New Results on the Integrated Analysis of Quality and...

New Results on the Integrated Analysis of Quality andQuantity in Production Lines

Stanley B. Gershwin∗ Irvin C. Schick Jongyoon Kim

FIFTH INTERNATIONAL CONFERENCE ONAnalysis of Manufacturing Systems — Production Management

Zakynthos Island, GreeceMay 23, 2005

*[email protected], 617-253-2149, http://web.mit.edu/manuf-sys

Copyright c©2005 Stanley B. Gershwin. All rights reserved.

Introduction

•Quantity: How much and when.

•Quality: How well.

•Most literature is all quantity or all quality.•However,

⋆ quality-motivated decisions affect quantity performance, and

⋆ quantity-motivated decisions affect quality performance.

•Therefore, integrated analyses (Q/Q) are needed.

Copyright c©2005 Stanley B. Gershwin. All rights reserved. 2

IntroductionRelated Literature

Very few papers deal with Q/Q. Some recent ones are:

• Inman, Blumenfeld, Huang, and Li, IJPR 2003

• Li and Blumenfeld IEEE Conference on Roboticsand Automation, 2005

•Kim, MIT PhD, 2004

•Kim and Gershwin, 2003 Aegean Conference andOR Spectrum, 2005

•Some other papers at this meeting?


Taxonomy ofIssues

•Failure dynamics• Inspection

⋆ Binary (good/bad) vs. measurement

⋆ Accuracy (false positives and negatives)

⋆ Spatial and temporal frequency

•Actions on parts and machines

•Topology of system

•Performance measures


FailureDynamics

Examples

•Bernoulli or common cause: independent.

•Persistent or special cause: all parts after the firstbad part are bad, until the repair.

•Multi-Yield : generalization of persistent.


FailureDynamics

Models of multi-yield failures

Operation following Information Feedback

Nominal Operation


Nominal Operation

L

D

H

1-pH-s1-pL

r

s

1 1

pHpL

1-rQ

L

D

H

1-pH-s1-pL

r

s

1 1

pHpL

L

D

H

1-pH-s1-pL

r

s

1 1

L

D

H

1-pH-s1-pL

r

s

1 1

pHpL

1-rQ


FailureDynamics


L

DQ

DH

H

DL

1-pH-s1-pL

1-rH1-rL

1

1-rQ

rQ

rL rH

s

1 1pL pH

1

L

DQ

DH

H

DL

1-pH-s1-pL

1-rH1-rL

1

1-rQ

rQ

rL rH

s

1 1pL pH

L

DQ

DH

H

DL

1-pH-s1-pL

1-rH1-rL

1

1-rQ

rQ

rL rH

s

1 1pL pH

1


Nominal Operation


Nominal Operation


FailureDynamics


L

DQ

DH′′′′

DH

H

DL

DL′′′′

1-pH-s1-pL

1-rL 1-rH

1-rH1-rL

1-rH1-rL

rH

rH

rL

rL

1-rQ

rQ

rL rH

s

1 1pL pH

L

DQ

DH′′′′

DH

H

DL

DL′′′′

1-pH-s1-pL

1-rL 1-rH

1-rH1-rL

1-rH1-rL

rH

rH

rL

rL

1-rQ

rQ

rL rH

s

1 1pL pH


Nominal Operation


Nominal Operation


FailureDynamics


Simplified aging model

D D D DDDD

H7 H6 H5 H4 H3 H1H2

D

Response to detection

Preventative maintenance

D

L

5 4 3 267L 1

Q


FailureDynamics

Performance Measures

•Expected total production rate

•Expected good production rate

•Yield

They are easy to calculate in a single-machine model.


Two-MachineLines•Continuous material

•Three-state machine•Quality information feedback

⋆ Defects produced by the first machine are detected, after adelay, by the second machine.

⋆ The length of the delay depends on the number of parts inthe buffer.

•As buffer size increases, total production rateincreases and yield decreases. But good productionrate behavior is harder to predict.


Two-MachineLines

Quality Information Feedback

Quality Information Feedback


Two-MachineLines

Performance Measures

•Expected total production rate

•Expected good production rate

•Yield

•Expected inventory.

The two-machine, one-buffer line with knownparameters can be solved using standard methods.


Two-MachineLines

Solution Technique

All parameters of the two-machine, one-buffer line areknown except h12, the transition rate from the badquality state of M1 to the down state due to theinspection at M2. This depends on the number ofparts in the buffer x̄.

Procedure:

• Guess x̄.

• Calculate h12.

• Solve the two-machine line. Recalculate x̄ and iterate.


Two-MachineLines

Intuition

•Quantity-oriented people tend to assume thatincreasing a buffer increases the production rate.

•Quality-oriented people tend to assume thatincreasing a buffer decreases the production rate ofgood items.


Two-MachineLines

Beneficial Buffer

0 5 10 15 20 25 30 35 40 45 500.65

0.7

0.75

0.8

Buffer Size

Effe

ctiv

e P

rodu

ctio

n R

ate

without feedbackwith feedback


Two-MachineLines

Harmful Buffer

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

Buffer Size

Effe

ctiv

e P

rodu

ctio

n R

ate

Without feedbackWith feedback


Two-MachineLines

Mixed-Benefit Buffer

0 5 10 15 20 25 30 35 40 45 500.37

0.375

0.38

0.385

0.39

0.395

0.4

Buffer Size

Effe

ctiv

e P

rodu

ctio

n R

ate


Long LinesSimulation

• Intuition: more inspection improves quality.

•Reality: increasing inspection can actually reducequality, if it is not done intelligently.



•We simulated a 15-machine, 14-buffer line.

•All machines and buffers were identical.•We looked at all possible combinations of inspection

stations in which all operations were inspected.⋆ Example: Inspection stations just after Machines 6, 9, 13,

and 15.⋆ The first inspection looks at the results from Machines 1 – 6;

the second looks at results from Machines 7, 8, and 9; thethird from 10 – 13; and the last from 14 and 15.

⋆ There is always one inspection after Machine 15.

•A total of 214=16,384 cases were simulated.



Range of Good Production Rates for Different Numbers of Inspection Stations

(15 five-state machines, 14 buffers, information feedback only)No inspection: 0.10040

0.295

0.305

0.315

0.325

0.335

0.345

0.355

0.365

0.375

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Inspection Stations

Go

od

Pro

du

cti

on

Rate

Best locations

Worst locations


Long LinesDecomposition

Three structures analyzed

M 1 B 1 M 2 M 3 M 4 B 2 B 3

Inspection

Inspection

M 1 B 1 M 2 M 3 M 4 B 2 B 3

Operational Failures Operational Failures

+ Quality Failures

Inspection

M 1

B 1

M 2

M 3

M 4 B 2 B 3

Operational Failures + Quality Failures



• Procedure:

⋆ Guess x̄i.

⋆ Calculate required hij parameters.

⋆ Transform the 3-state machines into approximate 2-statemachines.

⋆ Solve the resulting line by a standard decompositiontechnique.

⋆ Recalculate x̄i and iterate.

• Comparison with simulation is reasonable.



The system yield is the product of individual machineyields using the final hij values .

The effective production rate is the total productionrate times the system yield.


Conclusions

•Combining Q/Q produces unexpected behavior.

•Yield is a function of the system (including the sizesof buffers) and not just of the machines.

•Yield is not a simple function of machine yields.

•This is an important area with many kinds ofproblems to be studied.


Current andFuture Work

•Analyze real system data and compare with models.

• Incorporate more measurement quantities intomodels.

•Design preventative maintenance strategies.

•Analyze general two-machine line models.

•Develop inspection strategies using Bayesian riskmethods.


New Results on the Integrated Analysis of Quality and...

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