3-4 robust quality and doe [compatibility mode]

7/29/2019 3-4 Robust Quality and DOE [Compatibility Mode]

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Robust Quality/

Offline Quality Improvement method



Is Zero Defects Enough ???

Zero defects practitioners say:

The efforts to reduce process failure in the factory will

simultaneously reduce instances of product failure in the field.

Ta uchi’s Method ractitioners sa :

The efforts to reduce product failure in the field will



Zero Defects vs. Taguchi

• Consistent • On target• re c a e• But not on target

• ore var a y•Stack-up problem with many

trivial deviation from target avoided

Who’s the better shot?



Taguchi vs. Traditional Quality

Traditional Approach Taguchi Approach

z To minimize loss, monitor

the process variables duringroduction so that res onse

z In field, average response has to be

adjusted, and the variance must bereduced in order to minimize loss.

parameters fall within the

specified tolerances

z adds cost to manufacturingz Building quality into the product

during the design stage is ultimate goal.

the quality of the product.



Taguchi vs. Traditional Quality

•Quality has been defined by many as; "being within specifications,"

"zero defects," or "customer satisfaction." However, these definitions

do not offer a method of obtaining quality or a means of relating quality

to cost.

•Taguchi defines quality as, "The quality of a product is the (minimum)

loss imparted by the product to the society from the time product is

shipped" (Bryne and Taguchi, 1986).

• losses due to rework, waste of resources durin manufacture, warrant

costs, customer complaints and dissatisfaction, time and money spent by

customers on failing products, and eventual loss of market share.



Robust Design

Robust design:

z Taguchi method is a powerful problem solving technique

for improving process performance, yield andproductivity by designing high quality into the products.

z It reduces scrap rates, rework costs, and manufacturing

cos s ue o excess ve var a y n e process.

z end result is a design that has minimum sensitivity to

var a ons n uncon ro a e ac ors.



Method in Manufacturing



Taguchi Case -1

z In 1980s, Ford outsourced the construction of a

subassembly to several of its own plants and to a

Japanese manufacturer.

z Both US and Japan plants produced parts that

z Warranty claims on US built products was far greater!!!

z The difference? Variation

z Japanese product was far more consistent!



Different distributions for Sony?

z1980s, Sony had 2 TV production factories: USA & Japan.



Taguchi Case -2

z The color density of USA-TV were uniformly distributed & fell within

the tolerance limits of m ± 5 where m = tar et

z while Japan-TV followed a normal distribution, i.e. more TV were on

target but about 0.3% fell outside the limits.z The differences in customer perceptions of quality:

– Sony-USA pays attention only to meeting the tolerances whereas

– Son -Ja an the focus was on meetin the tar et and minimizin the

variance around that target.

z Customer’s preferred the televisions sets produced by

Sony-Japan over those produced by Sony-USA.



Taguchi Points::

z no amount of inspection can improve a product;

z quality must be designed into a product from the start.



Taguchi Loss Function

z Quality Loss Function measures quality of a product.

z The quality loss function is a continuous function that is

defined in terms of the deviation of a design parameter

from an ideal or tar et value

LSL USL



Taguchi Loss Function (a simple approx.)

This function penalizes the deviation of a parameter from the

s ecification value that contributes to deterioratin the

2

performance of the product, resulting in a loss to the customer.

NOMINAL−

L(y) = quality lost (often measured in$) = loss associated with particular y.

IS BEST

y = value of the quality characteristic

m = target value for y

k = quality loss coefficient = cost of counter-measure that the factory might

use to get on target or rectify the error.



High Loss

L o s s

Unacceptable

Poor

Fair

Low Loss

Good

Best

c y

Target-oriented quality

yields more product in

the "best" category

F r e q u

e

Conformance-orientedquality keeps products

within 3 standard

deviations

Target UpperLower

Distribution of Specifications for Products Produced



Number of Part (N)

z If a large number of parts are considered, say N,

z Average loss per part = [(∑QLF of each part)/ N].

e average qua y oss resu s rom ev a on aroun

the average µ from the target and the Standard

Deviation (S) of y around µ.

The average quality loss =



o ust es gn(The Taguchi Method)

Three Step Method for Creating Robust Designs::

z Concept Design or System Design

z Parameter Design

z Tolerance Design



1. System/Concept Design

z System design is the conceptualization and synthesis of a

pro uc or process o e use .

z The process of examining competing technologies (the right

, , .

for producing a product.

z Pro erl selectin rocess com onents and methods can

reduce costs and increase the quality of the finished product.

z To achieve an increase in quality at this level requires

innovation, and therefore improvements are not always

made.



2. Parameter Design

z Parameter design is related to finding the optimal levels

o var a es a managemen can con ro n a process o

make the system less sensitive to variations of

uncontrollable noise factors i.e. to make the systemrobust. The objective is to make the design Robust!

z The ”optimal” parameter levels can be determined

z Parameter design does not usually affect production

performance for the system.



’ Functional Characteristics

z Signal Factors: Factors which affect the mean performance of

the process. The success of obtaining the response is

dependent on Control Factors and Noise Factors.

z Control Factors: factors which can easily be controlled under

normal production condition such as material choice, cycle

time, or mold temperature in an injection molding process.

z Noise Factors: factors that are difficult or impossible or too

expensive to control.



Examples of Noise & Control Factors(adapted from Byrne and Taguchi, 1987)



3. Tolerance Design

z Tolerance design occurs when the tolerances (specification

sum of the manufacturing and lifetime costs of the product or

rocess.

z Tightening the tolerances results in an increase in production

costs, but also an increase in production quality.



Taguchi’s Parameter

Design ApproachNoise factors

System

Signal

factors

Measured

response

Control factors



Why Taguchi’s Parameter Design?

z Taguchi's approach to parameter design provides the design

engineer with a systematic and efficient method for

determining near optimum design parameters for

performance & cost (Phadke, 1989; Taguchi 1986).

z

parameters so that the product or process is most robust

.



Why Taguchi’s Parameter Design?

z To study impact of 13 design parameters with 3 levels each.

a s ou o

z

1,594,323 possible experimental evaluations.

z Takes : very long time & expensive

z aguc s approac to parameter es gn attemps to s mp y y

this issue.



DOE – Full Factorial Designs

z simplest design to create, but extremely inefficient

z each factor tested at each level of the factor

znumber of tests = x

Y N =,

z Ex:: 8 factors, 2 conditions each, N = 256 tests

zEffects:: cost in terms of resource, time, materials increases



23 Full Factorial Model

Full factorial model when no. of factors= 3 is given by:

Y = 0 + 1X1 + 2X2 + 3X3 + 12X1X2 + 13X1X3 + 23X2X3

+ 123X1X2X3 +

It is rare and very difficult to investigate the “three-factor

interaction” term.



Modified 23 Full Factorial Data Set

X1 X2 X3 X1X2 X1X3 X2X3 X1X2X3 Y

- - - + + + - Y1

- - + + - - + Y2

- + - - + - + Y3

- + + - - + - Y4

+ - - - + + + Y5

+ - + - + - - Y6

+ + - + - - - Y

+ + + + + + + Y8



DOE – Fractional Factorial Designs

Fractional Factorial Design is a factorial design in which

all possible treatment combinations of the factors are

.

factorial matrix. The resulting design matrix will not be

able to estimate some of the effects, often the interaction

effects. It is more efficient, but risk missing interactions

DOE use the concept of ORTHOGONAL ARRAYS



23 Factorial Design Data

X1 X2 X3 Y

- - - Y1

- - + Y2- + - Y3

- + + Y4

+ - - Y5

+ - + Y6

+ + - 7

+ + + Y8



Taguchi Approach to DOE

z Design of experiments techniques, specifically Orthogonal

rrays s sys ema ca y var es an es e eren

levels of each of the control factors with a small number of

.

over the entire experimental region spanned by the control

factors and their settin s Phadke 1989 .



Taguchi Approach to DOE

z It identifies right inputs and parameter levels for making a

g qua y pro uc or serv ce.

z Taguchi has simplified OA’s use by providing tabulated sets

of standard orthogonal arrays.

z

ommon y use s nc u e e 4, 8, 16 , 32 an 9, 12,,L27

, . . ,

Engineering Using Robust Design, Prentice-Hall, Englewood Cliffs, NJ,



Choosing Suitable OA

The choice of suitable orthogonal array is critical for the success of anexperiment and depends on:

– The goal of the experiment

– Resources and budget available and Time constraint

– The total degree of freedom required to study the main &interaction effects.

Degree of Freedom: The number of fair and independent comparisons that

can be made from a set of observations. In DOE, Degree of freedom is one less

than number of levels associated with the factors.• The no. of degree of freedom associated with a factor at Y level is (Y-1)

• The no. of de ree of freedom associated with the interaction is the

product of the no. of degree of freedom associated with each main effect

involved in interaction.



Choosing Suitable OA

THE NUMBER OF EXPERIMENTAL TRIALS MUST BE

GREATER THAN THE TOTAL DEGREE OF FREEDOM

(no. of degree of freedom associated with each individual

factors and between interaction) REQUIRED FOR

.



Ortho onal Arra s

z The columns in the OA indicate the factor and its corresponding levels,

and each row in the OA constitutes an experimental run which isperformed at the given factor settings.

z

levels for each control factor; typically either 2 or 3 levels are chosen for

each factor.



Orthogonal Arrays

• In OA, the columns are mutually orthogonal.

That is, for any pair of columns, all

combinations of factor levels occur; and they

occur an equal number of times.

• With four parameters A, B, C, and D, each at

three levels. This is called an "L9 " design, with

the 9 indicating the nine rows, configurations,

prototypes to be tested.

• Thus, L9 means that nine experiments are to be carried out to study 4 variables at 3 levels.

• This design reduces 81 ( ) configurations to 9 experimental evaluations.43

• There are greater savings in testing for the larger arrays.

• For example, using an L27 array, 13 parameters can be studied at 3 levels by running only

27 experiments instead of 1,594,323



2-Level OA’s of Taguchi

A total of 18 OA Tables



Array Selector



Design the Matrix Experiment

z To implement robust design, Taguchi advocates the use of an “inner

array” and “outer array” simulation based approach .

z The “inner array” consists of the OA that contains the control factor

“ ”

factors settings.

z The combination of the “inner array” and “outer array” constitutes

what is called the “product array” or “complete parameter design

layout.”

z The product array is used to systematically test various combinations of

the control factor settings over all combinations of noise factors.




- -




z The diversity of noise factors are studied by crossing the orthogonal

array of control factors by an orthogonal array of noise factors

z The results of the ex eriment actual hardware ex eriment, s stems of

mathematical equations, or computer models that can adequately model the response of

many products and processes) for each combination of control and noise

array experiment are denoted by Yi,j

each run using the following equations.




Mean Response =

Standard Deviation =




z After conducting experiments, optimal test parameter configuration

.

z The S/N ratio is a performance measure to choose control levels that best

cope with noise.z S/N equation depends on the criterion for the quality characteristic to be

optimised. Three standard S/N ratios:

– Biggest-is-best quality characteristic (strength, yield),

– Smallest-is-best quality characteristic (contamination),– Nominal-is-best quality characteristic (dimension).

.

z The signal to noise ratio are expressed in Decibels




z Smaller the better (for making the system response as small as possible):

z Nominal the best for reducin variabilit around a tar et :

z

Larger the better (for making the system response as large as possible):



Flowchart of Taguchi Method

Determine the Quality Characteristicto be Optimised

Identify the Control Factors

Identify the Noise Factors

and Test Conditions

an t e r ternat ve eve s

Design the Matrix Experiment and

Define the Data Analysis Procedure

Conduct the Matrix Experiment

Anal se the Data and determine

Undertaking a confirmatory run of experiments

Optimum Levels for Control Factors



aguc s xper men aDesi n Process

1. Determine the Quality Characteristic to be Optimized:– The quality characteristic is a parameter whose variation has a critical effect on

pro uc qua y.

– It is the output or the response variable to be observed. Examples are weight, cost,

corrosion, target thickness, strength of a structure, and electromagnetic radiation.

.

– identify the noise factors that can have a impact on system performance and quality.

Brainstorming tool

3. Identify the Control Parameters with significant effects and Their

Alternative Levels and possible interactions on the qualitycharacteristic. Brainstorming tool

4. Design the matrix experiment and define the data analysis procedure.

– First, the appropriate orthogonal arrays for the noise and control parameters to fit a

specific study are selected.

– Care taken to select number of trials, trial conditions, how to measure performance .



’Design Process

5. Conduct the Matrix Experiment and record results:

– actual hardware experiment, systems of mathematical equations, or computer

models that can adequately model the response of many products and processes.

6. Analyze the Data and Determine the Optimum Levels:

– ,

graphical approach to analyze the data.

– In the graphical approach, the S/N ratios and average responses are plotted for

each factor a ainst each of its levels.

– The graphs are then examined to “pick the winner,” i.e., pick the factor level whichbest maximize S/N ratio and bring the mean on target (or maximize or minimize

the mean, as the case may be).

7. Undertaking a confirmatory run of experiments: The results should be

validated by running experiments with all factors set to ”optimal” levels



Use of Graphical Analysis

Using graphical information:

z the control factors can also be rou ed as follows:

– Factors that affect both variation & average performance of the product.

– Factors that affect the variation only.

– .

– Factors that do not affect either the variance or the average.

z Factors in the first and second groups can be utilized to reduce the

variations in the system, making it more robust.

z Factors in the third group are then used to adjust the average to the

target value.

z Lastly, factors in the fourth group are set to the most economical level.



Taguchi Method Used in::

Useful at ALL Life-stages of a Process or Product:

stage 2: Manufacturing: Equipment, Raw material, manpower

stage 3: Packagingstage 4: Storage

stage 5: Transportation

s age : ns a a on an omm ss on ng

stage 7: Operation: Power supply, temperature, humidity, Improper use

stage 8: Maintenance

stage 9: Repair

stage 10: Discard and Salvage



Taguchi Method Advantages::

z Taguchi method can reduce R&D costs by improving the efficiency of

generating information needed to design systems that are insensitive to

usage conditions, manufacturing variation, and deterioration of parts.

z Development time can be shortened significantly; and important design

parameters affecting operation, performance, and cost can be identified.

z Furthermore, the optimum choice of parameters can result in wider

tolerances so that low cost components and production processes can be

used. Thus, manufacturing and operations costs can also be greatly

reduced.



Taguchi’s Quality Imperatives

z Robustness results primarily from product design than from online control

z o us pro uc s e vers s rong s gna s regar ess o ex erna no se an

with a minimum of internal noise. Any marked increase in S/N ratio improves

“robustness” of the product.z To set Targets at Maximum S/N ratio, develop a system of trials that allows you

to analyze change in overall system performance according to the average effect

of change in the component parts.

z Use experimental design to test component part interaction effectsz Quality Loss Function= (square of deviation from target value) X (cost of

z Trivial deviation from target may lead to “stack up”

z Reduction in field failures will reduce factory failures



Case - Parameter Desi n of

an Elastometric Connector



The Problem

z The experiment that is being conducted seeks to

determine a method to assemble an elastometric

connector to a nylon tube while delivering the requisite

pull-off performance suitable for an automotive

engineering application.

z The primary design objective is to maximize the pull-off force while secondary considerations are made to

minimize assembly effort and reduce the cost of the

connector and assembly.



4 Control and 3 Noise Factors

z The control factors are:

(A) n er erence,

(B) connector wall thickness,

(C) insertion depth, and(D) percent adhesive in connector pre-dip;

Each control factor is to be tested at three levels

(E) conditioning time,

(F) Conditioning temperature, and

(G) conditioning relative humidity.

Each noise factor is tested at two levels.



Levels of Control & Noise Factors



Design of Experiment

z Two experimental designs are selected to vary control factors and

no se ac ors.

z L9 orthogonal array (has 4 columns) is selected for the controllable

factors while an L8 orthogonal array (has 7 columns) for the noisefactors.

z Since there are only three noise variables, the remaining columns in

noise factors (e.g., ExF represents the interaction between

conditioning time, E, and temperature, F).

z Finally, the last column in the L8 array is used to estimate the

variance in the experiment.




zThe total set of experiments that are performed is obtained by

array of noise factors (the inner array).

zThe total number of experiments is the product of the number of runs of

eac array, .e., x or exper men s.

zFor each experiment, the pull-off force is measured using the specified

settings for each control factor level and noise factor level.

z

The average pull-off force for each combination of the control factors A-D noted.

- ,

the S/N ratio for “Larger is Better” is also computed for each set of runs.

zThese results are summarized




Pull-Off Force for Connector and

Tube Parameter Design Experiment



Data Analysis

z Taguchi’s graphical approach is used to plot the “marginal means” of

eac eve o eac ac or an p c e op ma o e erm ne e es

setting for each control factor.

z

The average pull-off force and S/N ratio for each level of each of thecontrol factors are computed by averaging the mean pull-off force or

S/NL for each factor for each level.

, -

of the insertion depth (Factor C) is obtained by averaging Runs 1, 6, and

8 i.e. (17.525 + 19.225 + 18.838)/3 = 18.4.

z The same procedure is employed to compute the average S/NL for each

level of each factor and the remaining pull-off force averages.



Data Analysis



Optimal Setting

z The best settings to maximize SNL are A(medium),

C(deep), B(medium), and D(low) based on the

experimental results for maximizing pull-off force.

z In the actual study, further analysis of the data revealed

that

– e var ance n e exper men was no cons an an epen e

on the specific levels of each control factor, and

– there were several interactions between some of the control

factors and noise factors.

3-4 robust quality and doe [compatibility mode]

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