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Design of Experiment (DOE)
9/27/2004 R. Roy/Nutek, Inc. Robust Product and
Process Designs http:/nutek-us.com 1
Overview
One of the effective ways to improve product and process quality is to reduce variation in performance that potentially results in reduced rework and rejects downstream. To assure minimum performance variation requires building robustness into the design. Robust products and processes are insensitive to the influence of uncontrollable variables which are the major causes of variation in performance. Use of the Design of Experiment (DOE) technique, in particular, the standardized version of DOE and robust design strategies proposed by Dr. Genechi Taguchi, is a proactive way to achieve robust design. In this workshop, Dr. Roy of Nutek, Inc. presents a brief overview of the basic principles of DOE methodologies and introduces strategies involved in achieving robust products. The use of Qualitek-4 software to accomplish experiment design and analysis of results tasks may be demonstrated.
Topics of Discussions
I. Overall Strategy
II. Making Quantum Improvement with Simple DOE
III. Going After Basic Robustness
IV. “Leaving No Stones Unturned” – Building Robustness for Expanded Application Capabilities
V. Qualitek-4 software for design and analysis tasks (time permitting)
Acceptance Sampling - 1910s
Economic Control of Quality of manufcd. products - 1920s
Design of experiments (DOE) - 1930s
Statistical quality control - 1940s
Management by objectives - 1950s
Zero Defects - 1960s
Participative problem solving, SPC, and quality circle - 1970s
Total quality control (TQM) - 1980s
Six Sigma - 1990s
Ref: The Evolution of Six Sigma, by Dr. S. Marash, Quality Digest, June
2001 Note: For some reason the author did not include ISO/QS 9000 which was popular
quality disciplines implemented by most manufacturing companies.
History of Quality Activities
Ref. Page 1-1
Where does DOE fit in the bigger picture?
Taguchi
Approach FMEA
DOE
SPC
Six Sigma TQM/
Lean
Ref. Page 1-2
Source of Topic Titles
Design of Experiments (DOE) Using The Taguchi Approach
What is DOE
Who is Taguchi What is it used for? How do we apply it?
Ref. Page 1-2
Product Engineering Roadmap (Opportunities for Building Quality)
Where do we do quality
improvement? * Design &
Analysis
* Design &
Development
* Test &
Validation
* Production
Return on
Investment
Ref. Page 1-5
Driving Questions For Quality Improvement (Opportunities for Building Quality)
* Customer Requirements and
Design Concepts (APQP)
* Design &
Development
* Test &
Validation
* Production
• Is the performance at its best or at optimum?
• Will it perform the same way all the time, under
all application environment?
• Is the design robust?
•Is the manufacturing process robust &
adequate?
DESIGN: New questions we may ask.
Leading Questions in Validation Test Planning (Opportunities for cost-effective testing)
* Customer Requirements and Design Concepts (APQP)
* Design & Development
* Test & Validation
* Production
• Will the product perform under extremes of application environment? • How can we cost-effectively test products under all conditions before release?
• What is the worst of all possible application conditions?
•Can we produce the optimized products profitably?
TEST: New questions we may ask.
CONSISTENCY OF PERFORMANCE: Quality may be viewed in terms of consistency of performance. To be consistent is to BE LIKE THE GOOD ONE’S ALL THE TIME.
REDUCED VARIATION AROUND THE TARGET: Quality of performance can be measured in terms of variations around the target.
New Definition of Quality
Ref. Page 1-7
This holds true also with performance of any product or
process.
Looks of Improvement
Figure 1: Performance Before Experimental Study
Figure 2: Performance After Study
m = (Yavg - Yo )
Yavg. Yo
new
Improve Performance = Reduce and/or Reduce m
Poor Quality Not so Bad
Better Most Desirable
Being on Target Most of the Time
Ref. Page 1-8
Making Quantum Improvement with Simpler DOE
A minimum first level of effort is to apply simpler experimental design techniques to achieve performance at the desired objective. This would help make the mean population performance move toward the expected level. Simpler DOE using orthogonal arrays generally offer a quantum improvement at a minimum cost.
Easier Ways to do DOE – The Taguchi Approach
Genechi Taguchi was born in Japan in 1924.
Worked with Electronic Communication Laboratory (ECL) of Nippon Telephone and Telegraph Co.(1949 - 61).
Major Attractions: standardized and simplified techniques.
What is the Design of Experiment (DOE)?
It all began with R. A. Fisher in England back in 1920’s.
Fisher wanted to find out how much rain, sunshine, fertilizer, and water produce the best crop.
Design Of Experiments (DOE):
statistical technique
studies effects of multiple variables simultaneously
determines the factor combination for optimum result
DOE Project Application Steps (Plan - Do - Act cycle by Dr. Deming)
PLAN Define project
Determine performance objectives
Identify factors to study
TEST & PREDICT
Conduct experiments Evaluate results
Predict improvements
CONFIRM ACHIEVEMENTS Test predicted design and verify that the
performance achieved is acceptable.
Need to follow a structured approach
Need to know the DOE technique
No new knowledge required
PARAMETER DESIGN: Taguchi approach generally refers to
the parameter design phase of the three quality engineering
activities (SYSTEM DESIGN, PARAMETER DESIGN and
TOLERANCE DESIGN) proposed by Taguchi.
Off-line Quality Control
Quality Loss Function
Signal To Noise Ratio(s/n) For Analysis
Reduced Variability, a Measure Of Quality
DOE - the Taguchi Approach - Seminar Contents
Ref. Page 1-10
EXAMPLE APPLICATION
It is an experimental technique that determines the solution with minimum effort.
In a POUND CAKE baking process with 5 ingredients, and with options to take HIGH and LOW values of each, it can determine the recipe with only 8 experiments.
Full factorial calls for 32 experiments. Taguchi approach requires only 8
How Does DOE Technique Work?
Ref. Page 1-10
FIVE factors at TWO levels each make 25 = 32 separate recipes (experimental condition) of the cake.
Ingredients for Baking Pound Cake
Factors Level-1 Level-2 A: Egg
B: Butter
C: Milk
E: Sugar
D: Flour
A2
A1
B1
B2
C1
C2
D1
D2
E1
E2
Ref. Page 1-11
A1
B1
C1
D1
E1
Condition #1
E2
A1
B1
C1
D1
Condition #2
Ref. Page N/A
Experimental Conditions
A1
B1
C1
E1
Condition #3
D2
E2
A1
B1
C1
Condition #4
D2
Ref. Page N/A
Experimental Conditions
A1
B1
D1
E1
Condition #5
E2
A1
B1
D1
Condition #6
C2
C2
Experimental Conditions
Ref. Page N/A
A1
B1
E1
Condition #7
D2
E2
A1
B1
Condition #8
D2
C2
C2
Experimental Conditions
Ref. Page N/A
Condition # 9 through 30 . . . . .
Experimental Conditions
E1
Condition #31
D2
E2
Condition #32
D2
C2
C2
A2
B2
A2
B2
Experimental Conditions
Ref. Page N/A
Experimental Trial Conditions by L-8 Orthogonal Array
Ref. Page N/A
Experiment Design Using L-8 Array Ref. Page N/A
3 2-L factors = 8 Vs. 4 Taguchi expts.
7 ‘‘ ‘‘ = 128 Vs. 8 Expts.
15 ‘‘ = over 32,000 Vs. 16 ‘‘
Fishing Net
Orthogonal Array - a Fish Finder
Ref. Page 1-11
Standardized application and data analysis
Higher probability of success
Option to confirm predicted improvement
Improvement quantified in terms of dollars
Why Taguchi Approach?
Ref. Page 1-12
The Clutch plate is one of the many precision components used in the automotive transmission assembly. The part is about 12 inches in diameter and is made from 1/8-inch thick mild steel.
Objective & Result - Reduce Rusts and Sticky
(a) Sticky Parts – During the assembly process, parts were found to be stuck together with one or more parts.
(b) Rust Spots – Operators involved in the assembly reported unusually higher rust spots on the clutch during certain period in the year.
Factors and Level Descriptions
Rust inhibitor process parameters was the area of study.
II. Experiment Design & Results
One 4-level factor and four 2-level factors in this experiment were studied using a modified L-8 array. The 4-level factor was assigned to column 1 modified using original columns 1, 2, and 3.
I. Experiment Planning
Project Title - Clutch Plate Rust Inhibition Process Optimization Study (CsEx-05)
Figure 1. Clutch Plate Fabrication Process
Stamping / Hobbing Clutch plate made from 1/16 inch thick rolled steel
Deburring Clutch plates are tumbled in a large container to remove sharp edges
Rust Inhibitor Parts are submerged in a chemical bath
Cleaned and dried parts are boxed for shipping.
Example Case Study (Production Problem Solving) Ref. Page 1-13
Applications in Analytical Simulations
W H
L
F
d
D
Elasticity, EI
K
For a cantilever beam, the deflection equation can be expressed as:
D = d + F/K + [4FL3 ]/ [EWH3] Since Deflection at end is Fl3/(3EI) where I = WH3 /12, d = initial displacement
Tools for Experiment Designs - Orthogonal Arrays
L4 (23) Array Cols>> Trial# 1 2 3 1 1 1 1 2 1 2 2 3 2 1 2 4 2 2 1
Use this array (L-4) to design experiments with three 2-level factors
L8(27 ) Array
Cols.>> TRIAL# 1 2 3 4 5 6 7 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 3 1 2 2 1 1 2 2 4 1 2 2 2 2 1 1 5 2 1 2 1 2 1 2 6 2 1 2 2 1 2 1 7 2 2 1 1 2 2 1 8 2 2 1 2 1 1 2
Use this array (L-8) to design experiments with seven 2-level factors
L (XY) n
No. of rows in the array
No. of levels in the
columns.
No. of columns in the array.
L9(34)
Trial/Col# 1 2 3 4 1 1 1 1 1 2 1 2 2 2 3 1 3 3 3 4 2 1 2 3 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 3 9 3 3 2 1
Use this array (L-9) to design experiments with four 3-level factors
•Experiment using Std. Orthogonal Arrays •Main effect studies and optimum condition
• Interactions • Mixed level factors
OEC Problem solving
DC Loss
Noise Factors, S/N Analysis, Robust Designs, ANOVA
There are More Steps to Climb
For better returns on investment, more sophisticated experiment design and analysis techniques need to be employed.
III. Going After Basic Robustness
To make design robust is to make its performance insensitive to the uncontrollable (Noise) factors. The strategy here is to select the most desirable combination of the controllable factors based on the performance while exposed to the influence of the noise conditions. The experiment design for such studies require stringent disciplines and care.
Detail can be seen from example applications….
Nature of Influences of Factors at Different Levels
Resu
lt/R
esp
onse
/QC
A1 A2 A3 A2
Res
ult/
Res
pons
e/Q
C
A1 A2 A3
Resu
lt/R
esp
onse
/QC
• Minimum TWO levels
• THREE levels desirable
• FOUR levels in rare cases
• Nonlinearity dictates levels for continuous factors only
A1 A2 A3 A4
Ref. Page 2-2
Combination Possibilities – Full Factorial Combinations
NOTATIONS:
A (A1,A2) or A represent 2-level factor
THREE 2-level factors create
EIGHT (23 = 8) possibilities.
A1B1C1 A1B1C2
A1B2C1 A1B2C2
A2B1C1 A2B1C2
A2B2C1 A2B2C2
Simpler notations for all possibilities or full factorial
Cond.# A B C
1 1 1 1
2 1 1 2
3 1 2 1
4 1 2 2
5 2 1 1
6 2 1 2
7 2 2 1
8 2 2 2
Ref. Page 2-3
ONE 2-level factor offer TWO test conditions (A1,A2). TWO 2-level factors create FOUR (22 = 4 ) test conditions A1B1 A1B2 A2B1 A2B2) .
3 Factors at 2 level 23 = 8
4 Factors at 2 level 24 = 16
7 Factors at 2 level 27 = 128
15 Factors at 2 level 215 = 32,768
What are Partial Factorial Experiments?
What are Orthogonal arrays and how are they used?
Full Factorial Experiments Based on Factors and Levels
Ref. Page 2-4
How are Orthogonal arrays used to design experiments?
What does the word “DESIGN” mean?
What are the common properties of Orthogonal Arrays?
Orthogonal Arrays– Experiment Design Tool
2-Level Arrays
L4 (23 ) L8 (27)
L12 (211)
L16 (215) . . . .
3-Level Arrays
L9 (34), L18 (21 37) . . .
4-Level Arrays
L16 (45) . . . .
L-4 Orthogonal Array Trial # 1 2 3 1 1 1 1 2 1 2 2 3 2 1 2 4 2 2 1
Ref. Page 2-4
Key observations: • First row has all 1's. There is no row that has all 2's. • All columns are balanced and maintains an order. • Columns of the array are ORTHOGONAL or balanced. This means that there are
equal number of levels in a column. The columns are also balanced between any two columns of the array which means that the level combinations exist in equal number.
• Within column 1, there are two 1's and two 2's. • Between column 1 and 2, there is one each of 1 1, 1 2, 2 1 and 2 2
combinations. • Factors A, B And C all at 2-level produces 8 possible combinations (full factorial)
Taguchi’s Orthogonal array selects 4 out of the 8. How does One-Factor-at-a-time experiment differ from the one designed using an
Orthogonal array?
L-4 Orthogonal Array Trial #A B C 1 1 1 1 2 1 2 2 3 2 1 2 4 2 2 1
Array Descriptions: 1. Numbers represent factor levels 2. Rows represents trial conditions 3. Columns accommodate factors 3. Columns are balanced/orthogonal 4. Each array is used for many experiments
Properties of Orthogonal Arrays
Ref. Page 2-5
Orthogonal Arrays for Common Experiment Designs
L (XY) n
No. of rows in the array
No. of levels in the columns.
No. of columns in the array.
Use this array (L-4) to design experiments with three 2-level
factors
1
1
2
2
1
2
2
1
1
2
1
2
1
2
4
3
xxx
xxx
xxx
xxx
C A B Trial# Results
Ref. Page 2-6
Orthogonal Arrays for Common Experiment Designs
L (XY) n
No. of rows in the array
No. of levels in the columns.
No. of columns in the array.
Use this array (L-8) to design experiments with seven 2-level factors
xx
xx
xx
xx
xx
xx
xx
xx
1
1
1
1
2
2
2
2
1
2
4
3
5
6
8
7
1
2
1
2
2
1
2
1
1
1
2
2
2
2
1
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
2
Results
E Trial# A C B F D G
Ref. Page 2-6
Orthogonal Arrays for Common Experiment Designs
L (XY) n
No. of rows in the array
No. of levels in the columns.
No. of columns in the array.
Use this array (L-9) to design experiments with four 3-level factors
Trial#
A B C D Results
1 1 1 1 1 xx
2 1 2 2 2 xx
3 1 3 3 3 xx
4 2 1 2 3 xx
5 2 2 3 1 xx
6 2 3 1 2 xx
7 3 1 3 2 xx
8 3 2 1 3 xx
9 3 3 2 1 xx
Ref. Page 2-7
Steps in Experiment Design
Factors Level-1 Levl-2
A:Time 2 Sec. 5 Sec.
B:Material Grade-1 Grade-2
C:Pressure 200 psi 300 psi
L-4 Orthogonal Array Trial #A B C 1 1 1 1 2 1 2 2 3 2 1 2 4 2 2 1
Step 1. Select the smallest orthogonal array
Step 2. Assign the factors to the columns (arbitrarily)
Step 3. Describe the trial conditions (individual experimental recipe)
Trial#1: A1B1C1 = 2 Sec. (Time), Grade-1 (Material), and 200 psi (Pressure)
Trial#2: A1B2C2 = 2 Sec. (Time), Grade-2 (Material), and 300 psi (Pressure)
Trial#3: A2B1C2 = 5 Sec. (Time), Grade-1 (Material), and 300 psi (Pressure)
Trial#4: A2B2C1 = 5 Sec. (Time), Grade-2 (Material), and 200 psi (Pressure)
Ref. Page 2-7
Experiment Designs With Seven 2-Level Factor Experiments with seven 2-level factors are designed using L-8 arrays.
An L-8 array has seven 2-level columns. The factors A, B, C, D, ... G can be assigned arbitrarily to the seven column as shown. The orthogonal arrays used in this manner to design experiments are called inner arrays.
Experiment Designs with More Factors?
L8 Orthogonal Array
1
1
1
1
2
2
2
2
1
2
4
3
5
6
8
7
1
2
1
2
2
1
2
1
1
1
2
2
2
2
1
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
2
E Trial# A C B F D G
Control Factors
Inner Array
Ref. Page 2-8
Full Factorial Arrangement with Seven 2-level Factors Ref. Page 2-9
2-Level Arrays
L4 (23)
L8 (27)
L12 (211)
L16 (215)
3-Level Arrays
L9 (34)
L18 (21 37)
4-Level Arrays
L16 (45)
Common Orthogonal Arrays
L (XY) n
No. of rows in the array
No. of levels in the columns.
No. of columns in the array.
Ref. Page 2-10
PLAN
• Identify Project and Select Project Team
• Define Project objectives Evaluation Criteria
• Determine System Parameters (Control Factors,
Noise Factors, Ideal Function, etc.)
DESIGN
• Select Array and Assign Factors to the columns
(inner and outer arrays)
CONDUCT EXPERIMENTS
ANALYZE RESULTS
• Factor Effects, Optimum Condition, Predicted
Performance, etc.
Planning Before Designing Experiments
Ref. Page 2-10
An ordinary kernel of corn, a little yellow seed, it just sits there. But add some oil, turn up the heat, and, pow. Within a second, an aromatic snack sensation has come into being: a fat, fluffy popcorn. Note: C. Cretors & Company in the U.S. was the first company to develop popcorn machines, about 100 years ago.
Popcorn Machine Performance Study (Example Experiment)
This example is used to demonstrate “cradle to grave”, mini planning, design, and analyses tasks involved in DOE.
Ref. Page 2-11
Project - Pop Corn Machine performance Study
Objective & Result - Determine best machine settings
Quality Characteristics - Measure unpopped kernels (Smaller is better)
Factors and Level Descriptions
Factor Level I Level II
A: Hot Plate Stainless Steel Copper Alloy
B: Type of Oil Coconut Oil Peanut Oil
C: Heat Setting Setting 1 Setting 2
Experiment Planning & Design
1
2
4
3
Trial# C: Ht. Setting
A: Hot plate B: Oil Type
C1: Setting 1 C1: Setting 1 C2: Setting 2 C2: Setting 2
A1: Stainless
A2: Copper
A1: Stainless
A2: Copper
B1: Coconut
B2: Peanut
B2: Peanut
B1: Coconut
1
1
2
2
C A B
1
2
2
1
1
2
1
2
1
2
4
3
Trial# Results
Ref. Page 2-12
Experiment Design & Results
1
2
4
3
Trial# C: Ht. Setting
A: Hot plate B: Oil Type
C1: Setting 1 C1: Setting 1 C2: Setting 2 C2: Setting 2
A1: Stainless
A2: Copper
A1: Stainless
A2: Copper
B1: Coconut
B2: Peanut
B2: Peanut
B1: Coconut
1
1
2
2
C A B
1
2
2
1
1
2
1
2
1
2
4
3
Trial# Results
Design Layout (Recipes)
Expt.1: C1 A1 B1 or [Heat Setting 1, Stainless Plate, & Coconut Oil] Expt.2: C1 A2 B2 or [Heat Setting 1, Copper Plate, & Peanut Oil ] Expt.3: C2 A1 B2 or [Heat Setting 2, Stainless Plate, & Peanut Oil ] Expt.4: C2 A2 B1 or [Heat Setting 2, Copper Plate, & Coconut Oil ] How to run experiments: Run experiments in random order when possible.
Ref. Page 2-12
Experimental Results and Analysis
A1 = __ (5 + 7)/2 = 6.0
1
1
2
2
C A B
1
2
2
1
1
2
1
2
1
2
4
3
Trial# Results
5
8
4
7
__ T = (5 + 8 + 7 +4)/4 =
6
1
1
2
2
C A B
1
2
2
1
1
2
1
2
1
2
4
3
Trial# Results
5
8
4
7 A2 = __ (8 + 4)/2 = 6.0
Ref. Page 2-13
• Trend of Influence:
• How do the factor behave?
What influence do they have to the variability of results?
How can we save cost? • Optimum Condition:
What condition is most desirable?
Calculations: ( Min. seven, 3 x 2 + 1)
(5 + 8) / 2 = 6.5 (7 + 4) / 2 = 5.5 (5 + 7) / 2 = 6.0 (8 + 4) / 2 = 6.0 (5 + 4) / 2 = 4.5 (8 + 7) / 2 = 7.5
_ C2 =
_ C1 =
_ A2 =
_ A1 =
_ B1 =
_ B2 =
Analysis of Experimental Results
A1 Hot plate A2 B1 Oil B2 C1 Heat Setting
C2
3
4
6
5
7
8
9 UNPOPPED KERNELS
Main Effects (Average effects of factor
influence)
Ref. Page 2-14
QC Plays a key roles in:
• Understanding factor influence
• Determination of the most desirable condition.
Quality Characteristics
Examples
Nominal is Best: 5” dia. Shaft,12 volt battery, etc.
Smaller is Better: noise, loss, rejects, surface roughness, etc.
Bigger is Better: strength, efficiency, S/N ratio, Income, etc.
Role of Quality Characteristics (QC)
Ref. Page 2-14
Estimate of Performance at the Optimum Condition
A1 Hot plate A2 B1 Oil B2 C1 Heat Setting
C2
3
4
6
5
7
8
9 UNPOPPED KERNELS
Main Effects (Also called: Factorial Effects or Column Effects)
A1 B1 C2
Based on QC: Smaller is better
Optimum condition: ( Assuming A1 is less expensive than A2) A1 B1 C2
= 6.0 + ( 6 – 6 ) + (4.5 – 6.0 ) + ( 5.5 – 6.0 ) = 4.0 (Assumption: Factor contributions are additive)
__ Yopt = T +
__ ( A1 -
_ ( C2 -
__ T )
__ ( B1 -
__ T ) +
__ T ) +
Ref. Page 2-15
Expected Performance:
What is the improved performance? How can we verify it? What is the boundary of expected performance?
(Confidence Interval, C.I.) Notes: Generally, the optimum condition will not be one that has already been tested. Thus you will need to run additional
experiments to confirm the predicted performance. Confidence Interval (C.I.) on the expected performance can be calculated from ANOVA calculation. These boundary
values are used to confirm the performance. Meaning: When a set of samples are tested at the optimum condition, the mean of the tested samples is expected to be
close to the estimated performance.
Interpretation of the Estimated Performance
3.5 Yavg. Yexp. = 4.0 4.5
Confidence level (C.L.), say 90%.
Confidence Interval, C.I. = +/- 0.50
(Calculation not shown)
Ref. Page 2-16
Performance Improvement
Improved performance from DOE =
Estimated performance at the optimum condition (Yopt)
Yopt = 4.0 (in this example)
The estimated performance can be expressed in terms of a percent improvement, if the current performance is known.
Assuming that the current performance is the grand average of performance (YCurrent ) = 6.0
Improvement = x 100
(Yopt - YCurrent ) YCurrent
= x 100 = - 33% (4 - 6 )
6
Ref. Page 2-16
Solve Problem 2A
Practice and Learn
Practice Problem # 2A: Experiment with L-4
Ref. Page 2-41
Practice Problem # 2A
• Which factor has the most influence to the variability of result?
• If you were to remove tolerance of one of the three factors studied, which factor will it be?
Ref. Page 2-41
Practice Problem # 2A
2. Determine the Optimum Condition. Optimum Condition (character notation) = Optimum Condition (level description) = 3. What is the grand average of performance? __ T = 4. Calculate the estimated value of the Expected Performance at the optimum condition. Yopt = 5. What is the estimated amount of total contributions from all significant factors? Total contributions from all factors = 6. Assuming that the result of trail # 2 represents the current performance, compute the % Improvement obtainable by adjusting the design to the optimum condition determined. % Improvement = [Answers: 1 - (Describe, Factor __ has the most influence, etc. ) 2 - Optimum Cond: 2,2,2, , 3 - Gd. Avg.=28.5, 4 - Yopt = 19, 5 - Contribution = 9.5, 6 - Improvement = 24% ]
Ref. Page 2-42
Group Exercise - Class Project
I. Experiment Planning
Project Title -
Objective & Result -
(Describe why you initiated the project and what you wish to accomplish)
Quality Characteristics: (Describe what you are after and how you would measure the results. Depending on what it is you are after, your quality characteristic will be bigger is better, smaller is better, or nominal is the best)
Factors and Level Descriptions
Notation/Factor Description Level I Level II
A:
B:
C: etc.
II. Experiment Design & Results
Our plan is to use _____ array. We/I want to complete design by assigning factors to the columns as.. Etc.
Experiment Designs with Noise Factors
Tr#
1 2 3
8
1 2 3 4 5 6 7
L 8
Control factors
Noise Factors
L 4
Outer Array
Inner Array
R e s u l t s 1 2 3 4
1
2
3
1 1 2 2
1 2 1 2
1 2 2 1
R R R R R R R R
R R R R R R R R
. . . . . . .
. . .. . . .. .. . . .. .
73
11
21
Oven type
Temperature
Humidity
*
Why AVERAGE of results is inadequate? Why do we need a new YARDSTICK? Nominal: MSD = [(Y1 -Yo) 2 +.(Y2 -Yo) 2 + (Y3 -Yo) 2 +. .]/n Smaller: MSD = [( Y1
2 + .Y 22 +Y 32 + . .)]/n Bigger: MSD = [(1 / Y1
2 + 1 / Y22 + 1/Y3
2 + ...... )]/n S/N = - 10 LOG10 (MSD)
Why -(Minus) Why base 10
Evaluating Performance Based on Reduced Variation
“Leaving no Stones Unturned” – Building Robustness for Expanded Application Capabilities
While most systems (product and process designs) tend to have a desired performance goal, there are others which need to respond in direct proportion to the strength of the input (called signal factor) condition. For such system, the goal is to achieve performance that maintains a fixed relationship with the magnitude of the input. Such systems are considered to have dynamic response characteristics and require special experiment setup and analysis methods for optimizing designs..
Dealing with Dynamic Systems – Process Diagram
Representing the subject product/process design as a system is a necessary step for understanding its behavior. The system is described in terms of its parameters like factors, signal, response, noise, etc. An absence of variable input/signal to the system renders it as a static system which are dealt with the standard designs discussed earlier.
Example of Dynamic System Response
Example Case: Fuel Gauge Reading
Response
(y)
M1 M2 M3 Signal (M)
** * * *
** * * *
** * * *
y = M
, Slope
y
M
Linear
Large variation
y
M
Nonlinear High variation
Least Desirable
Comparison of Strategies for Static and Dynamic System
Static System: Tiger Woods putting golf balls August 11, 2004 Top spot: Tiger Woods' hold on the world number one ranking is more tenuous now. “Vijay Singh has been on Tiger's heels for some time now, and if either Singh, or Ernie Ells were to win the PGA Championship, Woods would relinquish his spot atop the rankings.”
Dynamic System: Lance Armstrong biking for Tour de France Lance Armstrong rides into Paris, collects record sixth consecutive Tour title (Tour de France), Sunday July 25, 2004 5:39PM PARIS (AP) -- Lance Armstrong raced onto the crowd-lined Champs-Elysees as a yellow blur, bathed in the shimmering light of a 24-carat, gold-leaf bike, a golden helmet and the race leader's yellow jersey.
Dynamic System Examples
Example Case: Voltage Measuring Instrument Signal Factor (M): Battery voltage Response (y): Voltage reading Notes:
Response
(y)
M1 M2 M3 Signal (M)
** * * *
** * * *
** * * *
y = M
, Slope
Dynamic System Examples
Example Case: Weighing Scale Design Signal Factor (M): Weight of subject Response (y): Indicated weight Notes: Weight indicated should be the same as weight of the subject.
Response
(y)
M1 M2 M3 Signal (M)
** * * *
** * * *
** * * *
y = M
, Slope
Where to Apply and Why
Apply early in the engineering design stage to optimize process and product designs
WHY?
Very high return on investment (ROI)
Ranjit K. Roy, Ph.D., P.E. PMP, Fellow of ASQ., President, Nutek, Inc.
And
Suren N. Dwivedi,,Ph.D., P.E., Professor, Dept. of Mechanical Engineering
University of Louisiana at Lafayette
Presented
by
