This document discusses the analysis of covariates to account for variation from uncontrollable factors in experimental designs. It provides an example of using filament diameter as a covariate in an experiment investigating the effect of production lines on tensile strength. Accounting for diameter significantly increases the amount of variation explained. The document also examines using locator pin position as a covariate in an experiment on printed circuit board assembly.
Performance Management - What are the drivers of success?Rudy Parker
The two main drivers of success are personality and cognitive skills. This Project focuses on what are the drivers for success in the MBA program? GMAT Score, Undergraduate degree score, Undergraduate Major (what you studied), Age etc.
Performance Management - What are the drivers of success?Rudy Parker
The two main drivers of success are personality and cognitive skills. This Project focuses on what are the drivers for success in the MBA program? GMAT Score, Undergraduate degree score, Undergraduate Major (what you studied), Age etc.
Mémoire master II - La Conférence de Madrid (1934) : origines et fortune de ...Jean-Baptiste JAMIN
Adoptant comme référence la Conférence de Madrid organisée par l'Office International des Musées en 1934, ainsi que sur le manuel Muséographie – architecture et aménagement des musées d'art qui en découle – dont il s'agira de démontrer en quoi ils constituent des jalons –, cette étude s'intéresse plus largement à l'évolution de la muséographie au XXe siècle.
De l'analyse critique de Louis Réau sur l'organisation des musées aux leçons de Georges Henri Rivière, en passant par le discours d'Henri Focillon, l'œuvre de l'Office International des Musées, l'Exposition internationale de 1937 et les cours de Germain Bazin à l'École du Louvre (entre autres), ce mémoire s'attache donc, à défaut d'en retracer l'histoire, à présenter la muséographie à travers quelques moments clés.
Et si l'architecture muséale et les techniques de mise en valeur des collections constituent le principal du développement, l'aspect éminemment social et pédagogique du musée en demeure le corolaire permanent.
TOGETHER: TOpology GEneration THrough HEuRisticsSubin Mathew
Network Virtualization is a growing technological process that combines the hardware and software elements in the physical networks and brings it together on a software level. The aim of this project is to develop the process of deploying virtual networks easily. The project involves a software developed by us called “TOGETHER: TOpology GEneration THrough HEuRistics"written in Perl in its simplest form without dependencies so that it could be deployed on any environment. TOGETHER is an isomorphic graph modelling solution used to allow users to make use of topology generators and software like AutoNetkit to make topologies that work on virtual systems.TOGETHER is designed to work in Juniper Networks Virtual Private Cloud architecture and has possibilities for supporting much more. TOGETHER also manages how multiple topologies are interconnected and aims to help researchers work with network virtualization.
Poka-Yoke is concept which stops you from doing mistakes.It is reintroduced by the top consultant of Toyota Production System,he developed it for his workers,so that they can work easily without forgetting any steps to prepare the product.
Mémoire master I - Vesunna, étude du musée de site : conception, fonctionne...Jean-Baptiste JAMIN
Ce mémoire a pour sujet le site-musée gallo-romain de Périgueux, Vesunna. Comme l'indique le titre, cette étude s'attachera à en aborder l'historique de création, le bilan des modes de fonctionnement et les orientations envisageables.
En effet, choisi à l'origine uniquement pour le caractère exceptionnel de sa mise en valeur, ce musée s'est révélé comme étant des plus intéressants pour aborder de nombreux aspects relatifs à la vie d'un musée, qu'il s'agisse des domaines politiques, scientifiques, administratifs et sociaux.
Ainsi ce mémoire concentre des thématiques telles que la découverte et la mise en valeur progressive d'un site archéologique, la réalisation d'un projet architectural exceptionnel, le passage d'une délégation de service public à une régie municipale, la diversité des opérations de médiation qui peuvent être menées dans une structure muséale ou encore la relation d'un musée avec son territoire.
Ever given a thought on how machine intelligent the softwares are getting nowadays? Lets imagine a situation when you surf a video on youtube and you are not given any recommendations for similar videos, Or a situation when none of the irritating mails we get automatically go to our spam folder? Life would not be as easy as it currently is.
Machine learning is getting in trend and so we thought about Integrating Apache Mahout with AEM to simply make our AEM applications smarter and interesting!
Mahout helps us in 3 different ways:
1. Recommendations
2. Classification
3. Clustering
We will focus on a typical use case of developing E-commerce applications in AEM and providing product recommendations on the basis of user search history.
Mémoire master II - La Conférence de Madrid (1934) : origines et fortune de ...Jean-Baptiste JAMIN
Adoptant comme référence la Conférence de Madrid organisée par l'Office International des Musées en 1934, ainsi que sur le manuel Muséographie – architecture et aménagement des musées d'art qui en découle – dont il s'agira de démontrer en quoi ils constituent des jalons –, cette étude s'intéresse plus largement à l'évolution de la muséographie au XXe siècle.
De l'analyse critique de Louis Réau sur l'organisation des musées aux leçons de Georges Henri Rivière, en passant par le discours d'Henri Focillon, l'œuvre de l'Office International des Musées, l'Exposition internationale de 1937 et les cours de Germain Bazin à l'École du Louvre (entre autres), ce mémoire s'attache donc, à défaut d'en retracer l'histoire, à présenter la muséographie à travers quelques moments clés.
Et si l'architecture muséale et les techniques de mise en valeur des collections constituent le principal du développement, l'aspect éminemment social et pédagogique du musée en demeure le corolaire permanent.
TOGETHER: TOpology GEneration THrough HEuRisticsSubin Mathew
Network Virtualization is a growing technological process that combines the hardware and software elements in the physical networks and brings it together on a software level. The aim of this project is to develop the process of deploying virtual networks easily. The project involves a software developed by us called “TOGETHER: TOpology GEneration THrough HEuRistics"written in Perl in its simplest form without dependencies so that it could be deployed on any environment. TOGETHER is an isomorphic graph modelling solution used to allow users to make use of topology generators and software like AutoNetkit to make topologies that work on virtual systems.TOGETHER is designed to work in Juniper Networks Virtual Private Cloud architecture and has possibilities for supporting much more. TOGETHER also manages how multiple topologies are interconnected and aims to help researchers work with network virtualization.
Poka-Yoke is concept which stops you from doing mistakes.It is reintroduced by the top consultant of Toyota Production System,he developed it for his workers,so that they can work easily without forgetting any steps to prepare the product.
Mémoire master I - Vesunna, étude du musée de site : conception, fonctionne...Jean-Baptiste JAMIN
Ce mémoire a pour sujet le site-musée gallo-romain de Périgueux, Vesunna. Comme l'indique le titre, cette étude s'attachera à en aborder l'historique de création, le bilan des modes de fonctionnement et les orientations envisageables.
En effet, choisi à l'origine uniquement pour le caractère exceptionnel de sa mise en valeur, ce musée s'est révélé comme étant des plus intéressants pour aborder de nombreux aspects relatifs à la vie d'un musée, qu'il s'agisse des domaines politiques, scientifiques, administratifs et sociaux.
Ainsi ce mémoire concentre des thématiques telles que la découverte et la mise en valeur progressive d'un site archéologique, la réalisation d'un projet architectural exceptionnel, le passage d'une délégation de service public à une régie municipale, la diversité des opérations de médiation qui peuvent être menées dans une structure muséale ou encore la relation d'un musée avec son territoire.
Ever given a thought on how machine intelligent the softwares are getting nowadays? Lets imagine a situation when you surf a video on youtube and you are not given any recommendations for similar videos, Or a situation when none of the irritating mails we get automatically go to our spam folder? Life would not be as easy as it currently is.
Machine learning is getting in trend and so we thought about Integrating Apache Mahout with AEM to simply make our AEM applications smarter and interesting!
Mahout helps us in 3 different ways:
1. Recommendations
2. Classification
3. Clustering
We will focus on a typical use case of developing E-commerce applications in AEM and providing product recommendations on the basis of user search history.
A Statistical Approach to Optimize Parameters for Electrodeposition of Indium...Arkansas State University
A Statistical Approach to Optimize Parameters for Electrodeposition of Indium (III) Sulfide Films, Potential Low-Hazard Buffer Layers for Photovoltaic Applications
Role of Simulation in Deep Drawn Cylindrical PartIJSRD
Simulation is widely used in forming industry due to its speed and lower cost and it has been proven to be effective in prediction of formability and spring back behavior. The purpose of finite element simulation in the sheet metal forming process is to minimize the time and cost in the design phase by predicting key outcomes such as the final shape of the part, the possibility of various defects and the flow of material. Such simulation is most useful and efficient when it is performed in the early stage of design by designers, rather than by analysis specialists after the detailed design is complete. The accuracy of such simulation depends on knowledge of material properties, boundary conditions and processing parameters. In the industry today, numerical sheet metal forming simulation is very important tool for reducing load time and improving part quality. In this paper finite element model for the deep-drawing of cylindrical cups is constructed and the simulation results are obtained by using different simulation parameters, i.e. punch velocity, coefficient of friction and blank holder force of the FE mesh-elements and these results are compared with experimental work.
Fatigue life predictions analysis should be performed according to standards in order to avoid uncertainties regarding assumptions for loads and component capacity.
Design and Analysis of Flange CouplingIJERA Editor
The approach utilizes standard design equations of these couplings and links them together in computer software to determine the design parameters of the couplings. In general, most flange coupling is available in transformation system and automobile industries. A flange coupling usually applies to a coupling having two cast iron flanges. To achieve a require goal, a design of bolted unprotected flange coupling is modeled in to a cad package named Solid works. Furthered the finite element analysis module is created in ANSYS Workbench by using ANSYS Static Structural module which has a predefined process to obtain optimum results.
Application of Design of Experiments (DOE) using Dr.Taguchi -Orthogonal Array...Karthikeyan Kannappan
The Taguchi method involves reducing the variation in a process through robust design of experiments. The experimental design proposed by Taguchi involves using orthogonal arrays to organize the parameters affecting the process and the levels at which they should be varies. Instead of having to test all possible combinations like the factorial design, the Taguchi method tests pairs of combinations. The Taguchi arrays can be derived or looked up. Small arrays can be drawn out manually; large arrays can be derived from deterministic algorithms. Generally, arrays can be found online. The arrays are selected by the number of parameters (variables) and the number of levels (states).
In this paper, the specific steps involved in the application of the Taguchi method will be described with example.
Comparative Study on Anchorage in Reinforced Concrete Using Codes of Practice...IJERA Editor
This paper (Part II) reports a comparative study for BS8110 and EC2 of practice and those expressions by Batayneh and Neilsen on tests from literature. These have been treated under straight bar anchorages with transverse pressure. The aim of this study is to evaluate the reliability of the existing equations for bond strength of straight bars by applying to the available tests in the literature .The most important parameters were examined in these tests are concrete strength, anchorage length, concrete covers, bar diameter and transverse pressure. 264 tests from the literature have been chosen, which are all for straight bars with transverse pressure. The specimens are pull-out specimens with small concrete covers, beams ends and slabs. For both comparative studies in Part I and Part II, the conclusions and recommendations are presented here together.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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Javier Garcia - Verdugo Sanchez - Six Sigma Training - W4 Analysis of Covariates
1. Page 1/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
2520151050
10
5
0
Introduction into the
Analysis of Covariates
Advanced DOE Tool
for Black Belts Week 4
Page 2/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
The analysis of process variation is often determined by effects
which are hardly to detect with classical designs. These factors are
difficult to control or to manipulate. We call them noise factors.
The following possibilities are already discussed:
• Blocking
Mostly attributive factors can be included in the design. (e. g.
supplier; A vs. B; shift: 1 vs. 2)
•Randomization of experimental runs
Here we try to avoid a miss interpretation from noise effects showing
up over time.
Now we will to discuss how to include continuous measurable but
uncontrollable factors into the design.
Example: Measure material characteristics incoming inspection.
Factors like temperature and humidity cannot be manipulated. But it
is easy to measure these factors and also to evaluate their effects.
About this Module
2. Page 3/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
4321
70
65
60
55
Factor
Response The “classical” ANOVA
2520151050
10
5
0
Covariate
Response
Effects of Covariates
Slope = b1
Graphical Display
Page 4/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Y = bo + b1x
Null Hypotheses Ho : b1 is equal or close to 0
Alternative Hypotheses Ha : b1 is unequal 0 or larger than
determined by the probability of error
The Mathematical Model
The procedure to receive information about non manipulated variables
is to measure and to include them as a factor in the analysis. This is
called the analysis of covariance (ANCOVA).
Covariates can be included as factors in fractional and full factorial
experiments.
For each covariate we need one degree of freedom to calculate the
effect. The degree of freedom is taken from the unexplained Variation
(error). In the case that the covariate has no significant effect we should
remove it from the analysis.
Several covariates can be included in the analysis.
3. Page 5/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
An engineer likes to investigate the influence from the production line to
the tensile strength of the produced fiber filaments. He knows that the
tensile strength is strong effect by the filament diameter. Therefore he
measured the filament diameter and include the diameter as a covariate
into the experiment.
Please determine the effect of the lines with and without the covariate.
What is your conclusion?
Example: Tensile Strength
File: mo57417.mtw
Stat
>ANOVA
>General Linear Model…
Stat
>ANOVA
>General Linear Model…
Page 6/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
General Linear Model: Tensile strength versus Line
Factor Type Levels Values
Line fixed 3 1; 2; 3
Analysis of Variance for Tensile strength, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
Line 2 140,40 140,40 70,20 4,09 0,044
Error 12 206,00 206,00 17,17
Total 14 346,40
S = 4,14327 R-Sq = 40,53% R-Sq(adj) = 30,62%
General Linear Model: Tensile strength versus Line
Factor Type Levels Values
Line fixed 3 1; 2; 3
Analysis of Variance for Tensile strength, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
Diameter 1 303,35 175,24 175,24 62,68 0,000
Line 2 12,30 12,30 6,15 2,20 0,157
Error 11 30,76 30,76 2,80
Total 14 346,40
S = 1,67214 R-Sq = 91,12% R-Sq(adj) = 88,70%
Example: Tensile Strength
Without covariate
With covariate
Attention!
4. Page 7/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
A more complex example of PCB manufacturing
A device of an automatic manufacturing line places components on a
PCB. The position of the components is controlled by a locator pin.
This pin is included by the supplier into the PCB in accordance to our
requirements.
Considerable variation in the positioning (x or y) has been detected in
the past time.
Two factors (A and B) of the positioning device are known, as easy to
manipulated. We have decided to perform a a small experiment with
two factors. The target is to redefine the optimum device settings to
improve the placement of the components.
Example: Printed Circuit Board Assembly
Page 8/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Our design is completely randomized and
includes 4 replications
The factors A & B of the devise have been
manipulated
The result is the position of the mounted
component.
The positions of the locator pin (covariate)
have been documented for every trial.
Assignment: Calculate the effect of the
factors A & B with and without the covariate
(Can be done under GLM and DOE)
Comment the results, is there a significant
effect of the factors or there are other
sources for the observed variation (locator
pin, noise)?
A B covar response
-1 -1 192,278 312,928
-1 -1 197,866 366,014
-1 -1 195,834 347,726
-1 -1 195,326 327,66
-1 1 197,612 327,66
-1 1 199,39 361,442
-1 1 194,056 311,912
-1 1 196,088 317,754
1 -1 197,612 313,69
1 -1 195,58 295,148
1 -1 198,882 325,12
1 -1 197,104 297,434
1 1 193,548 330,2
1 1 191,77 328,676
1 1 194,056 352,552
1 1 195,58 363,982
File:
ANCOVA.mtw
Example: Printed Circuit Board Assembly
5. Page 9/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
The evaluation without covariate
Fractional Factorial Fit
Estimated Effects and Coefficients for response
Term Effect Coef StDev Coef T P
Constant 329.994 4.886 67.53 0.000
A -8.287 -4.143 4.886 -0.85 0.413
B 13.557 6.779 4.886 1.39 0.191
A*B 22.447 11.224 4.886 2.30 0.040
Analysis of Variance for response
Source DF Seq SS Adj SS Adj MS F P
Main Effects 2 1009.88 1009.88 504.9 1.32 0.303
2-Way Interactions 1 2015.52 2015.52 2015.5 5.28 0.040
Residual Error 12 4584.17 4584.17 382.0
Pure Error 12 4584.17 4584.17 382.0
Total 15 7609.56
Stat
>DOE
>Factorial
>Analyze Factorial Design…
Stat
>DOE
>Factorial
>Analyze Factorial Design…
Attention!
Example: Printed Circuit Board Assembly
R-Sq = 39,76%
Page 10/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Example: Printed Circuit Board Assembly
B
Mean
1-1
345
340
335
330
325
320
315
310
A
-1
1
Interaction Plot (data means) for response
6. Page 11/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Interval plots for the
evaluations of the co
variable vs. factor level
over the distribution of the
covariate.
Example: Printed Circuit Board Assembly
Stat
>ANOVA
>Interval Plot…
>One Y with groups
Stat
>ANOVA
>Interval Plot…
>One Y with groups
response
A
B
1-1
1-11-1
380
360
340
320
300
280
Interval Plot of response vs A; B
95% CI for the Mean
Page 12/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
General Linear Model
Factor Levels Values
A 2 -1 1
B 2 -1 1
Analysis of Variance for response
Source DF Seq SS Adj SS Adj MS F P
covar 1 305.9 3892.2 3892.2 61.88 0.000
A 1 210.5 40.7 40.7 0.65 0.438
B 1 1015.2 1987.5 1987.5 31.60 0.000
A*B 1 5386.0 5386.0 5386.0 85.62 0.000
Error 11 691.9 691.9 62.9
Total 15 7609.6
Term Coef StDev T P
Constant -1503.1 233.0 -6.45 0.000
covar 9.363 1.190 7.87 0.000
Stat
>ANOVA
>General Linear Model…
Stat
>ANOVA
>General Linear Model…
Example: PCB, Evaluation with Covariate
R-Qd = 90,91%
7. Page 13/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Fractional Factorial Fit (Analyze Custom Design)
Estimated Effects and Coefficients for response
Term Effect Coef StDev Coef T P
Constant -1503 233.039 -6.45 0.000
covar 9 1.190 7.87 0.000
A -3 -2 2.009 -0.80 0.438
B 23 12 2.079 5.62 0.000
A*B 46 23 2.482 9.25 0.000
Analysis of Variance for response
Source DF Seq SS Adj SS Adj MS F P
Covariates 1 305.9 3892.2 3892.23 61.88 0.000
Main Effects 2 1225.7 2060.3 1030.14 16.38 0.001
2-Way Interactions 1 5386.0 5386.0 5386.03 85.62 0.000
Residual Error 11 691.9 691.9 62.90
Total 15 7609.6
Stat
>DOE … Factorial
>Analyze Factorial Design…
Stat
>DOE … Factorial
>Analyze Factorial Design…
The portion of the explained variation has been significantly increased
due to the model with the covariate. The question, how can that
variable be controlled?
Example: PCB, Evaluation with Covariate
R-Qd = 90,91%
Page 14/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Interpretation of the Results
• 16 runs has been performed. Due to the inclusion of the covariate the error
term has 11 degrees of freedom instead of 12.
• The portion of the non explained variation has been reduced by the
covariate from 4584 to 692.
• Only if the variation of the locator pins can be reduced we have the
possibility to control the mounting process with the factors A and B.
• The experiment with 16 runs shows us clearly how to improve the mounting
process.
• For the discussion with the supplier and/or the designer we may have
discovered important facts.
• If the evaluations don’t include the major sources of the variation we can
get misleading results. This could cause high cost.
8. Page 15/1503 BB W4 Covariates 07, D. Szemkus/H. Winkler
Summary
The evaluation of covariates offers us an
additional possibility to describe models for
special applications.
These adapted models increases the certainty of
our conclusions.
Here again 3 important hints for your
experiments:
• Maximize randomization of your experiments
• Include variables as a block factor
• Use this technique to evaluate the covariates