SlideShare une entreprise Scribd logo
1  sur  20
Télécharger pour lire hors ligne
DESIGN OF EXPERIMENTS
(DOE)
A presentation by
THE SOCIETY
OF
STATISTICAL QUALITY CONTROL ENGINEERS
BHOPAL
What is DOE
DOE is a process optimization
technique that relies on planned
experimentation and statistical
analysis of results
LIMITATIONS OF TRADITIONAL
METHODS OF EXPERIMENTATION:
 One factor studied at a time, requiring enormous
time to complete the experiment.
 Interactions i.e. effect of one factor on another, are
ignored leading to erroneous results.
 Complex processes involving a number of factors,
levels, interactions can not be studied by traditional
approach.
DOE ADVANTAGES:
 Optimizes process parameters with minimum number
of trials, thus saving time and resources on
experimentation.
 Interactions (effect of one factor on another) also taken
into consideration.
 Results analysed using ANOVA technique for
objective judgement.
 Orthogonal Arrays (OA) technique used for finding
efficient designs of experiments.
DESIGN OF EXPERIMENTS:
STEPS TO BE FOLLOWED
1 Define the objective:
Example – “To optimize the process of annealing”
2 List out variable factors:
Example – Temperature, time duration, nature of medium etc.
3 List out fixed factors:
Example – room temperature, humidity etc.
4 Decide upon responses:
Example – hardness, tensile strength etc.
DESIGN OF EXPERIMENTS:
STEPS TO BE FOLLOWED (Contd.)
5 Fix-up the levels of variable factors:
Example:
Level Temperature
1 200°C
2 300°C
3 400°C
6 Define the levels of fixed factors:
Example: Room temperature 25±5°C
7 Identify the interactions which need to be studied
DESIGN OF EXPERIMENTS:
STEPS TO BE FOLLOWED (Contd.)
8 Design a suitable experiment – full factorial/ fractional factorial/OA
9 Conduct the experiment
10 Record data on response for each trial
11 Analyse the experimental data (responses) using ANOVA technique
12 Find out significant factors and insignificant factors
13 Find out significant interactions and insignificant interactions
14 Plot response curves to find out optimum levels of significant
factors.
15 Report optimum levels of process parameters as final result
FULL FACTORIAL EXPERIMENT
Vs.
FRACTIONAL FACTORIAL EXPERIMENT
 To study the effect all factors and interactions, full factorial experiment needs to be
conducted i.e. all possible combination of factors and levels have to be tried. With factors
limited to two or three, full factorial experiment is practically possible and is recommended.
 However when several factors are involved, full factorial experiment requires a
large number of trials. For example, full factorial experiment for 10 factors each at two
levels requires 210
= 1024 trials. Normally it is not possible to conduct such large
experiments due to constraints of time and material resources.
 The solution, therefore, lies in reducing the number of trials by ignoring higher order
interactions and considering only selected first order interactions on the basis process
knowledge. The main effects and selected interactions can then be studied by conducting
fractional factorial experiment using standard OA (Orthogonal Array) designs.
ABOUT ORTHOGONAL ARRAY DESIGNS
Published orthogonal array designs are available for various experimental sizes
which are in powers of 2,3,4 etc. Depending on the number of factors, levels and
number of interactions to be estimated, a suitable design can be arrived at using
these tables.
Some standard Orthogonal tables are:
2 level series : L8 (27
), L16 (215
), L32 (231
)
3 level series : L9 (34
), L 27 (313
)….
Mixed series : L18 (21
x 37
),
L50 (21
x 5 11
) etc
Thus in L16 (215
), 16 represents the number of experimental trials, 2 the number of
levels at which each factor is examined and 15 the number of columns in the
design.
The allocation of factors and interactions to columns is done with the aid of Linear
Graphs.
EXAMPLESEXAMPLES
EXAMPLE 1:
FULL FACTORIAL EXPERIMENT
Surface finish in a machining operation is influenced by feed rate and depth
of cut. To optimise this process, a full factorial experiment is conducted with
three different feed rates and four different depths of cut. Observations of
surface finish in micro inch (response) is recorded in a
two way table. Analyse the data and find out:
i) Does feed rate have significant effect on surface finish?
ii) Does depth of cut have significant effect on surface finish?
iii) Is interaction between feed rate and depth of cut significant?
iv) What is the optimum combination of feed rate and depth of cut to get best
finish.
DATA TABLE
(Surface finish in μ inch)
Feed
Rate
(inch /min)
depth of cut (inch)
0.15 0.18 0.20 0.25
0.20
0.25
0.30
74,64,60
92,86,88
99,98,102
79,68,73
98,104,88
104,99,95
82,88,92
99,108,95
108,110,99
99,104,96
104,110,99
114,111,107
Source
of
Variation
Degrees
of
freedom
Sum of
Squares
Mean
Squares
“F”-ratio Critical F-ratio
(from statistical
tables)
Between
depths of
cut
Between
feed rates
(Depth of
cut x feed
rate)
Error
3
2
6
24
2125.11
3160.5
557.05
689.34
708.37
1580.25
92.84
28.72
24.66 **
(against error)
17.02 **
(against
interaction)
3.23 *
(against error)
F3
24 =4.72(1%)
F2
6=10.92(1%)
F6
24=3.67(1%)
= 2.51(5%)
Total 35 6532
ANOVA TABLE
* : Significant
** : Very significant
Conclusions
1) Effect of feed rate is very significant
2) Effect of depth of cut is very significant
3) Interaction between feed rate and depth of cut is
significant.
4) Optimum combination is: feed rate 0.2 inch /min and depth
of cut 0.15 inch
EXAMPLE 2:
DESIGNING EXPERIMENT USING ORTHOGONAL ARRAYS
No. of factors = 4 (A, B, C, D)
1st Order interactions = AxB, AxC, AxD, BxC, BxD, CxD
2nd Order interactions = AxBxC, BxCxD, CxDxA, DxAxB
3rd Order interaction = AxBxCxD
In practice, only few first order interactions are of interest. Rest of the
interactions can be neglected. In this case , it is given that only two interactions
AxC and CxD are to be considered.
O.A. TABLE FOR L 8 (27
)
Trial
No.
Column
1 2 3 4 5 6 7
1 1 1 1 1 1 1
1
2 1 1 1 2 2 2 2
2
Design of Experiments
ASSIGNING MAIN EFFECTS AND INTERACTIONS
TO COLUMNS
Trial
No.
Column
1
(C)
2
(A)
3
(AXC)
4
(B)
5
(e)
6
(CXD)
7
(D)
1 1 1 1 1 1 1 1
2 1 1 1 2 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
LAYOUT OF THE EXPERIMENT BASED UPON L8 (27
)
TRIAL
FACTORS RESPONSE
A B C D
1 1 1 1 1
2 1 2 1 2
3 2 1 1 2
4 2 2 1 1
5 1 1 2 2
6 1 2 2 1
7 2 1 2 1
8 2 2 2 2
Design of Experiments

Contenu connexe

Tendances

Response surface method
Response surface methodResponse surface method
Response surface methodIrfan Hussain
 
Factorial design \Optimization Techniques
Factorial design \Optimization TechniquesFactorial design \Optimization Techniques
Factorial design \Optimization TechniquesPriyanka Tambe
 
RESPONSE SURFACE METHODOLOGY.pptx
RESPONSE SURFACE METHODOLOGY.pptxRESPONSE SURFACE METHODOLOGY.pptx
RESPONSE SURFACE METHODOLOGY.pptxSreeLatha49
 
Optimization techniques
Optimization techniquesOptimization techniques
Optimization techniquesprashik shimpi
 
Design of Experiments (DOE)
Design of Experiments (DOE)Design of Experiments (DOE)
Design of Experiments (DOE)Imdad H. Mukeri
 
Design of Experiments (Pharma)
Design of Experiments (Pharma)Design of Experiments (Pharma)
Design of Experiments (Pharma)VaishnaviBhosale6
 
introduction to design of experiments
introduction to design of experimentsintroduction to design of experiments
introduction to design of experimentsKumar Virendra
 
Central Composite Design
Central Composite DesignCentral Composite Design
Central Composite DesignRuchir Shah
 
factorial design.pptx
factorial design.pptxfactorial design.pptx
factorial design.pptxSreeLatha98
 
Blocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorialsBlocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorialsHimanshu Sharma
 
Experimental design
Experimental designExperimental design
Experimental designDollySadrani
 
Design of experiments-Box behnken design
Design of experiments-Box behnken designDesign of experiments-Box behnken design
Design of experiments-Box behnken designGulamhushen Sipai
 
General Factor Factorial Design
General Factor Factorial DesignGeneral Factor Factorial Design
General Factor Factorial DesignNoraziah Ismail
 
design of experiments
design of experimentsdesign of experiments
design of experimentssigma-tau
 
presentation of factorial experiment 3*2
presentation of factorial experiment 3*2presentation of factorial experiment 3*2
presentation of factorial experiment 3*2D-kay Verma
 
Resource Surface Methology
Resource Surface MethologyResource Surface Methology
Resource Surface MethologyPRATHAMESH REGE
 
Confounding in Experimental Design
Confounding in Experimental DesignConfounding in Experimental Design
Confounding in Experimental DesignMdShakilSikder
 

Tendances (20)

Response surface method
Response surface methodResponse surface method
Response surface method
 
Factorial design \Optimization Techniques
Factorial design \Optimization TechniquesFactorial design \Optimization Techniques
Factorial design \Optimization Techniques
 
RESPONSE SURFACE METHODOLOGY.pptx
RESPONSE SURFACE METHODOLOGY.pptxRESPONSE SURFACE METHODOLOGY.pptx
RESPONSE SURFACE METHODOLOGY.pptx
 
Optimization techniques
Optimization techniquesOptimization techniques
Optimization techniques
 
Design of Experiments (DOE)
Design of Experiments (DOE)Design of Experiments (DOE)
Design of Experiments (DOE)
 
Design of Experiments (Pharma)
Design of Experiments (Pharma)Design of Experiments (Pharma)
Design of Experiments (Pharma)
 
introduction to design of experiments
introduction to design of experimentsintroduction to design of experiments
introduction to design of experiments
 
Central Composite Design
Central Composite DesignCentral Composite Design
Central Composite Design
 
Factorial Design.pptx
Factorial Design.pptxFactorial Design.pptx
Factorial Design.pptx
 
factorial design.pptx
factorial design.pptxfactorial design.pptx
factorial design.pptx
 
Blocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorialsBlocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorials
 
Experimental design
Experimental designExperimental design
Experimental design
 
2^3 factorial design in SPSS
2^3 factorial design in SPSS2^3 factorial design in SPSS
2^3 factorial design in SPSS
 
Design of experiments-Box behnken design
Design of experiments-Box behnken designDesign of experiments-Box behnken design
Design of experiments-Box behnken design
 
General Factor Factorial Design
General Factor Factorial DesignGeneral Factor Factorial Design
General Factor Factorial Design
 
design of experiments
design of experimentsdesign of experiments
design of experiments
 
Optimization techniques
Optimization techniquesOptimization techniques
Optimization techniques
 
presentation of factorial experiment 3*2
presentation of factorial experiment 3*2presentation of factorial experiment 3*2
presentation of factorial experiment 3*2
 
Resource Surface Methology
Resource Surface MethologyResource Surface Methology
Resource Surface Methology
 
Confounding in Experimental Design
Confounding in Experimental DesignConfounding in Experimental Design
Confounding in Experimental Design
 

Similaire à Design of Experiments

Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)
Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)
Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)Teck Nam Ang
 
Module 5 lecture_4_final
Module 5 lecture_4_finalModule 5 lecture_4_final
Module 5 lecture_4_finalAmol Wadghule
 
Experimental design
Experimental designExperimental design
Experimental designSandip Patel
 
Design of experiments
Design of experimentsDesign of experiments
Design of experiments9814857865
 
design of experiments.ppt
design of experiments.pptdesign of experiments.ppt
design of experiments.ppt9814857865
 
Chetan dhal-Optimization techniques in pharmaceutics, formulation and processing
Chetan dhal-Optimization techniques in pharmaceutics, formulation and processingChetan dhal-Optimization techniques in pharmaceutics, formulation and processing
Chetan dhal-Optimization techniques in pharmaceutics, formulation and processingChetan Dhal
 
Application Of Taguchi Method For Optimization Of Process.pdf
Application Of Taguchi Method For Optimization Of Process.pdfApplication Of Taguchi Method For Optimization Of Process.pdf
Application Of Taguchi Method For Optimization Of Process.pdfmetwallyabdallahabde
 
Optimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOL
Optimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOLOptimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOL
Optimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOLSiddanna Balapgol
 
Paper id 23201426
Paper id 23201426Paper id 23201426
Paper id 23201426IJRAT
 
Optimization of the Superfinishing Process Using Different Types of Stones
Optimization of the Superfinishing Process Using Different Types of StonesOptimization of the Superfinishing Process Using Different Types of Stones
Optimization of the Superfinishing Process Using Different Types of StonesIDES Editor
 
Design of Experiment ppt by Ganesh Asabe
Design of Experiment ppt by Ganesh AsabeDesign of Experiment ppt by Ganesh Asabe
Design of Experiment ppt by Ganesh AsabeGanesh355057
 
Mcv4Ua Practice Test Essay
Mcv4Ua Practice Test EssayMcv4Ua Practice Test Essay
Mcv4Ua Practice Test EssaySheena White
 
Laser drilling
Laser drillingLaser drilling
Laser drillingSpringer
 
Optimization of parameters affecting the performance of passive solar distill...
Optimization of parameters affecting the performance of passive solar distill...Optimization of parameters affecting the performance of passive solar distill...
Optimization of parameters affecting the performance of passive solar distill...IOSR Journals
 

Similaire à Design of Experiments (20)

Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)
Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)
Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)
 
RM_05_DOE.pdf
RM_05_DOE.pdfRM_05_DOE.pdf
RM_05_DOE.pdf
 
Optimization
OptimizationOptimization
Optimization
 
Module 5 lecture_4_final
Module 5 lecture_4_finalModule 5 lecture_4_final
Module 5 lecture_4_final
 
Experimental design
Experimental designExperimental design
Experimental design
 
Design of experiments
Design of experimentsDesign of experiments
Design of experiments
 
design of experiments.ppt
design of experiments.pptdesign of experiments.ppt
design of experiments.ppt
 
Chetan dhal-Optimization techniques in pharmaceutics, formulation and processing
Chetan dhal-Optimization techniques in pharmaceutics, formulation and processingChetan dhal-Optimization techniques in pharmaceutics, formulation and processing
Chetan dhal-Optimization techniques in pharmaceutics, formulation and processing
 
Application Of Taguchi Method For Optimization Of Process.pdf
Application Of Taguchi Method For Optimization Of Process.pdfApplication Of Taguchi Method For Optimization Of Process.pdf
Application Of Taguchi Method For Optimization Of Process.pdf
 
Optz.ppt
Optz.pptOptz.ppt
Optz.ppt
 
Optimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOL
Optimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOLOptimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOL
Optimizationinpharmaceuticsprocessing SIDDANNA M BALAPGOL
 
Paper id 23201426
Paper id 23201426Paper id 23201426
Paper id 23201426
 
Optimization of the Superfinishing Process Using Different Types of Stones
Optimization of the Superfinishing Process Using Different Types of StonesOptimization of the Superfinishing Process Using Different Types of Stones
Optimization of the Superfinishing Process Using Different Types of Stones
 
Design of Experiment ppt by Ganesh Asabe
Design of Experiment ppt by Ganesh AsabeDesign of Experiment ppt by Ganesh Asabe
Design of Experiment ppt by Ganesh Asabe
 
Mcv4Ua Practice Test Essay
Mcv4Ua Practice Test EssayMcv4Ua Practice Test Essay
Mcv4Ua Practice Test Essay
 
9. design of experiment
9. design of experiment9. design of experiment
9. design of experiment
 
Laser drilling
Laser drillingLaser drilling
Laser drilling
 
optimization.pdf
optimization.pdfoptimization.pdf
optimization.pdf
 
om
omom
om
 
Optimization of parameters affecting the performance of passive solar distill...
Optimization of parameters affecting the performance of passive solar distill...Optimization of parameters affecting the performance of passive solar distill...
Optimization of parameters affecting the performance of passive solar distill...
 

Plus de The Society of Statistical Quality Control Engineers, Bhopal (11)

LEAN
LEANLEAN
LEAN
 
5 S
5 S5 S
5 S
 
Acceptance Sampling
Acceptance SamplingAcceptance Sampling
Acceptance Sampling
 
Control Charts
Control ChartsControl Charts
Control Charts
 
KAIZEN
KAIZENKAIZEN
KAIZEN
 
Quality Management
Quality ManagementQuality Management
Quality Management
 
Statistical Process Control
Statistical Process ControlStatistical Process Control
Statistical Process Control
 
STATISTICAL QUALITY CONTROL
STATISTICAL QUALITY CONTROLSTATISTICAL QUALITY CONTROL
STATISTICAL QUALITY CONTROL
 
TOTAL QUALITY MANAGEMENT
TOTAL QUALITY  MANAGEMENTTOTAL QUALITY  MANAGEMENT
TOTAL QUALITY MANAGEMENT
 
Quality circle
Quality circleQuality circle
Quality circle
 
Six Sigma
Six SigmaSix Sigma
Six Sigma
 

Dernier

Project Brief & Information Architecture Report
Project Brief & Information Architecture ReportProject Brief & Information Architecture Report
Project Brief & Information Architecture Reportamberjiles31
 
Scrum Events & How to run them effectively
Scrum Events & How to run them effectivelyScrum Events & How to run them effectively
Scrum Events & How to run them effectivelyMarianna Nakou
 
Plano de marketing- inglês em formato ppt
Plano de marketing- inglês  em formato pptPlano de marketing- inglês  em formato ppt
Plano de marketing- inglês em formato pptElizangelaSoaresdaCo
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHelene Heckrotte
 
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessQ2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessAPCO
 
Anyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyAnyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyHanna Klim
 
MC Heights construction company in Jhang
MC Heights construction company in JhangMC Heights construction company in Jhang
MC Heights construction company in Jhangmcgroupjeya
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarNathanielSchmuck
 
Intellectual Property Licensing Examples
Intellectual Property Licensing ExamplesIntellectual Property Licensing Examples
Intellectual Property Licensing Examplesamberjiles31
 
Amazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the companyAmazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the companyfashionfound007
 
Trauma Training Service for First Responders
Trauma Training Service for First RespondersTrauma Training Service for First Responders
Trauma Training Service for First RespondersBPOQe
 
Fabric RFID Wristbands in Ireland for Events and Festivals
Fabric RFID Wristbands in Ireland for Events and FestivalsFabric RFID Wristbands in Ireland for Events and Festivals
Fabric RFID Wristbands in Ireland for Events and FestivalsWristbands Ireland
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursKaiNexus
 
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxChapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxesiyasmengesha
 
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...AustraliaChapterIIBA
 
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISINGUNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISINGlokeshwarmaha
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003believeminhh
 
MoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor PresentationMoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor Presentationbaron83
 
PDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfPDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfHajeJanKamps
 
Personal Brand Exploration Presentation Eric Bonilla
Personal Brand Exploration Presentation Eric BonillaPersonal Brand Exploration Presentation Eric Bonilla
Personal Brand Exploration Presentation Eric BonillaEricBonilla13
 

Dernier (20)

Project Brief & Information Architecture Report
Project Brief & Information Architecture ReportProject Brief & Information Architecture Report
Project Brief & Information Architecture Report
 
Scrum Events & How to run them effectively
Scrum Events & How to run them effectivelyScrum Events & How to run them effectively
Scrum Events & How to run them effectively
 
Plano de marketing- inglês em formato ppt
Plano de marketing- inglês  em formato pptPlano de marketing- inglês  em formato ppt
Plano de marketing- inglês em formato ppt
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
 
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessQ2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
 
Anyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyAnyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agency
 
MC Heights construction company in Jhang
MC Heights construction company in JhangMC Heights construction company in Jhang
MC Heights construction company in Jhang
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry Webinar
 
Intellectual Property Licensing Examples
Intellectual Property Licensing ExamplesIntellectual Property Licensing Examples
Intellectual Property Licensing Examples
 
Amazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the companyAmazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the company
 
Trauma Training Service for First Responders
Trauma Training Service for First RespondersTrauma Training Service for First Responders
Trauma Training Service for First Responders
 
Fabric RFID Wristbands in Ireland for Events and Festivals
Fabric RFID Wristbands in Ireland for Events and FestivalsFabric RFID Wristbands in Ireland for Events and Festivals
Fabric RFID Wristbands in Ireland for Events and Festivals
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, Ours
 
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxChapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
 
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
IIBA® Melbourne - Navigating Business Analysis - Excellence for Career Growth...
 
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISINGUNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
 
MoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor PresentationMoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor Presentation
 
PDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfPDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdf
 
Personal Brand Exploration Presentation Eric Bonilla
Personal Brand Exploration Presentation Eric BonillaPersonal Brand Exploration Presentation Eric Bonilla
Personal Brand Exploration Presentation Eric Bonilla
 

Design of Experiments

  • 1. DESIGN OF EXPERIMENTS (DOE) A presentation by THE SOCIETY OF STATISTICAL QUALITY CONTROL ENGINEERS BHOPAL
  • 2. What is DOE DOE is a process optimization technique that relies on planned experimentation and statistical analysis of results
  • 3. LIMITATIONS OF TRADITIONAL METHODS OF EXPERIMENTATION:  One factor studied at a time, requiring enormous time to complete the experiment.  Interactions i.e. effect of one factor on another, are ignored leading to erroneous results.  Complex processes involving a number of factors, levels, interactions can not be studied by traditional approach.
  • 4. DOE ADVANTAGES:  Optimizes process parameters with minimum number of trials, thus saving time and resources on experimentation.  Interactions (effect of one factor on another) also taken into consideration.  Results analysed using ANOVA technique for objective judgement.  Orthogonal Arrays (OA) technique used for finding efficient designs of experiments.
  • 5. DESIGN OF EXPERIMENTS: STEPS TO BE FOLLOWED 1 Define the objective: Example – “To optimize the process of annealing” 2 List out variable factors: Example – Temperature, time duration, nature of medium etc. 3 List out fixed factors: Example – room temperature, humidity etc. 4 Decide upon responses: Example – hardness, tensile strength etc.
  • 6. DESIGN OF EXPERIMENTS: STEPS TO BE FOLLOWED (Contd.) 5 Fix-up the levels of variable factors: Example: Level Temperature 1 200°C 2 300°C 3 400°C 6 Define the levels of fixed factors: Example: Room temperature 25±5°C 7 Identify the interactions which need to be studied
  • 7. DESIGN OF EXPERIMENTS: STEPS TO BE FOLLOWED (Contd.) 8 Design a suitable experiment – full factorial/ fractional factorial/OA 9 Conduct the experiment 10 Record data on response for each trial 11 Analyse the experimental data (responses) using ANOVA technique 12 Find out significant factors and insignificant factors 13 Find out significant interactions and insignificant interactions 14 Plot response curves to find out optimum levels of significant factors. 15 Report optimum levels of process parameters as final result
  • 8. FULL FACTORIAL EXPERIMENT Vs. FRACTIONAL FACTORIAL EXPERIMENT  To study the effect all factors and interactions, full factorial experiment needs to be conducted i.e. all possible combination of factors and levels have to be tried. With factors limited to two or three, full factorial experiment is practically possible and is recommended.  However when several factors are involved, full factorial experiment requires a large number of trials. For example, full factorial experiment for 10 factors each at two levels requires 210 = 1024 trials. Normally it is not possible to conduct such large experiments due to constraints of time and material resources.  The solution, therefore, lies in reducing the number of trials by ignoring higher order interactions and considering only selected first order interactions on the basis process knowledge. The main effects and selected interactions can then be studied by conducting fractional factorial experiment using standard OA (Orthogonal Array) designs.
  • 9. ABOUT ORTHOGONAL ARRAY DESIGNS Published orthogonal array designs are available for various experimental sizes which are in powers of 2,3,4 etc. Depending on the number of factors, levels and number of interactions to be estimated, a suitable design can be arrived at using these tables. Some standard Orthogonal tables are: 2 level series : L8 (27 ), L16 (215 ), L32 (231 ) 3 level series : L9 (34 ), L 27 (313 )…. Mixed series : L18 (21 x 37 ), L50 (21 x 5 11 ) etc Thus in L16 (215 ), 16 represents the number of experimental trials, 2 the number of levels at which each factor is examined and 15 the number of columns in the design. The allocation of factors and interactions to columns is done with the aid of Linear Graphs.
  • 11. EXAMPLE 1: FULL FACTORIAL EXPERIMENT Surface finish in a machining operation is influenced by feed rate and depth of cut. To optimise this process, a full factorial experiment is conducted with three different feed rates and four different depths of cut. Observations of surface finish in micro inch (response) is recorded in a two way table. Analyse the data and find out: i) Does feed rate have significant effect on surface finish? ii) Does depth of cut have significant effect on surface finish? iii) Is interaction between feed rate and depth of cut significant? iv) What is the optimum combination of feed rate and depth of cut to get best finish.
  • 12. DATA TABLE (Surface finish in μ inch) Feed Rate (inch /min) depth of cut (inch) 0.15 0.18 0.20 0.25 0.20 0.25 0.30 74,64,60 92,86,88 99,98,102 79,68,73 98,104,88 104,99,95 82,88,92 99,108,95 108,110,99 99,104,96 104,110,99 114,111,107
  • 13. Source of Variation Degrees of freedom Sum of Squares Mean Squares “F”-ratio Critical F-ratio (from statistical tables) Between depths of cut Between feed rates (Depth of cut x feed rate) Error 3 2 6 24 2125.11 3160.5 557.05 689.34 708.37 1580.25 92.84 28.72 24.66 ** (against error) 17.02 ** (against interaction) 3.23 * (against error) F3 24 =4.72(1%) F2 6=10.92(1%) F6 24=3.67(1%) = 2.51(5%) Total 35 6532 ANOVA TABLE * : Significant ** : Very significant
  • 14. Conclusions 1) Effect of feed rate is very significant 2) Effect of depth of cut is very significant 3) Interaction between feed rate and depth of cut is significant. 4) Optimum combination is: feed rate 0.2 inch /min and depth of cut 0.15 inch
  • 15. EXAMPLE 2: DESIGNING EXPERIMENT USING ORTHOGONAL ARRAYS No. of factors = 4 (A, B, C, D) 1st Order interactions = AxB, AxC, AxD, BxC, BxD, CxD 2nd Order interactions = AxBxC, BxCxD, CxDxA, DxAxB 3rd Order interaction = AxBxCxD In practice, only few first order interactions are of interest. Rest of the interactions can be neglected. In this case , it is given that only two interactions AxC and CxD are to be considered.
  • 16. O.A. TABLE FOR L 8 (27 ) Trial No. Column 1 2 3 4 5 6 7 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 2
  • 18. ASSIGNING MAIN EFFECTS AND INTERACTIONS TO COLUMNS Trial No. Column 1 (C) 2 (A) 3 (AXC) 4 (B) 5 (e) 6 (CXD) 7 (D) 1 1 1 1 1 1 1 1 2 1 1 1 2 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
  • 19. LAYOUT OF THE EXPERIMENT BASED UPON L8 (27 ) TRIAL FACTORS RESPONSE A B C D 1 1 1 1 1 2 1 2 1 2 3 2 1 1 2 4 2 2 1 1 5 1 1 2 2 6 1 2 2 1 7 2 1 2 1 8 2 2 2 2