Arne Thesen and Akachai Jantayavichit Slide 1

A new approach to tolerance improvement

through real-time selective assembly

Arne Thesen and Akachai Jantayavichit

Department of Industrial EngineeringUniversity of Wisconsin-Madison

1513 University Ave, Madison, WI 53706, U.S.A.

thesen@engr.wisc.edu

Arne Thesen and Akachai Jantayavichit Slide 2

Research Objective

Pins Bushings

Selective Assembly Process

Assembly Station

Tol. 10-3

Tol. 10-4

Tol. 10-3

To develop and evaluate efficient algorithms for tolerance improvement of assembly parts through selective assembly

3 +10-3 3 +10-3

5x10- 4

Arne Thesen and Akachai Jantayavichit Slide 3

Previous research focuses on batch process

Arne Thesen and Akachai Jantayavichit Slide 4

Example: An artificial heart valveMust avoid leakage

Arne Thesen and Akachai Jantayavichit Slide 5

Previous work

1985 Boyer and A statistical selective assembly method Nasemetz (SSA) for a real time process

1990 Malmquist OMID heuristic: determine the batch size

1992 Pugh SSA for a batch process

1993 Robin and Multiple Regression modeling Mazharsolook

1996 Zhang and Set theory and probability method

Fang

1997 Coullard et al. Matching theory

1999 Chan and Linn Balanced probability and unequal tolerance zone

1999 Thesen and Evaluate scroll compressor shells for Jantayavichit real time process

Arne Thesen and Akachai Jantayavichit Slide 6

The production system

Arne Thesen and Akachai Jantayavichit Slide 7

We focus on real-time applications in high-speed assembly systems (6 sec cycle times)

Arne Thesen and Akachai Jantayavichit Slide 8

The compressor

Arne Thesen and Akachai Jantayavichit Slide 9

Example: A SCROLL COMPRESSORNeeds close tolerances to maintain high pressure

Arne Thesen and Akachai Jantayavichit Slide 10

A high-speed selective assembly stationNote: This is presently a three-operator manual operation

Robot

Rejects

FIFO Input buffersMeasuring

stationRandom accessassembly buffe r

Tops

Bottoms

Arne Thesen and Akachai Jantayavichit Slide 11

Tolerance improvement

-3 -2.3 -1.5 -0.8 0 0.75 1.5 2.25 3 -3 -2.25 -1.5 -0.75 0 0.75 1.5 2.25 3

• Worst-case gap without selective assembly is 6

PIN BUSHING

Arne Thesen and Akachai Jantayavichit Slide 12

Tolerance improvement• Classify components by size into tolerance classes• Worst-case gap using 2 classes and matching identical classes is 3

– Resulting system is unstable

PIN BUSHING

Arne Thesen and Akachai Jantayavichit Slide 13

Tolerance improvement withdirect matching

s

Tolerance classes

Class coverage

Largest gap

Relative size of gap

Tolerance improvement

1 6 6 100.00 % 0 2 3 3 50.00 % ½ 4 1.5 1.5 25.00 % 1/4 8 0.75 0.75 12.50 % 1/8

16 0.38 0.38 6.25 % 1/16 32 0.19 0.19 3.62% 1/32

Arne Thesen and Akachai Jantayavichit Slide 14

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 20 40 60 80 100

Buffer capacity

Per

cent

Tolerance improvement Direct matching

Buffer utilization

Yield

8 tolerance classes

Arne Thesen and Akachai Jantayavichit Slide 15

Tolerance improvement Direct matching

• For reject rates less than 1%– Very large buffer capacities needed

– Very high buffer utilizations expected

Arne Thesen and Akachai Jantayavichit Slide 16

Tolerance improvement with neighbor search

• Allow matching with component in neighbor class• Worst case using 8 classes is 1.5

Arne Thesen and Akachai Jantayavichit Slide 17

Tolerance improvement Allowing matches with neighbor class

s

Tolerance classes

Class coverage

Largest gap

Relative size of gap

Tolerance improvement

1 6 2 3 6 100.00 % 0 4 1.5 3 50.00 % ½ 8 0.75 1.5 25.00 % 1/4

16 0.38 0.75 12.50 % 1/8 32 0.19 0.38 6.25 % 1/16

Arne Thesen and Akachai Jantayavichit Slide 18

Neighbor search Matching strategies

• Random• Direct match first• Least likely first• Most likely first

Arne Thesen and Akachai Jantayavichit Slide 19

Performance Analysis

• Performance measure: Yield

• Assuming that– All system states can be enumerated– Decisions in a given state are always made the same way

• Then we can compute steady state probability for– being in each state– making any state transition

• Decision rules for state space with 100,000 can be easily evaluated

• Simulation will be used for large models

Arne Thesen and Akachai Jantayavichit Slide 20

Neighbor search: Yield

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

Buffer Capacity

Yie

ld (

%)

Least Likely

Random

Reverse

DirectFirst

Arne Thesen and Akachai Jantayavichit Slide 21

Neighbor search: Buffer utilization

0

10

20

30

40

50

0 5 10 15 20 25 30 35 40 45 50

Buffer Capacity

Avg

bu

ffe

r p

op

ula

tio

n

Least Likely

Random

Reverse

DirectFirst

Arne Thesen and Akachai Jantayavichit Slide 22

Neighbor search, least likely first Buffer Capacity = 48, Discard upon deadlock

0

10

20

30

40

50

60

70

10 15 20 25 30 35 40 45 50

Tolerance classes

Av

era

ge

Bu

ffe

r P

op

ula

tio

n

Discard rate Average populationunlimited capacity

Averagepopulation

0.03

0.04

0.05

0.02

0.01

0.06

Ret

urn

Rat

e

Arne Thesen and Akachai Jantayavichit Slide 23

Establish required level of tolerance reduction

From this set number of tolerance classes

Establish algorithm for selecting componentsNeighborhood

Decide how to deal with deadlock Discard

Return

Specify buffer capacity

Designing a real-time assembly station

Arne Thesen and Akachai Jantayavichit Slide 24

RecommendationsUse neighbor search with most unlikely first

Tolerance improve-

ment

Buffer capacity

Expected population

Discard rate (%)

Return rate (%)

1/4 12 3.1 0.01 0.4

1/8 28 12.5 0.29 0.6

1/12 48 24.3 0.16 0.8

1/16 60 36.3 0.29 0.8

1/20 72 45.0 0.29 1.0

Arne Thesen and Akachai Jantayavichit Slide 25

CONCLUSION

• Significant tolerance improvement is possible.

• Must use neighborhood matching rule.

• Results only valid for identical distributions.

• Extensions to unequal distributions under way.

Arne Thesen and Akachai Jantayavichit Slide 26

Thank you

Any Questions ?Any Questions ?