Repairable Inventory Management with increase … t_jin.pdfWorldwide ATE Market Trend 5 ... Disk...

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


10


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



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




Defective module transit time


Failure intensity

µµµµ(t)


E[N(t)] & Var(N(t))

Transit timett ~Normal


E[tr] & Var(tr)




orE[td] & Var(td)

Rate of return


Repair rate

γγγγm=m/td

Service Index


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





Defective module Repair time tr

Failure intensity

µµµµ(t)


E[N(t)] & Var(N(t))



E[tr] & Var(tr)




orE[td] & Var(td)

Rate of return


Repair rate

γγγγm=m/td

Service Index


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






Failure intensity

µµµµ(t)


E[N(t)] & Var(N(t))



E[tr] & Var(tr)




orE[td] & Var(td)

Rate of return


Repair rate

γγγγm=m/td

Service Index


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

Repairable Inventory Management with increase … t_jin.pdfWorldwide ATE Market Trend 5 ... Disk...

Documents

Transcript of Repairable Inventory Management with increase … t_jin.pdfWorldwide ATE Market Trend 5 ... Disk...