This chapter presents the assumptions, principles, and techniques necessary to gain
insight into data via EDA–exploratory data analysis.
1. EDA Introduction
What is EDA?
EDA vs Classical & Bayesian
EDA vs Summary
EDA Goals
The Role of Graphics
An EDA/Graphics Example
General Problem Categories
2. EDA Assumptions
Underlying Assumptions .
Importance Techniques for Testing Assumptions
Interpretation of 4-Plot .
Consequences
3. EDA Techniques
Introduction
Analysis Questions
Graphical Techniques: Alphabetical
Graphical Techniques: By Problem
Category
Quantitative Techniques
Probability Distributions
4. EDA Case Studies
Introduction
By Problem Category
Detailed Chapter Table of Contents
References
Dataplot Commands for EDA Techniques
II.Measurement Process Characterization
1. Characterization
Issues
Check standards
2. Control Issues
Bias and long-term variability
Short-term variability
3. Calibration
Issues
Artifacts
Designs 3.
Catalog of designs
Artifact control
Instruments
Instrument control
4. Gauge R & R studies
Issues
Design
Data collection
Variability
Bias
Uncertainty
5. Uncertainty analysis
Issues
Approach .
Type A evaluations
Type B evaluations
Propagation of error
Error budget
Expanded uncertainties
Uncorrected bias
6. Case Studies
Gauge study
Check standard
Type A uncertainty
Type B uncertainty
III.Production Process Characterization
The goal of this chapter is to learn how to plan and conduct a Production Process
Characterization Study (PPC) on manufacturing processes. We will learn how to model
manufacturing processes and use these models to design a data collection scheme and to
guide data analysis activities. We will look in detail at how to analyze the data collected
in characterization studies and how to interpret and report the results. The accompanying
Case Studies provide detailed examples of several process characterization studies.
1. Introduction
Definition
Uses Terminology/Concepts
PPC Steps
2. Assumptions
General Assumptions
Specific PPC Models
3. Data Collection
Set Goals
Model the Process
Define Sampling Plan
4. Analysis
First Steps
Exploring Relationships
Model Building
Variance Components
Process Stability
Process Capability
Checking Assumptions
5. Case Studies
Furnace Case Study
Machine Case Study
IV.Process Modeling
The goal for this chapter is to present the background and specific analysis techniques
needed to construct a statistical model that describes a particular scientific or
engineering process. The types of models discussed in this chapter are limited to those
based on an explicit mathematical function. These types of models can be used for
prediction of process outputs, for calibration, or for process optimization.
1. Introduction
Definition
Terminology
Uses
Methods
2. Assumptions
Assumptions
3. Design
Definition
Importance
Design Principles
Optimal Designs
Assessment
4. Analysis
Modeling Steps
Model Selection
Model Fitting
Model Validation
Model Improvement
5. Interpretation & Use
Prediction
Calibration
Optimization
6. Case Studies
Load Cell Output
Alaska Pipeline
Ultrasonic Reference Block
Thermal Expansion of Copper
V.Process Improvement
1. Introduction
Definition of experimental design
Uses
Steps
2. Assumptions
Measurement system capable
Process stable
Simple model
Residuals well-behaved
3. Choosing an Experimental Design
Set objectives
Select process variables and levels
Select experimental design
Completely randomized designs
Randomized block designs
Full factorial designs
Fractional factorial designs
Plackett-Burman designs
Response surface designs
Adding center point runs
Improving fractional design resolution
Three-level full factorial designs
Three-level, mixed-level and fractional factorial designs
4. Analysis of DOE Data
DOE analysis steps
Plotting DOE data
Modeling DOE data
Testing and revising DOE models
Interpreting DOE results
Confirming DOE results
DOE examples
Full factorial example
Fractional factorial example
Response surface example
5. Advanced Topics
When classical designs don’t work
Computer-aided designs
D-Optimal designs
Repairing a design
Optimizing a process
Single response case
Multiple response case
Mixture designs
Mixture screening designs
Simplex-lattice designs
Simplex-centroid designs
Constrained mixture designs
Treating mixture and process
variables together
Nested variation
Taguchi designs
John’s 3/4 fractional factorial designs
Small composite designs
An EDA approach to experiment design
Case Studies
Eddy current probe sensitivity study
Sonoluminescent light intensity
study
References
VI.Process or Product Monitoring and Control
This chapter presents techniques for monitoring and controlling processes and signaling
when corrective actions are necessary.
1. Introduction
History
Process Control Techniques
Process Control
“Out of Control”
“In Control” but Unacceptable
Process Capability
2. Test Product for Acceptability
Acceptance Sampling
Kinds of Sampling Plans
Choosing a Single Sampling Plan
Double Sampling Plans
Multiple Sampling Plans
Sequential Sampling Plans
Skip Lot Sampling Plans
3. Univariate and Multivariate Control
Charts
Control Charts
Variables Control Charts
Attributes Control Charts
Multivariate Control charts
4. Time Series Models
Definitions, Applications and Techniques
Moving Average or Smoothing
Techniques
Exponential Smoothing
Univariate Time Series Models
Multivariate Time Series Models
5. Tutorials
What do we mean by “Normal” data?
What to do when data are non-normal
Elements of Matrix Algebra
Elements of Multivariate Analysis
Principal Components
6. Case Study
Lithography Process Data
Box-Jenkins Modeling Example
VII.Product and Process Comparisons
This chapter presents the background and specific analysis techniques needed to
compare the performance of one or more processes against known standards or one
another.
1. Introduction
Scope
Assumptions
Statistical Tests
Confidence Intervals
Equivalence of Tests and Intervals
Outliers
Trends
2. Comparisons: One Process
Comparing to a Distribution
Comparing to a Nominal Mean
Comparing to Nominal Variability
Fraction Defective
Defect Density
Location of Population
Values
3. Comparisons: Two Processes
Means: Normal Data
Variability: Normal Data
Fraction Defective
Failure Rates
Means: General Case
4. Comparisons: Three +
Processes
Comparing Populations
Comparing Variances
Comparing Means
Variance Components
Comparing Categorical
Datasets
Comparing Fraction
Defectives
Multiple Comparisons
VIII. Assessing Product Reliability
This chapter describes the terms, models and techniques used to evaluate and predict
product reliability.
1. Introduction
Why important?
Basic terms and models
Common difficulties
Modeling “physical acceleration”
Common acceleration models
Basic non-repairable lifetime distributions
Basic models for repairable systems
Evaluate reliability “bottom-up”
Modeling reliability growth
Bayesian methodology
2. Assumptions/Prerequisites
Choosing appropriate life distribution
Plotting reliability data
Testing assumptions .
Choosing a physical acceleration model
Models and assumptions for Bayesian methods
Reliability Data Collection
Planning reliability assessment tests
4. Reliability Data Analysis
Estimating parameters from censored data
Fitting an acceleration model
Projecting reliability at use conditions
Comparing reliability between two or more populations
Fitting system repair rate models
Estimating reliability using a Bayesian gamma prior
Assessing Product Reliability
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