Product and Process Improvement Through The Use of Taguchi Method

(TM)

Presented ByJafri Mohd. Rohani

Department of Manufacturing and Industrial Engineering,

Faculty of Mechanical EngineeringUniversiti Teknologi Malaysia

April, 2002

Objectives

• On completion of this module, the student will be able to :ØDescribe Taguchi OA Experimental DesignØDefine what is meant by factors & levels, and

explain the notation used for Taguchi OA experimental designØExplain main effects & interactionsØ Set-up and analyze Taguchi OA experiment using

Simple plots for mean and S/N

Module Content

• Key basic concept• Quality Loss Function• Experimental Designs• Orthogonal Arrays & Linear Graph• Analysis of Means & S/N Ratio• Examples of Experimental Design• Case Study

The key basic concept of Taguchi Approach: Why current mind-set

needs to be changed ?

• “Goalpost mentality” – to stay within a customer’s specification limits

• Doesn’t encourage manufacturers to produce goods that are on target because the products that are close to the upper and lower specification limits are equal status to those with the desired target value

• Taguchi’s approach is to produce goods with the least possible variation, with the goal of on target 100 % of the

time, lead to more satisfied customers

What poor quality really means to society?

• Each time a poor-quality product is shipped, there is a loss imparted to society.

• Developed Quality Loss Function(QLF) Model – The resulting graph of QLF model is parabola, with zero loss when the quality characteristics is equal to the target value

• Taguchi’s approach is to strive for zero loss

How to produce high-quality goods?

• Taguchi approach emphasizes building quality into the design of products and their processes

• A product’s designer needs to select those parameters that define the product and reduce variability in the performance

• The process of selecting a product’s important parameters is called parameter design

Brief history of TM

• Japanese engineer who developed an interest in statistics and experimental design methods in the 1950’s

• Methods used extensively in Japanese industry since 1950 with great success

• Used initially for improvement of production processes

• Used later for improvement of product design

Taguchi’s 7 Principles1. The quality of a product can be quantified by

the loss it imparts to society- Society, as well as the end user, is affected by quality of a

product- Eg. If a product uses more energy than necessary, the

ownership/running costs are higher for the customer

2. Quality improvement and cost reduction are necessary to survive

- High quality, low cost likely to be the market leader

- low quality, high cost no chance of survival

Taguchi’s 7 principles

3. Continuous quality improvementprogramme should be based on reducing product/process variation

-Every product/process has a target performance

-The bigger the average variation, the less likely the performance will be acceptable and reliable

Taguchi’s 7 Principles

4. Financial loss due to variation is approximately proportional to the square deviation from target

-Loss(RM) = k(dev. From target)^2- Loss occurs even within specifications

5. Final quality and product cost are determined largely by design

-When product has high variability, it acts in an unpredictable and unreliable manner. Good design leads to product and/or processes that are robust in the face of causes of variation.

Taguchi’s 7 Principles

6. Performance variations can often be reduced by exploiting non-linear effects that some design factors have on performance

7. Statistically planned experiments to find factor values that minimizes variation in performance

- Other methods include: “One-factor at a time method”, full factorial, trial-and-error, orthogonal array.

Quality Loss Function (QLF)

• Quality is the losses a product imparts to society. These include losses caused by functional variation from target.

• Quality should be measured quantitatively by some loss function

• Taguchi’s loss function has 2 uses:1. To evaluate specification2. To evaluate the impact of engineering improvements

Taguchi Notation

- m : “mid-value” : manufacturing target where performance minimizes L(y)

- L(y): “Loss function” : Total loss (RM) associated with performance y- ? 0 : “customer allowance” : The limits m ± ? 0 describe the products

functional range as viewed by the customer- ? : “Manufacturer’s allowance” : The limits m ± ? describe the

manufacturer’s tolerance range- A0 : “Society Loss” : The total cost to customer when the performance

characteristics exceeds the customer’s tolerance tolerance limit m ± ? 0

- A : “manufacturer’s Loss” : The cost (RM) to manufacturer for repairing or scrapping a non-conforming product

Taguchi’s Quadratic Loss Function

L (y) = K (y – m)2

- y : The performance characteristics- K : The loss parameter- m : The performance target

Expected Loss Functions, E[L(y)]

- Expected Loss, E[L(y)]: The mean loss over many instances of the product.

E[L(y)] = E[ K (y – m)2]= K[var(y) + (µ – m)2 ]= K(Mean Squared Deviation, MSD)

MSD = S(yi – m)2 / n Where n represents sample of n items

House of Quality ( Hauser & Clausing, 1988)

Example QLF

Suppose it costs RM 50 to fix the product that exceeds the customer tolerance limits. The customer tolerance limits for the high are: 1.5 ± 0.02 m. 10 products selected randomly and yield the following height: 1.53, 1.49, 1.5, 1.49, 1.48, 1.52, 1.54, 1.53, 1.51, 1.52.

Question: 1. What is the loss function, L(y)2. Find the average loss per product per unit,

E[L(y)]

Evaluating Impact of Improving the process- Suppose that the cost of improved process by

reducing variability is estimated to be RM 5.50 / unit. Annual production = 20,000 units. 8 units are selected randomly from improved process and yields the following: 1.51, 1.5, 1.49, 1.52, 1.52, 1.5, 1.48, 1.51

Question: 1. Is the new process cost efficient ?2. If so, what is the annual savings ?

Process Investigation

Process Operation > Data > Information > Knowledge

How to generate or collect data: statistical design

How to extract the information contained in the data: statistical data analysis

Types of Data Acquisition

• Passive : Routine Operating Data

• Statistically Design of Experiments

Taguchi Strategy For the Design Process

System Design Parameter Design Tolerance Design

Design Process(Products and Processes)

Design Process: System Design

- A conceptual stage in which scientific and engineering knowledge is used to select the appropriate technology to achieve the desired function

- Taguchi offers nothing new here, system design requires know how, experience, etc.

Design Process: Parameter Design

A stage where functional quality can be improved without extra cost through statistical designed experiments.

It is the acts of selecting the nominals of the system and to find the combination of nominals that is robust despite this component variability.

Tolerances should be kept as wide as possible at the parameter design stage

Design Process: Tolerance Design

- A stage in which functional variability can be further reduced if parameter design hasn’t achieved sufficient improvement. Tolerance design includes tightening up tolerances, upgrading materials, specifying better processes etc. and therefore involves extra cost.

- System design and tolerance design are expensive and only parameter design offers the opportunity for improved quality and reduced cost.

- We need an experimental methods to find out how design factors affect functional variation.

What is an experimental method or design of experiments(DOE)?

- DOE is a test or a series of test in which purposeful changes are made to the input variables of a process or system that we may observe and identify the reasons for changes in the output response (Montgomery, 1991)

Attacking The Issue Through DOE approach

• Practical Problem: Eg. Too many auto accidents

• Convert to Statistical Problem: How can we improve that auto accidents (Y) are reduced to less than 0.1 % of cars per year?

• Y = Auto Accidents = f (X1, X2,…, Xn)

Converting the issue

• Convert from statistical problem to statistical solution: What do we know about the problem?

• Y = Auto Accidents = f (X1, X2,…, Xn)• What are the Xs? (eg. Speed, DUI) • What are the specifications limits for the

Xs?• Use brainstorming session

Solving the issue

• Convert from statistical solution to practical solution

• Change spec. limits on key variables (speed limit; DUI)

• Implement controls to maintain variables (speed traps, jail terms)

Focus of DOE: Y = f (X) To get results, should we focus our

behavior on the Y or X?

• Y• Dependent• Output• Effect• Symptom• Monitor

• X1….Xn

• Independent• Input-Process• Cause• Problem• Control

The problem solving methodology

Controlling Critical X’s

3-6Control Plans/SPC

Found Critical X’s

4 - 8Experimentation

Screened List8 - 10Multi-Vari Studies

1st “Hit List”10 - 15C&E Diagram & FMEA

All X’s+30 inputsProcess Map

Types of Experimental Methods

1. One-Factor-at-a –time(OFAT)2. Full Factorial Design3. Trial-and-error4. Taguchi Method

DOE Notation• -Output Response : A measured result

of interest• Factor : A variable being explicitly

manipulated in an experiment

1. OFAT

• To investigate several factors is to fix them all and change only one factor at a time

• The experimental plan would consist of (1 + n) trials where n is the number of factors being investigated

Eg. Suppose we want to investigate the effects of two factors, A and B, on a product or process and that each factor has two possible values – low and high represented by 1 and 2 respectively.

OFAT Example

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OutputResponse

Factor BFactor ATrials

OFAT Example• What is the effect of Factor A ?Effect of Factor A = What is the effect of Factor B ?Effect of Factor B =

Weaknesses of OFAT strategy

1. Doesn’t consider all possible permutations of A and B and the information gathered is therefore incomplete. Eg. The combination A2, B2 isn’t considered.

2. Factors effects are based upon results of a single trial instead of all trials and the information gathered is unreliable.

3. Doesn’t take account of possible interactions between factors. We don’t know what might happen if these factors were changed, not individually, but together.

Interactions Between Factors

• An interaction is present when the combined effect of two or more factors is bigger or smaller than the sum of their individual effects. It means that the factors are affecting each other as well as the product or process performance.

• Eg. Suppose we want to make a cup of sweet tea, adding sugar and stirring are two factors that affect the result. Stirring alone has no effect, adding sugar alone has some effect. Doing both has a big effect. Variability is reduced since the tea is uniformly sweet.

Comparison of Full Factorial vs. Taguchi OA

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4L43823

Total runs

Taguchi OA

# of Factors

Total Runs

# of Level

# of Factors

2-Level Orthogonal Arrays(OA) and Linear Graph

• Each Factor is Varied Over Two Levels• Also referred to as fractional factorial

designs since they are the subsets from full factorials, and therefore, reduce the amount of experimental time and cost

• Useful designs for identifying key factors

L4 Orthogonal Array(OA)

• This designed is used for:1. Evaluating two factors and their

interaction, or2. Evaluating three factors assuming there

are no interaction

Linear Graph For L4

• Taguchi uses linear graph with OA’s to deal with interaction. These graphs show the assignment of factors to the column of OA and help us visualize interaction between factors.

• For two factors, use column 3 to represents the interaction between factors (column 1 & 2)

L8 OA – This design is used to evaluate 3 –7 factors

Linear Graph for L8

Linear Graph for L8 Explaination

• The numbers refer to the seven column of L8 OA

• Columns represented by nodes (1,2,4) are purely for single factors

• Columns represented by lines between nodes (3,5 and 6) are where the 2-factor interaction effects between factors at the nodes will appear

L8 OA Example

• For example, the interaction between factors in column 1 and 2 will influence column 3. If that interaction is thought likely to besignificant, then, no factor is assigned to column 3. Since the effect of the factor would be confused with that of the interaction.

• Column/node 7 is where the three-factor interaction effect between the factors at column 1, 2 and 4 will appear.

• Fifth, sixth, and seventh single factors can be included when the two-factor interactions are not likely to be significant

• The L8 OA can be used for three factors with three significant interactions or seven factors with no significant interactions.

Rules for selecting Standard OA for 2-Level

L1612 – 15

L128 - 11

L84 - 7

L42 - 3

OA to be usedNo of factors

Rules for selecting Standard OA for 3-Level

L1612 – 15

L128 - 11

L84 - 7

L42 - 3

OA to be usedNo of factors

L275 - 7

L92 - 4

OA to be usedNo of factors

Inner Array Definition

• Sometimes referred as design factors and controllable factors

• The factors in which the experimenter can or wants to control

• The factors that the design parameters need to be optimized

Outer Array Definition

• Sometimes referred as uncontrollable factors or noise factors

• The factors in which for various reasons cannot or will not be controlled, but, whose influence should be known

Signal-to-Noise(S/N) Ratio: Target is Best

• Response at the target value with reduced variation

• S/N = 10 Log10 [y2/s2]Where y = sample mean

s = sample standard deviation of the output response variable, y

Signal-to-Noise(S/N) Ratio: Smaller is Better

• Reduced value of original response with reduced variation. Target value of zero

• Eg. Wear rate, fuel consumption• S/N = -10 Log10 [(1/n ) S y2 ]Where n = number of replicates

Signal-to-Noise(S/N) Ratio: Larger is Better

• Increased value of original response with reduced variation

• Eg. Weld strength• S/N = -10 Log10 [(1/n ) S (1/ y2) ]Where n = number of replicates

Case Study

• Suppose an engineer is interested in studying the following factors in order to reduce the wear on a slider pump. The following 2-level factors were considered: Slider Material (A), Weight (B), Surface Roughness (C), Clearance (D), and Side Material (E). Interactions A X B and A X C were thought likely. The wear was measured (in µm) at eight points on the slider of the pump, the wear at each point being considered to be of equal importance. These eight measurement points were assumed to reflect the effect of noise factors. The experiment was carried out using L8 OA. Carry out necessary analysis for

optimization of the factor settings.

L8 OA Experimental Results

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Case Study

• Step 1 : Select an appropriate S / N Ratio• Step 2 : Calculate S/N and X-bar(mean) for

each control factor combination (Analyse by rows)

Case Study

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S/N (dB)Mean (µm)Trial

Analysis of Means

Level 2

Level 1

Factor E

Factor D

Factor C

Factor B

Factor A

Analysis of S/N Ratio

Level 2

Level 1

Factor E

Factor D

Factor C

Factor B

Factor A

Plot Response Graph for Mean

Plot Response Graph For S/N Ratio

Calculate interaction effects

• A 2-way interaction between factors with 2-level gives four combination

• Eg. A x B Interaction, the 4 combinations are: A1B1, A2B1, A1B2, A2B2

• A1B1 (mean) = (11.125 + 8.625)/2 = 9.88 µm

• A1B1 (S/N) = (-20.9 –20.6)/2 = -21.25 dB

A x B Interaction effects for Mean

Factor B : Level 2

9.88Factor B : Level 1

Factor A: Level 2

Factor A: Level 1

A x B Interaction effects for S/N

Factor B : Level 2

-21.25Factor B : Level 1

Factor A : Level 2

Factor A : Level 1

Exercise: Calculate interaction effects for A x C

Plot Interaction effects for mean and S/N

Predicted Performance

• Predicted Outcome = Overall average experimental results + Respected Significant factor Settings

Where the respected significant factor setting = average for that factor at that level – overall experimental results

If the trials confirm the predicted outcome, the experiment succeeds. If not, possible interactions have to be considered and catered for in a new experiment.