Growth”,
Logistics Spectrum Winter
, 1992
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/product Shipment Defective module Transition time Defective module Repair time Failure intensity µ µµ µ(t) System installed N(t) or E[N(t)] & Var(N(t)) Transition time tt~Normal FM Pareto & repair time tror
E[tr] & Var(tr) Failures δδδδt(T) or E[ δ δ δ δt(T)] & Var(δδδδt(T)) Defective timetd=tt+tr or E[td] & Var(td) Rate of return φ φ φ φt(T)=δδδδt(T)/T Repair rate γγγγm=m/td Service Index Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R Tune m
Reliability Growth vs. Degradation
t
System 1
t
System 2
t
System 3
X
X
X
X
X
X
X
X
X
X
Crown Reliability Growth Estimate
Failure Intensity Rate with various Beta
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
8
9
10
Time (t)
F
au
lt
s
P
er
U
n
it
T
im
e
beta=1
beta=1.5
beta=0.5
alpha=1 for all lines
1
)
(
t
=
αβ
t
β
−
u
Reliability Growth Test and Estimate
Normal
Renew vs. Non-Renew
Lewis-Robinson Test
(LRT)
Normal
Renew vs. Non-Renew
Pairwise Comparison
Non-parametric Test
(PCNT)
Normal
NHPP v. HPP
Laplace Test
Chi-square
NHPP v. HPP
Crow/AMSSA
Test Statistics
Test for What
Test Name
HPP= Homogeneous Poisson Process
NHPP= Non-homogenous Poisson Process
Renew= Renewal Process
References:
1). P. Wang, T. Jin, D. Coit, “Repairable System Reliability: Planning and Assessment Tools”, Quality and Reliability Engineering Center Report, QRE report number 99-2, October 1999, Rutgers University, New Jersey, USA
2). T. Jin, H. Liao, Z. Xiong, “Computerized Reparable Inventory Management with Reliability Growth and Increased Product Population”, submitted to CASE 2006, Oct 8-9, Shanghai, China
Test Reliability Growth Trend Test Flow Chart
Trend Test
NHPP
Yes
Goodness-fit-Test
HPP
Yes
Renew Process
Start
No
No
Data Input
Crow/AMSSA
Laplace Test
PCNT
LR Test
Renewal Process vs. HPP
∑
=
=
n
i
i
n
Y
J
1
HPP processes: if each
Y
1
,
Y
2
,
Y
3
,... is i.i.d. and
exponentially distributed. Then it is HPP
Renewal processes: The renewal processes
are used to model
independent identically distributed occurrences.
Definition 3.7 Let
Y
1
,
Y
2
,
Y
3
,... be i.i.d. and positive stochastic
variables, defining a new random variable
And the renewal interval is [
J
n
,
J
n
+1
]. Then the random
X
t
given by
}
:
max{
n
J
t
Crow Model Parameters Estimation Tool
Trend Test
Parameter
Estimation
Single System Failure Return Model
βα
τ
τ
)
(
)
(
)
(
0T
t
d
u
T
t
m
T t+
=
=
+
∫
+ β βτ
α
αβτ
τ
τ
d
d
t
u
t
m
t t=
=
=
∫
∫
− 0 1 0)
(
)
(
1. Failure Intensity (faults per unit time) at time
t
2. Cumulative Failures at time
t
3. Cumulative Failures at time
t+T
4. Cumulative Failures between [
t
,
t+T
]
1
)
(
t
=
αβ
t
β−u
[
β β]
α
t
T
t
t
m
T
t
m
(
+
)
−
(
)
=
(
+
)
−
Multiple Systems - Deterministic
For
N
multiple systems, the total cumulative Failures between [
t
,
t+T
]
(
)
[
β
β
]
α
δ
t
T
t
N
t
m
T
t
m
N
T
t
−
+
=
−
+
=
)
(
)
(
)
(
)
;
(
This means that given
N
systems in the field, the expected faults occurred
Between
t
and
t
+
T
is
δ
(
t
).
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/product Shipment Defective module transit time Defective module Repair time Failure intensity µ µµ µ(t) System installed N(t) or E[N(t)] & Var(N(t)) Transit time tt~Normal FM Pareto & repair time tror
E[tr] & Var(tr) Failures δδδδt(T) or E[ δ δ δ δt(T)] & Var(δδδδt(T)) Defective timetd=tt+tr or E[td] & Var(td) Rate of return φ φ φ φt(T)=δδδδt(T)/T Repair rate γγγγm=m/td Service Index Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R Tune m
Failures Considering Install Base Expansion
Demand of A Type of High Speed Digital Testing Module
0
500
1000
1500
2000
2500
0
2
4
6
8
1
0
1
2
1
4
1
6
1
8
2
0
2
2
2
4
2
6
2
8
3
0
3
2
3
4
3
6
3
8
4
0
4
2
Time (Month)
C
u
m
u
la
ti
v
e
I
n
s
ta
ll
B
a
s
e
s
0
100
200
300
400
500
600
700
800
900
1000
M
o
n
th
ly
S
h
ip
m
e
n
t
Q
ty
Monthly Ship Qty
System Installation modeling
!
)
(
}
)
(
Pr{
n
e
t
n
t
N
t
n
λ
λ
=
=
Where:
λ
= system install rate (e.g. quantity per unit time)
n
= number of systems installed by time
t
for
n
=0, 1, 3, ….
t
t
N
E
[
(
)]
=
λ
t
t
N
Var
(
(
))
=
λ
Multiple Systems - Stochastic
For
N
(
t
) multiple systems, the total cumulative Failures between [
t
,
t+T
]
(
)
[
β
β
]
α
δ
t
T
t
t
N
t
m
T
t
m
t
N
T
t
−
+
=
−
+
=
)
(
)
(
)
(
)
(
)
(
)
;
(
This means that given
N
(
t
) systems in the field by time
t
, the expected faults
occurred Between
t
and
t
+
T
is
E
[
δ
(
t;T
)].
(
1
)
)
(
)]
;
(
[
δ
t
T
=
αλ
t
t
+
T
β
−
t
β
+
E
(
)
2
2
)
(
))
;
(
(
δ
t
T
α
λ
t
t
T
β
t
β
Var
=
+
−
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/product Shipment Defective module transit time Defective module Repair timetr Failure intensity µ µµ µ(t) System installed N(t) or E[N(t)] & Var(N(t)) Transit time tt~Normal FM Pareto & repair time tror
E[tr] & Var(tr) Failures δδδδt(T) or E[ δ δ δ δt(T)] & Var(δδδδt(T)) Defective timetd=tt+tr or E[td] & Var(td) Rate of return φ φ φ φt(T)=δδδδt(T)/T Repair rate γγγγm=m/td Service Index Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R Tune m
Repair and Stock Centers
Philippines
Boston
Costa Rica
Repairable Module Cycle Time
Good Stock
Inventory
ATE System in Field Worldwide
Part Tested/Repaired
at Repair Center
(repair time
t
r)
GCS Inspection/defective
Inventory
t
t
1Defective
Part
returned
Good Part
received
t
t
2t
t
3t
t
4t
t
=
t
t
1
+
t
t
2
Defective Module Transition Time
t
t
1. Based on historical data, transition time
t
t
from
different customer sites to the repair center can
generally modeled by normal distribution.
2. If
t
t
follows other types of distributions, it is also
applicable.
Defective Module Transition Time
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 5 10 15 20 25 30 35 Time p d f
µ
tσ
tDefective Module Repair Time
t
r
PCBA Failure Mode and Repair Time
0 5 10 15 20
Cold Solder Defective ASICS Bad Relays Corrupted EEPROM Q ty 0 20 40 60 80 100 120 140 R e p a ir t im e ( m in u te s ) Qty Repair Time
1. Repair time
t
r
depends on the failure mode.
2. Using weighted average to estimate
t
r
∑
==
=
n i i i r rE
t
E
w
1]
[
]
[
τ
µ
∑
=
=
=
n
i
i
i
r
r
Var
t
Var
w
1
2
2
)
(
)
(
τ
σ
Total Time in Defective Status
r
t
r
t
d
d
=
E
t
=
E
t
+
E
t
=
µ
+
µ
µ
[
]
[
]
[
]
2
2
2
)
(
)
(
)
(
d
t
r
t
r
d
=
Var
t
=
Var
t
+
Var
t
=
σ
+
σ
σ
r
t
d
t
t
t
=
+
The total time the module in defective status include:
1). transition time; and 2) repair times. That is
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/product Shipment Defective module transit time Defective module Repair time Failure intensity µ µµ µ(t) System installed N(t) or E[N(t)] & Var(N(t)) Transit time tt~Normal FM Pareto & repair time tror
E[tr] & Var(tr) Failures δδδδt(T) or E[ δ δ δ δt(T)] & Var(δδδδt(T)) Defective timetd=tt+tr or E[td] & Var(td) Rate of return φ φ φ φt(T)=δδδδt(T)/T Repair rate γγγγm=m/td Service Index Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R Tune m
Robust Inventory Service Quality Monitor
Where
d
m
t
m
=
γ
T
T
t
t)
;
(
δ
φ
=
m
= number of repair channels
R
= customer satisfaction level (95% or 99% etc)
{
}
{
t
t
mT
}
R
T
t
t
m
d
d
t
m
=
δ
≥
≥
δ
≥
=
φ
≥
γ
Pr
(
)
Pr
(
)
Pr
repair rate under
m
repair channels
Illustrative Example
Repair Channels with 95% Confidence Level
0
25
1
2
3
4
5
m
Defective return rate (mean) = 20 /day
Mean of repair time E[
t
d
]=10 days
E[
t
d]=5 days
))
;
(
(
t
T
Var
δ
)
(
t
dVar
Conclusions
1. A robust inventory control model is developed to
address reliability growth and the expansion of
systems.
2. A weighted estimate is proposed to compute the
repair time of the defective module
3. The explicit link between the repair channel and the
service index are established, based upon which
management team can tune the service quality using
the repair resources.
4. Future research work can incorporate defective
Thanks
Questions and
Comments
