Post on 18-Mar-2018
1Because Technology
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
(Note: Dr. Jin current is a faculty in TAMIU from 9/1/2006)
2
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
3
Challenge Yourself, Drive Product Growth
GR
OW
ING
The rec
eipt f
or succ
ess i
n
sem
iconducto
r industr
y
4
Outlines
• ATE and Semiconductor Industry Overview
• ATE Reliability Growth Model
• Defective Module Repair Time Estimate
• Repairable Inventory Service Controller
• Conclusions
Note: ATE= Automatic Test Equipment
5
Worldwide ATE Market Trend
Source: www.altera.com
World population=6 billionYou contribute= 38 US$ (or 304 RMB/year)
6
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 GroupReproduction prohibitedPreliminary
7
Lowering the cost of capacity
Who Need ATE Systems?
8
Semiconductor Manufacturing Process
Source: From Young Soon Song et. al. “Semiconductor electronics design project”.
ATE
9Semiconductor Manufacturing Process
Fundamental Processing Steps
1.Silicon Manufacturinga) Czochralski method.
b) Wafer Manufacturing
c) Crystal structure
2.Photolithographya) Photoresists
b) Photomask and Reticles
c) Patterning
Source: From Young Soon Song et. al. “Semiconductor electronics design project”.
10
Source: From Young Soon Song et. al. “Semiconductor electronics design project”.
Semiconductor Manufacturing Process (cnt’d)
3.Oxide Growth & Removala) Oxide Growth & Deposition
b) Oxide Removal
c) Other effects
d) Local Oxidation
4. Diffusion & Ion Implantationa) Diffusion
b) Other effects
c) Ion Implantation
11
ATE Semitest Market Segments
Broadband
Wireless / RF
Computing
Mass StorageDatacom
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
Source: ASE Integration Meeting, July 15, 2004, San Jose, CA
12
Automatic Test Equipment
ATE Cost: 1~3 million US$
PCB Module: 30,00 ~ 100,000 US$Useful Lifetime: 5 to 10 years
System MTBF: 1,500 to 3,000 hoursModule MTBF: 40,000-60,00 hours
Mainframe
Testhaed
DIB Cover
Dock Ctrl
PCB Module
Instrumentations:
• High-speed digital• Analog
• DC• Memory
13
ATE Operation Principle
Source: www.maxim-ic.com
Square waves or arbitrary analog wave
Square waves or arbitrary analog wave
14
Two Factors for Repairable Inventory
1.System and instrument reliability growth
- failure intensity rate reduced per system
2. Expansion of the system installations
- total failure quantity may increase
15
Bathtub Failure Rate Curve
Source: http://www.weibull.com
fau
lts
per
un
it t
ime
16MTBF and Installations Impact Field Returns
Failure Returns Per Week with Different Sytem Installation Rate and MTBF
0
10
20
30
40
50
60
70
1 3 5 7 9 11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
51
Week No.
Fai
lure
s P
er W
eek
Install 10 sys/wk, MTBF=1500
Install 10 sys/wk, MTBF=2500
Install 5 sys/wk, MTBF=1500
Failures=58
Failures=39
Failures=25
17
Benefit of High MTBF to Inventory
1. High MTBF means customer satisfaction
2. More than 31 million$ holding cost (1500 vs 2500 hrs)
3. Less repair facility and logistic costs
4. Lower backorders and quick response
18
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
19
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/productShipment
Defective module Transition time
Defective module Repair time
Failure intensity
µµµµ(t)
System installedN(t) or
E[N(t)] & Var(N(t))
Transition timett ~Normal
FM Pareto& repair time tr or
E[tr] & Var(tr)
Failures δδδδt(T)or
E[ δ δ δ δt(T)] & Var(δδδδt(T))
Defective time td=tt+tr
orE[td] & Var(td)
Rate of return
φφφφt(T)=δδδδt(T)/T
Repair rate
γγγγm=m/td
Service Index
Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R
Tune m
20
Reliability Growth vs. Degradation
t
System 1
t
System 2
t
System 3
X X X
X X X
X X X X
21
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 10Time (t)
Fau
lts
Per
Un
it T
ime beta=1
beta=1.5
beta=0.5
alpha=1 for all lines
1)( −= βαβttu
22
Reliability Growth Test and Estimate
NormalRenew vs. Non-RenewLewis-Robinson Test
(LRT)
NormalRenew vs. Non-RenewPairwise Comparison
Non-parametric Test
(PCNT)
NormalNHPP v. HPPLaplace Test
Chi-squareNHPP v. HPPCrow/AMSSA
Test StatisticsTest for WhatTest 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
23
Test Reliability Growth Trend Test Flow Chart
Trend Test NHPPYes
Goodness-fit-Test HPPYes
Renew Process
Start
No
No
Data Input
Crow/AMSSA
Laplace Test
PCNT
LR Test
24
Renewal Process vs. HPP
∑=
=n
i
in YJ1
HPP processes: if each Y1,Y2,Y3,... 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 Y1,Y2,Y3,... be i.i.d. and positive stochastic
variables, defining a new random variable
And the renewal interval is [Jn, Jn+1]. Then the random Xt given by
}:max{ tJnX nt ≤=
25
Crow Model Parameters Estimation Tool
Trend Test
Parameter
Estimation
26
Single System Failure Return Model
βαττ )()()(0
TtduTtm
Tt
+==+ ∫+
ββ αταβτττ tddutm
tt
=== ∫∫−
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)( −= βαβttu
[ ]ββα tTttmTtm −+=−+ )()()(
27
Multiple Systems - Deterministic
For N multiple systems, the total cumulative Failures between [t, t+T]
( )[ ]ββα
δ
tTtN
tmTtmNTt
−+=
−+=
)(
)()();(
This means that given N systems in the field, the expected faults occurred
Between t and t+T is δ(t).
The key factor is N is a random variable, not deterministic
28
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/productShipment
Defective module transit time
Defective module Repair time
Failure intensity
µµµµ(t)
System installedN(t) or
E[N(t)] & Var(N(t))
Transit timett ~Normal
FM Pareto& repair time tr or
E[tr] & Var(tr)
Failures δδδδt(T)or
E[ δ δ δ δt(T)] & Var(δδδδt(T))
Defective time td=tt+tr
orE[td] & Var(td)
Rate of return
φφφφt(T)=δδδδt(T)/T
Repair rate
γγγγm=m/td
Service Index
Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R
Tune m
29
Failures Considering Install Base Expansion
Demand of A Type of High Speed Digital Testing Module
0
500
1000
1500
2000
25000 2 4 6 8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
Time (Month)
Cu
mu
lati
ve
In
sta
ll B
as
es
0
100
200
300
400
500
600
700
800
900
1000
Mo
nth
ly S
hip
me
nt
Qty
Monthly Ship Qty
Cum Ship Qty
30
System Installation modeling
!
)(})(Pr{
n
etntN
tn λλ==
Where:
λ= system install rate (e.g. quantity per unit time)
n = number of systems installed by time t
for n=0, 1, 3, ….
ttNE λ=)]([
ttNVar λ=))((
31
Multiple Systems - Stochastic
For N(t) multiple systems, the total cumulative Failures between [t, t+T]
( )[ ]ββα
δ
tTttN
tmTtmtNTt
−+=
−+=
)()(
)()()();(
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)()];([ +−+= ββαλδ tTttTtE
( )22 )());(( ββλαδ tTttTtVar −+=
32
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/productShipment
Defective module transit time
Defective module Repair time tr
Failure intensity
µµµµ(t)
System installedN(t) or
E[N(t)] & Var(N(t))
Transit timett ~Normal
FM Pareto& repair time tr or
E[tr] & Var(tr)
Failures δδδδt(T)or
E[ δ δ δ δt(T)] & Var(δδδδt(T))
Defective time td=tt+tr
orE[td] & Var(td)
Rate of return
φφφφt(T)=δδδδt(T)/T
Repair rate
γγγγm=m/td
Service Index
Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R
Tune m
33
Repair and Stock Centers
Philippines
Boston
Costa Rica
Memphis
34
Repairable Module Cycle Time
Good Stock
Inventory
ATE System in Field Worldwide
Part Tested/Repaired
at Repair Center
(repair time tr)
GCS Inspection/defective
Inventory
tt1
Defective
Part
returned
Good Part
received
tt2
tt3
tt4
tt=tt1+tt2
35
Defective Module Transition Time tt
1. Based on historical data, transition time tt from
different customer sites to the repair center can
generally modeled by normal distribution.
2. If tt 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
pd
f
µt
σt
36
Defective Module Repair Time tr
PCBA Failure Mode and Repair Time
0
5
10
15
20
Cold Solder Defective ASICS Bad Relays Corrupted
EEPROM
Qty
0
20
40
60
80
100
120
140
Repair t
ime (
min
ute
s)
Qty
Repair Time
1. Repair time tr depends on the failure mode.
2. Using weighted average to estimate tr
∑=
==n
i
iirr wEtE1
][][ τµ
∑=
==n
i
iirr wVartVar1
22 )()( τσ
37
Total Time in Defective Status
rtrtdd tEtEtE µ+µ=+==µ ][][][
222 )()()( rtrtdd tVartVartVar σ+σ=+==σ
rtd ttt +=
The total time the module in defective status include:
1). transition time; and 2) repair times. That is
38
Road Map to Manage ATE Repairable Inventory
Reliability growth test and estimate
system/productShipment
Defective module transit time
Defective module Repair time
Failure intensity
µµµµ(t)
System installedN(t) or
E[N(t)] & Var(N(t))
Transit timett ~Normal
FM Pareto& repair time tr or
E[tr] & Var(tr)
Failures δδδδt(T)or
E[ δ δ δ δt(T)] & Var(δδδδt(T))
Defective time td=tt+tr
orE[td] & Var(td)
Rate of return
φφφφt(T)=δδδδt(T)/T
Repair rate
γγγγm=m/td
Service Index
Pr{γγγγm≥≥≥≥ φφφφt(T)}≥≥≥≥R
Tune m
39
Robust Inventory Service Quality Monitor
Where
d
mt
m=γ
T
Ttt
);(δφ =
m = number of repair channels
R = customer satisfaction level (95% or 99% etc)
{ } { } RmTttT
t
t
md
d
tm ≥≥δ=
δ
≥=φ≥γ )(Pr)(
PrPr
repair rate under m repair channels
failure rate at time t
40
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[td]=10 days E[td]=5 days
));(( TtVar δ
)( dtVar
41
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
scrap, multiple repair centers, and cost analysis etc.
42
Thanks
Questions and
Comments