Abstract - Due to the development of information technology,

computer is becoming a useful and effective tool to support

engineering activities in product design and manufacturing.

A numerical model of product created in CAD environment

is used to perform engineering simulation such as

kinematics, dynamics, failure, etc. However, it is a nominal

representation of product and does not deal with variations

generated along the product life cycle. The risk is then that

the designed product does not fully meet the requirements of

customers and users. Thus, this paper proposes a method

that allows managing the quality of product during its life

cycle. The method permits to model variation sources during

the product life cycle and managing causes and

consequences of these variations at design stage.

Keywords – Product Quality Management, Product life

cycle, manufacturing simulation, robust design

I. INTRODUCTION

Today, the requirements of customers concerning the

product they buy are more and more tight and high. Thus,

satisfaction of these such as quality, reliability,

robustness, innovativeness and cost plays an important

role in context of global and competitive economy. Due to

the development of information technology, computers

are becoming a useful and effective tool to support

engineering activities in product design and

manufacturing. Product designers usually create a

numerical model of product with CAD software and then

use this model to perform engineering simulation.

However, the product model created in this environment

is a nominal representation of product and thus does not

deal with variations generated along the product life

cycle. The question is then how to manage this

performance variability in order to reduce it and at least

ensure that it is compatible with the customer satisfaction.

The risk is that the designed product does not fully meet

the requirements of customers and users. The main issue

for the designer is: Does the “real” product satisfy the

customers’ requirements from the point of view of

product quality? Thus, the management of variation

sources throughout the product life cycle is an important

issue in product-process design and concurrent

engineering.

Some answers exist today in the academic research to

answer this question. There are many studies to model

geometrical variations in manufacturing and assembly

stage during the product life cycle. In manufacturing, they

can be classified into two different approaches. One is

based on the concept of a state space to model

dimensional error propagation along multistage

machining processes [1], [2]. Another is based on the

concept of small displacement torsor to model

geometrical deviations of surfaces of manufactured part

generated and accumulated by each set-up of the

manufacturing processes [3], [4].

Many studies for analysis of dimensional variation in

assembly stage have been done by using different

approaches. The first one is based on the State Transition

Model approach to propagate and control variation in

mechanical assemblies [5]. The second one is based on

Stream of Variation Model approach for 3D rigid

assemblies’ dimensional variation propagation analysis in

multi-station processes [6], [7], [8] and [9]. The last one is

based on the concept of small displacement torsor for

modeling geometric deviations of each surface of part in

the mechanism assembly [10], [11], [12].

The geometrical variations in assembly stage are

modeled by these models presented above. However, they

are not linked to any model proposed by [1], [2], [13], [3]

and [14] which model the variation from the

manufacturing stage. It is necessary to develop a global

model that can cover the whole production stages of the

product life cycle. Moreover, all robust design

methodologies as presented by [15], [16] and [17] only

work for an accurate model since they need to know the

mathematical relationship between the performance of

product and the variation sources during its life cycle.

This accurate model is difficult to obtain due to complex

process (manufacturing and assembly process), complex

dynamics, and complex geometrical boundary conditions.

Therefore, the paper proposes a new method that allows

taking the variation sources during the product life cycle

into account design stage. The quality of product designed

is ensured throughout whole stages of its life cycle.

II. METHOD DESCRIPTION

The overview of the method is shown in figure 1. It

can be separated into three distinct parts according to

stages of the product life cycle. The first one consists in

the generation of the geometrical deviation model (GDM)

by simulation of manufacturing and assembly stage of the

product life cycle. This model is based on the concept of

small displacement torsor proposed by [18]. It includes

the model of manufactured part (MMP) proposed by [14].

This model allows modeling the geometrical deviations

generated by manufacturing processes. The geometric

deviations of each surface of the manufactured part are

modeled by the small displacement torsor in this model.

A Method for Product Quality Management throughout Its Life Cycle

Dinh-Son Nguyen1

1Danang University of Technology,

The University of Danang, Vietnam

(ndson@dut.udn.vn; nguyen.dson@gmail.com)

978-1-4673-2945-3/12/$31.00 ©2012 IEEE 329

Then the manufactured part will be assembled at the

assembly stage. The geometrical deviations accumulated

by assembly processes are modeled by model of

assembled part [19]. Thus, variation sources in

manufacturing and assembly stage are integrated by MMP

and MAP. These two models are called geometrical

deviation model (GDM).

The second one is a method that allows integrating

these deviations modeled by GDM into the simulation of

product performance under conditions of the user in the

use stage. Firstly, the mathematical relationship between

the product performance and the parameters of the

geometrical deviations is established by using design of

experiment method. Then, an image of a population of

product performance is generated using Monte-Carlo

simulation with input data being the parameters of

variation sources in manufacturing and assembly stage.

As a result, the product designer can verify the

compliance of the designed product with customer's

requirements.

The third one is a method that permits to identify and

classify the influence of parameters of variation sources in

manufacturing and assembly stage on the product

performance. From this result, the actors of the product

life cycle such as designer, manufacturer, assembler and

user can know how to manage the parameter of variation

sources so that their effects on the performance of product

can be eliminated. In addition, this method allows

determining the variance of the performance of product

relative to these parameters. Robust solution can be found

by minimizing the variance of the product performance.

Fig. 1. The overview of proposed method.

1) Reminding geometrical deviation model:

The geometrical deviations generated by a machining

process modelled by model of manufactured part (MMP)

presented by [14]. They are considered to be the result of

two independent phenomena: the positioning and the

machining deviations accumulated over the successive

set-ups. The positioning deviation of workpiece Pi in set-

up Sj is the deviation of the nominal workpiece Pi relative

to the nominal machine. It is modelled by a small

displacement torsor , i

Sj PT . The machining deviations of

machined surface j of workpiece Pi in the set-up Sj are

modelled by a small displacement torsor , i

jSj PT . The

manufactured deviations of surface relative to its nominal

position are expressed by the parameters of the small

displacement torsor ,i i

jP PT as given in (1)

, , ,i i i ij jP P Sj P Sj P

T T T= − + (1)

In assembly stage, the geometrical deviations of each

surface of assembled part are modelled by model of

assembled part (MAP) proposed by [19]. This model uses

the geometrical behaviour laws based on the small

displacement. The positioning deviations of part relative

its nominal position in the assembly coordinate system are

modelled by a small displacement torsor iPP

T,

. This

torsor is determined by (2).

, , , , ,i k k k k i i in n m mP P P P P P P P P P

T T T T T= + + − (2)

Where the torsor ,k i

n mP PT models deviation of connection

between surface m of the manufactured part i and surface

n of the manufactured part k. The torsor kPPT

, models the

positioning deviation of part k relative its nominal

position in assembly frame.

Finally, the geometrical deviations of surface j of the

part i relative to its nominal positions in the assembly

frame of product can be calculated by (3).

, , ,i i i ij jP P P P P P

T T T= + (3)

The GDM establishes the mathematical relation

between the deviation sources from the manufacturing

and assembly stage and deviations of product surfaces.

2) Simulation of product performance:

From the geometrical deviation model, the set of M

products with geometrical deviations is virtually produced

by using Monte-Carlo simulation method. As a result,

product designers can be aware of the variation range of

the geometrical deviation for each surface of product.

These deviations obviously have an influence on the

performance of product.

In order to ensure the quality of product throughout

its life cycle, it is necessary to integrate these deviations

into the simulation of the product performance. Thus,

paper proposes a method that allows establishing the

mathematical relationship between product performance

and the parameters of variation sources. They are

parameters of manufacturing and assembly processes that

generate the geometrical deviations on the product

produced. This method includes some strategies of design

of experiments such as factorial design, Taguchi design

and random design to determine the relationship.

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330

3) Influence factor analysis:

An image of performance of the real products with

geometrical deviations generated in manufacturing and

assembly stage is given by using Monte-Carlo simulation

as presented above. The variation sources from the

product life cycle have an influence on the performance of

product. It is necessary to determine how much effect of

each parameter of the variation sources on the product

performance. Thus, the paper proposes a method based on

global sensitivity analysis to determine the effect of each

parameter of geometrical deviations that influences on the

performance variability of the product.

The goal of sensitivity analysis is to determine how

uncertainty in output of a model depends upon the

different sources of uncertainty in model input [20]. The

model of geometrical deviations and the product

performance function are complex in themselves. Thus,

the global sensitivity indices proposed by Sobol [21] will

be used in this case due to the simple formulation and

analysis procedure.

Sobol’s indice is used to test the sensitivity indices of

the input parameters { }1 2, ,.., nX x x x= relative to

output function f(X). Let's consider the integrable function

f(X) in the unit hypercube ( )0 1n

H X≤ ≤ can be

expanded in (4):

( ) 0 12.. 1

1

( ) ( , ) .. ( ,.., )

n

i i ij i j n n

i i j

f X f f x f x x f x x

= <

= + + + +∑ ∑ (4)

The total variance of function f(X) is calculated by (5):

1

1

..

1 ...u

u

n

i i

u i i

V V

= < <

=∑ ∑ (5)

Where 1 1

12

.. .. 1 2 10

( , ,.., ) ,..,u u u ui i i i i iV f x x x dx x= ∫ is called

partial variances. It measures the joint effect of a set of

input parameters { }1 2, ,.., nx x x on the output function

f(X).

A global sensitivity index is defined as a partial

variance contributed by an effect on the total variance V.

It is expressed by (6):

1

1

..

..u

u

i i

i i

VS

V= (6)

For one-dimensional index ii

VS

V= shows the effect

of the single factor xi on the output f(x). In order to

estimate the total influence of the factor, it is necessary to

determine the total partial variance. The input variables

{ }1 2, ,.., nX x x x= can consider two complementary

subsets of variables Y and Z,

with { } { }1 1 1,..., ,1 ... , ,...,

mi i m mY x x i i n K i i= ≤ ≤ ≤ ≤ = .

The variance corresponding to a set Y is defined by

(7):

1 11( ... ) ..u u

n

Y u i i K i iV V= < < ∈=∑ ∑ (7)

In order to quantify the total influence of each

individual variable induced by both its main effect and

interactions with other variables, the total variance

corresponding to a set Y is defined by (8):

tot

Y ZV V V= − (8)

Finally, the corresponding total sensitivity index is

expressed in (9):

tottot YY

VS

V= (9)

III. A CASE STUDY

In order to explain the method proposed, an example

of centrifugal pump design presented by [19] is reused

and developed to demonstrate how to manage the quality

of the centrifugal pump (flowrate of the pump) during its

life cycle. The CAD model of the centrifugal pump is

represented in figure 2 with following specifications:

• Flowrate: 250m3/h

• Total Head: 100m

• Revolution speed: 2000RPM

• Liquid: Water

• Temperature: 20°C

Fig. 2. The parts of designed centrifugal pump [19]. 1) Geometrical deviation model of pump:

The geometrical deviation model of the centrifugal

pump is presented clearly by [19]. In this case, the gap

between the casing (part 3) and the impeller (part 5) and

the translation (Tx, Ty) according to axis OX and OY of

the impeller of the pump are considered. Because they are

important factors that have a strong influence on the

flowrate of the pump [22], [23].

2) Performance simulation of the pump:

The relationship between the performance of the

pump (flowrate) and the selected parameters (Gap, Tx,

Ty) is determined by using the factorial design method.

The procedure to determine this relationship is explained

by [24]. The mass flowrate Q of the pump function of the

gap between the impeller and the casing of the pump

(Gap) and the translation of the impeller relative to two

perpendicular axes (Tx, Ty) is described by (12).

Part 3

O Z

Y

X Part 6 Part 1

Part 4

Part 2

C4

P1 P9

C5

C7

C3 P4

P5

C4

C6

C2

P8

C4

P5

Part 5

C: Cylinder

P: Plane

Proceedings of the 2012 IEEE IEEM

331

Q = 7.97795×106

+1.13956×106 Gap - 40373.3 Gap

2 -

9.47196×107 Tx + 1.33071×10

7 Gap Tx - 467397 Gap

2

Tx + 6.1493×108 Tx

2 - 8.64763×10

7 Gap Tx

2 +

3.04026×106 Gap

2 Tx

2 + 1.72515×10

8 Ty -2.42049×10

7

Gap Ty + 849043 Gap2 Ty + 26307 Tx Ty - 225203 Tx

2

Ty + 1.547×109 Ty

2 - 2.1753×10

8 Gap Ty

2 + 7.64703×10

6

Gap2 Ty

2 + 347389. Tx Ty

2 – 523800 Tx

2 Ty

2 (g/s). (10)

3) Global sensitivity analysis:

From the relationship between performance and

selected factors (Gap, Tx, Ty), the function of the

flowrate Q of the pump can be expressed by (12). Each

parameter of geometrical deviations (Gap, Tx and Ty)

varies in an interval that is not the hypercube

interval ( )0 1n

H X≤ ≤ . Thus, it is necessary to

normalise these parameters (Gap, Tx and Ty) into the

interval [ ]0,1 by (13):

{ }

{ } { }

{ }

{ } { }

{ }

{ } { }

N

N

N

Gap min GapGap

max Gap min Gap

Tx min TxTx

max Tx min Tx

Ty min TyTy

max Ty min Ty

−=

− −

=−

−=

−

(11)

The function of the flowrate of the pump Q can be

rewritten by (14):

(12)

The global sensitivity indices for each parameter Gap,

Tx, Ty is then calculated by (15):

12

0

12

0

12

0

(769.26 271.47 )

( 566.71 74.34 )

(514.85 206.37 )

Gap N N N

Tx N N N

Ty N N N

S Gap Gap dGap

S Tx Tx dTx

S Ty Ty dTy

= −

= − +

=

+

∫

∫

∫

(13)

The result of global sensitivity analysis is expressed

in table 1.

TABLE I

THE RESULT OF GLOBAL SENSITIVITY ANALYSIS

Parameters

Global

sensitivity

indices

Total

sensitivity

indices

Interaction

Global

sensitivity

indices

Gap 0.5247 0.5758 GapTx 0.0013

Tx 0.1444 0.1767 GapTy 0.0497

Ty 0.2487 0.3295 TxTy 0.0309

The global sensitivity indices of each parameter are

also shown in figure 4. The global sensitivity index of the

Gap is obviously the greatest. Thus, the gap between the

impeller and the casing of the pump is clearly the most

significant parameter that strongly effects on the flowrate

of the pump. The effect of two parameters Tx and Ty on

the flowrate of the pump are equal in this case. The effect

of interaction between the Gap and Ty on the flowrate is

stronger than others according to global sensitivity index.

It agrees with the study of [25] because the variation of

Ty will affect the relative position between the impeller

and the tongue of the volute casing of the pump.

Fig. 4. Global sensitivity indices of design parameters

IV. DISCUSSION

In this case, the gap between the impeller and the

casing of the pump is a design factor that has the greatest

effect on the flowrate of the pump. If the flowrate of the

pump does not satisfy the client, the designer has to

manage the variation of the gap first, and the variation of

Ty and Tx later. By the other method, manufacturer and

assembler can verify the influence of the parameters of

the manufacturing and assembly processes. For example,

the manufacturer can adjust parameters of the

manufacturing process to manufacture the impeller and

the casing of the pump in order to reduce the gap. Thus,

the manufacturer needs to manage variation of these

parameters if the mass flowrate does not satisfy the client.

The manufacturer can change parameters of the

manufacturing process based on the capabilities of

production means and the cost. Moreover, the assembly

can verify parameters of assembly processes to increase

the precision of the impeller position.

In brief, the analysis result only proposes factors of

the product life cycle to modify in order to adjust the

performance of product. The aim is to satisfy the client

and make the design robust and reliable.

V. CONCLUSION

A global methodology is proposed in this paper to

manage quality of product under variation sources during

the product life cycle. A mathematical relationship

between the performance of product (a factor of product

quality) and parameters of variation sources in

manufacturing and assembly stage of the product life

cycle where geometrical deviations of product are

generated and accumulated is established by design of

experiment method. An image of population of “real”

product with geometrical deviations is created by using

Proceedings of the 2012 IEEE IEEM

332

Monte-Carlo simulation. As a result, product designers

can verify satisfaction of product with requirements of

users and customers. In addition, the global sensitivity

analysis approach proposed in the paper can help the

product designers identify and classify the effect of the

parameters of geometrical deviations of product on

performance. From this result, the actors of the product

life cycle such as designers, manufacturers, assemblers,

users and customers as well can adjust parameters of

variation sources in each stage to ensure the quality of

product produced satisfying the requirements of user and

customer. Especially, the product designer in design stage

can modify the nominal product designed in order to

obtain a reliable and robust design, although disturbances

during the product life cycle.

REFERENCES

[1] S. Zhou, Q. Huang, and J. Shi, “State Space Modeling of

Dimensional Variation Propagation in Multistage

Machining Process Using Differential Motion Vectors,”

IEEE Transactions on Robotics and Automation, vol. 19,

no. 2, pp. 296-309, 2003.

[2] Q. Huang, J. Shi, and J. Yuan, “Part Dimensional Error and

Its Propagation Modeling in Multi-Operational Machining

Processes,” Journal of Manufacturing Science and

Engineering, vol. 125, pp. 256-262, 2003.

[3] F. Villeneuve, O. Legoff, and Y. Landon, “Tolerancing for

manufacturing: a three-dimensional model,” International

Journal of Production Research, vol. 39, no. 8, pp. 1625 -

1648, 2001.

[4] S. Tichadou, O. Legoff, and J.-Y. Hascoet, "3D

Geometrical Manufacturing Simulation: Compared

approaches between integrated CAD/CAM systems and

small displacement torsor models," Advances in Integrated

Design and Manufacturing in Mechanical Engineering, D.

B. A. Bramley, D. Coutellier and C. McMahon, ed., pp.

201-214: Springer Netherlands, 2005.

[5] R. Mantripragada, and D. E. Whitney, “Modeling and

Controlling Variation Propagation in Mechanical

Assemblies,” IEEE Transactions on Robotics and

Automation, vol. 15, no. 1, pp. 124-140, 1999.

[6] D. J. Ceglarek, and M. Szafarczyk, “Multivariate Analysis

and Evaluation of Adaptive Sheet Metal Assembly

Systems,” CIRP Annals - Manufacturing Technology, vol.

47, no. 1, pp. 17-22, 1998.

[7] J. Jin, and J. Shi, “State Space Modeling of Sheet Metal

Assembly for Dimensional Control,” Journal of

Manufacturing Science and Engineering, vol. 121, no. 4,

pp. 756-762, 1999.

[8] W. Huang, J. Lin, M. Bezdecny et al., “Stream-of-Variation

Modeling—Part I: A Generic Three-Dimensional Variation

Model for Rigid-Body Assembly in Single Station

Assembly Processes,” Journal of Manufacturing Science

and Engineering, vol. 129, pp. 821-831, 2007.

[9] W. Huang, J. Lin, Z. Kong et al., “Stream-of-Variation

(SOVA) Modeling—Part II: A Generic 3D Variation Model

for Rigid Body Assembly in Multistation Assembly

Processes,” Journal of Manufacturing Science and

Engineering, vol. 129, pp. 832-842, 2007.

[10] E. Ballot, and P. Bourdet, “A mathematical model of

geometric errors in the case of specification and 3D controll

of mechanical parts,” Advances in Mathematics for applied

Sciences, Advanced Mathematical & Computational Tools

in Metrology IV pp. 11-20, 2000.

[11] J.-Y. Dantan, F. Thiebaut, A. Ballu et al., “Functional and

Manufacturing Specifications - Part 1: Geometrical

Expression by Gauge with Internal Mobilities,” in

Proceedings of the 4th International Conference on

Integrated Design and Manufacturing in Mechanical

Engineering, 2000.

[12] J.-Y. Dantan, F. Thiebaut, A. Ballu et al., “Functional and

Manufacturing Specifications -Part 2 : Validation of a

Process Plan,” in Proceedings of the 4th International

Conference on Integrated Design and Manufacturing in

Mechanical Engineering, 2000.

[13] H. Wang, Q. Huang, and R. Katz, “Multi-Operational

Machining Processes Modeling for Sequential Root Cause

Identification and Measurement Reduction,” Journal of

Manufacturing Science and Engineering, vol. 127, pp. 512-

521, 2005.

[14] F. Vignat, and F. Villeneuve, "Simulation of the

Manufacturing Process, Generation of a Model of the

Manufactured Parts," Digital Enterprise Technology, S. US,

ed., pp. 545-552, 2007.

[15] C. Wei, J. K. Allen, K.-L. Tsui et al., “A Procedure for

Robust Design: Minimizing Variations Caused by Noise

Factors and Control Factors,” Journal of Mechanical

Design, vol. 118, no. 4, pp. 478-485, 1996.

[16] I. Gremyr, M. Arvidsson, and P. Johansson, “Robust

Design Methodology: Status in the Swedish Manufacturing

Industry,” Journal of Quality and Reliability Engineering

International, vol. 19, pp. 285-293, 2003.

[17] P. Gu, B. Lu, and S. Spiewak, “A New Approach for

Robust Design of Mechanical Systems,” CIRP Annals -

Manufacturing Technology, vol. 53, no. 1, pp. 129-133,

2004.

[18] P. Bourdet, “Contribution à la mesure tridimensionnelle :

Modèle d'identification des surfaces, Métrologie

fonctionnelle des pièces mécaniques, Correction

géométrique des machines à mesurer tridimensionnelle,”

Thèse d'Etat, Nancy I - LURPA ENS CACHAN, 1987.

[19] D. S. Nguyen, F. Vignat, and D. Brissaud, “Taking into

account geometrical variation effect on product

performance,” International Journal of Product Lifecycle

Management, vol. 5, no. 2-3, pp. 102-121, 2011.

[20] A. Saltelli, M. Ratto, T. Andres et al., Global Sensitivity

Analysis: The Primer: John Wiley & Sons, 2008.

[21] I. M. Sobol, “On sensitivity estimation for nonlinear

mathematical models,” Matem. Mod., vol. 2, no. 1, pp. 112–

118, 1990.

[22] D. O. Baun, L. Köstner, and R. D. Flack., “Effect of

Relative Impeller-to-Volute Position on Hydraulic

Efficiency and Static Radial Force Distribution in a Circular

Volute Centrifugal Pump,” Journal of Fluids Engineering,

vol. 122, no. 3, pp. 598-605, 2000.

[23] E. Tahsin, and G. Mesut, “Performance Characteristics of a

Centrifugal Pump Impeller With Running Tip Clearance

Pumping Solid-Liquid Mixtures,” Journal of Fluids

Engineering, vol. 123, no. 3, pp. 532-538, 2001.

[24] D. S. Nguyen, F. Vignat, and D. Brissaud, “Geometrical

Deviation Model of product throughout its life cycle,”

International Journal of Manufacturing Research, vol. 6,

no. 3, pp. 236-255, 2011.

[25] Y.-W. Wong, W.-K. Chan, and W. Hu, “Effects of Tongue

Position and Base Circle Diameter on the Performance of a

Centrifugal Blood Pump,” Artificial Organs, vol. 31, no. 8,

pp. 639-645, 2007.[1-25]

Proceedings of the 2012 IEEE IEEM

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