Taguchi Method to IE's[1]

Robust Engineering Design

Taguchi Method to Industrial Engineers

Teaching Taguchi Method

To Industrial Engineers

Submitted by: Vic C. Breganza Submitted to: Charlton Inao



Introduction

Dr. Genichi Taguchi is a Japanese quality management consultant who has developed and promoted a philosophy and methodology for continuous quality improvement in products and process. Within this philosophy.

Taguchi shows how the statistical design of experiments (SDOE or DOE) can help industrial engineers design and manufacture products that are both of high quality and low cost.

His approach is primarily focused on eliminating the causes of poor quality and on making product performance insensitive to variation.

DOE is a powerful statistical technique for determining the optimal factor settings of a process and thereby achieving improved process performance, reduced process variability and improved manufacturability of products and processes.

Taguchi (1986) advocates the use of orthogonal array designs to assign the factors chosen for the experiment. The most commonly used orthogonal array designs are L8 (i.e. eight experimental trials), L16 and L18.



Issues on improper application of experimental design techniques

The word “statistics” invokes fear in many industrial engineers. Many engineers in the UK leave universities without a complete understanding of the power of statistics and are therefore likely to avoid the use of statistical techniques in their subsequent careers.

Few graduating engineers have been exposed to applied statistical quality techniques such as DOE, robust design, etc. This is another symptom of the statistical education of the engineering fraternity.

Engineers consistently avoid the use of applied statistical techniques in tackling process optimisation and quality control problems. Where techniques are in use, e.g. the use of control charts for process analysis and monitoring, there often appears to be a lack of a full understanding of the basic and fundamental principles behind their application (Morrison 1997).

Many textbooks and courses on DOE primarily focus on the statistical analysis of the problem under study. However, this is but one component of DOE which involves planning, design, execution, analysis and interpretation of results.



A lack of communication between the academic and industrial worlds, and between functional specialists restricts the application of the Taguchi method ™ and DOE (Antony et al., 1998a). It is important, though too rare, that quality, manufacturing, process, design and operational departments communicate and work effectively with one another

Issues on improper application of experimental design techniques



Process/ productProcess/ product Nature of problemNature of problem Experiment Experiment sizesize BenefitsBenefits

Injection moulding process

High scrap rate due to excessive process variability

8 trials Annual savings were estimated to be over f 40,00

Diesel injector High rework rate 16 trials Annual savings were estimated to be over f 10,000

Welding process Low weld strength 16 trials Annual savings were estimated to be over f 16,000

Chemical process Low process yield 8 trials Process yield was improved by over 10 per cent

Biscuit Excessive variability in biscuit length

16 trials Biscuits length variability was reduced by over 25 per cent

Wire-bonding process

Low wire pull strength 16 trials Annual savings were over f 30,000

Table ITable I Typical applications of Tm in manufacturing



Typical applications in service industry

The use of Tm in service industries is not often reported. This may be because:

Service performance I often more difficult to measures; The performance of a service process depends a great deal on the behavior and

attitude of the service provider and it varies with time; and The identification and measurement of control factors an their influence on

performance characteristic(s) is often difficult

However, there clearly are possible applications of Tm in the service sector. Example include:

Reducing the time taken to respond to customer complaints; Reducing errors on service orders; and Reducing the length of stay in an emergency room in hospital



Steps in performing a Taguchi experiment

The process of performing a Taguchi experiment follows a number of distinct steps:

Step 1: formulation of the problem – the success of any experiment is dependent on a full understanding of the nature of the problem.

Step 2: identification of the output performance characteristics most relevant to the problem

Step 3: identification of control factors, noise factors and signal factors (if any).Control factors are those which can be controlled under normal production

conditions. Noise factors are those which are either too difficult or too expensive to control under normal production conditions. Signal factors are those which affect the mean performance of the process

Step 4: selection of factor levels, possible interactions and the degrees of freedom associated with each factor and the interaction effects

Step 5: design of an appropriate orthogonal array (QA) Step 6: preparation of the experiment Step 7: running of the experiment with appropriate data collection Step 8: statistical analysis and interpretation of experimental results Step 9: undertaking a confirmatory run of the experiment.



Paper helicopter experiment

The objective of the exercise was to identify the optimal settings of control factors which would maximise the flight time of paper helicopters (with minimum variation). Here control factors refer to those which can be easily controlled and varied by the designer or operator in normal production conditions. A brainstorming session by a group of students identified six control factors which were thought to influence the time of flight (refer to table II)

In order to simplify the experiment, each factor was studied at two levels. The “level” of a factor here refers to the specified value of a setting. For example, in the experiment, body width was studied at 2cm and 3cm. Factors at three (and higher) levels make analysis more complicated – and are therefore not used in awareness-raising sessions.

Having identified the control factors, it is important to list the interactions which are to be studied for the experiment. Interaction exists when the effect of one factor is not the same at different levels of the other factor. An effect refers to the change in response due to the change in level of a factor (Antony et al., 1998b). Consider, for example, the factors wing length and body length of the paper helicopter. Assume each factor was kept at two-levels for the study. Time of flight is the response (or quality characteristic) of interest. Interaction between wing length and body length exists when the effect of wing length on time of flight at two different levels of body length is different.



Control factorControl factor LabelsLabels Level 1Level 1 Level 2Level 2

Paper type A Regular Bond

Body length B 8cm 12cm

Wing length C 8cm 12cm

Body width D 2cm 3cm

Number of clips

E 1 2

Wing shape F Flat Angled

Table IITable II Control factors and their range of settings for the experiment



Paper helicopter experiment (cont..)

For this experiment, three interactions were identified (from the brainstorming session) as being of interest:

(1) Body length x wing length (B x C or BC);(2) Body legnth x body width (B x D or BD); and(3) Paper type x body length (A x B or AB)

The following noise factors were identified (as having some impact on the flight time but being difficult to control):

• Operators;• Draughts;• Reaction time; and• Ground surface



Figure 1Figure 1 Template for paper helicopter design

Fold

Cut

E

1 cm

D

B

C



Choice of orthogonal array design

Orthogonal arrays allow one to compute the main and interaction effects via a minimum number of experimental trials (Ross, 1988). “Degrees of freedom” refers to the number of fair and independent comparisons that can be made from a set of observations. In the context of SDOE, the number of levels associated with the factor. In other words, the number of degrees of freedom associated with a factor at p-levels is (p-1).

Column 1 – body width (D), column 2 – wing length ©, column 4 – body length (B), column 5 – body width x body length (B x D), column 6 – wing length x body length (B x C), column 7 – wing shape (F), column 8 – paper type (A), column 12 – body length x paper type (AB) and column 14 – number of clips (E).



Table IIITable III Experimental layout

Column no. 1 2 4 5 6 7 8 12 14

Factors/interactions

D C B BD BC F A AB E Flight time

Trial no.

1 1 1 1 1 1 1 1 1 1 2.76, 2.83

2 1 1 1 1 1 1 2 2 2 2.20, 2.13

3 1 1 2 2 2 2 1 2 2 1.93, 2.30

4 1 1 2 2 2 2 2 1 1 2.19, 2.10

5 1 2 1 1 2 2 1 1 2 2.40, 2.50

6 1 2 1 1 2 2 2 2 1 2.82, 2.31

7 1 2 2 2 1 1 1 2 1 3.39, 3.01

8 1 2 2 2 1 1 2 1 2 2.62, 2.39

9 2 1 1 2 1 2 1 1 1 2.46, 2.12

10 2 1 1 2 1 2 2 2 2 2.08, 1.90

11 2 1 2 1 2 1 1 2 2 2.14, 2.29

12 2 1 2 1 2 1 2 1 1 2.05, 2.12

13 2 2 1 2 2 1 1 1 2 2.96, 2.70

14 2 2 1 2 2 1 2 2 1 2.47, 2.60

15 2 2 2 1 1 2 1 2 1 2.62, 2.91

16 2 2 2 1 1 2 2 1 2 2.32, 2.41



Statistical analysis and interpretation of results

Taguchi advocates the use of signal-to-noise ratio (SNR) – the need is to maximise the performance of a system or product by minimising the effect of noise while maximising the mean performance. The SNR is treated as a response (output) of the experiment, which is a measure of variation when uncontrolled noise factors are present in the system

For LTB quality characteristics, the SNR is given by the following equation:

SNR = - 10log [ * ] (1)

Where n = number of values ate each trial condition (i.e., 2 from Table II) and y; = each observed value

1n

1y2



Trial numberTrial number SNRSNR Trial numberTrial number SNRSNR

1 8.93 9 7.12

2 6.71 10 5.95

3 6.41 11 6.89

4 6.62 12 6.38

5 7.78 13 9.01

6 8.05 14 8.07

7 10.06 15 8.80

8 7.95 16 7.47

Table IVTable IV SNR table



A half-normal probability plot (HNPP) is obtained by plotting the absolute values of the effects (both main and/or interaction effects) along the X-axis and the per cent probability along the Y-axis. The per cent probability can be obtained by using the following equation:

Pi = x 100 (2)

Where: n = number of estimated effects (n = 15) and I is the rank of the estimated effect when arranged in the ascending order of magnitude (e.g. for factor C, I = 15)

(i – 0.5) n



Table V Table V Average SNR table

Factors or Factors or interactionsinteractions DD CC BB BDBD BCBC FF AA ABAB EE

SNR1 7.816.88 7.70 7.63 7.87 8.00 8.12 7.66 8.00

SNR2 7.46 8.40

7.57 7.65 7.40 7.27 7.15 7.62 7.28

Effect estimate -0.35

1.52

-0.13

0.02 -0.47 -0.73 -0.97 -0.04 -0.72



Figure 2Figure 2 Half-normal plot of effects

99 –

97 –95 –

90 –

85 –80 –

70 –60 –

40 –

20 –

0 –

Half Normal plot

0.0 0.3 0.7 1.1 1.5

DESIGN-EXPERT Plot

A AB BC CD DE EF F

Effect

C

A

EF



Figure 3Figure 3 Main effects plot of the control factors

Paper type Body length Wing length Body width Number of clips

Wing shape

8.4 –

8.0 –

7.2 –

7.6 –

6.8 –

Factors

– Bond

– Reg

ular

– 8 – 8 – Angled

– Flat

– 12– 12

– 3 – 1 – 2– 2

SN

Rad

io



Determination of the optimal control factor settings

The selection of optimal settings depends on the objective of the experiment or the nature of the problem under study. For the helicopter example, the objective was to maximise the flight time. In Taguchi experiments, the objective is to identify the factor settings will generally produce a consistent and reliable product. Moreover, the process which produces the product will be insensitive to various sources of uncontrollable variation. For the paper helicopter experiment, the optimal control factor settings based on the highest SNR have been determined. These are shown in Table VII. In order to decide which level is better for maximising flight time, the SNR values at both low (level 1) and high (level 2) levels of each factor are compared.

One of the optimal settings are established, it is useful to undertake a confirmation trial before onward actions are undertaken (Antony, 1996). Three helicopters were made using the optimal factor settings and the average flight time was recorded as 3.56 seconds. This shows an improvement of above 30 per cent on the average flight time using the range of variable settings. The results also reveal that flight time increases for larger wing length and smaller body length.



Table IVTable IV Average SNR values

Body lengthBody length Body widthBody width Average SNRAverage SNR

1 1 7.87

1 2 7.54

2 1 7.76

2 2 7.39



Figure 4Figure 4 Interaction plot between body length and body width

7.8 –

7.6 –

7.7 –

7.5 –

Body width

Mean

SN

R

7.4 –

1 2

Body length 1 2 1 --- 2



Summary and conclusions

As the experiment itself was simple, it was found to be a clear illustration of the process of:

defining the problem; identifying the control variables and possible interactions; defining the required levels for each variable/factor; determining the response of interest; selecting the most suitable orthogonal array; performing the experiment; undertaking the analysis; and interpreting the results to obtain a better understanding of the situation under reviw



Table VIITable VII Optimal control factor settings

Control factorsControl factors Optimum levelOptimum level

Paper type Regular (level 1)

Body length 8cm (level 1)

Wing length 12cm (level 2)

Body width 2cm (level 1)

Number of clips 1 (level 1)

Wing shape Flat (level 1)


Taguchi Method to Industrial EngineersAppendixAppendixTable AITable AI Coded design matrix of an L16 (215) orthogonal array

Column

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

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2

4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1

5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2

6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1

7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1

8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2

9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1

11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1

12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2

13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1

14 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1

15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2

16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1



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