1. Statistical Methods for Product and Processes Development
ENME 392, Summer 2012
Statistical Methods for Product and Processes Development
Instructor: Dr. David Bigio
Introduction

2. There are three kinds of lies: lies, damned lies, and statistics.*
You’ve heard it said
There are three kinds of lies:
lies, damned lies, and statistics.*
Why is statistics a required course?
What do engineers need statistics for?
The phrase popularized by Mark Twain; for more information see
Introduction

3. How many of you think that this course will be
boring confusing frustrating useless?
I hope to show you that it’s not, that it’s
useful interesting powerful profitable!
Introduction

4. Why take ENME392?
Engineers must evaluate new designs, procedures, and materials. Statistics provide a scientific basis for choice.
Applications of Statistics
Process Control -- identify problems before too much damage is done
Assess Quality -- are components good enough to use, or reject them?
Model and Find Relationships – relate e.g. film thickness with deposition temperature.
Assess Reliability – determine product/system reliability over lifespan.
Estimate Costs – estimate bid for project so that job will make profit?
Experimental Design – do as few experiments as possible if a large number of variables must be investigated
Introduction

5. Meaning and Role of Statistics
Decision-making under uncertainty
“Statistics is the analysis of numerical data for the purpose of reaching a decision or communicating information in the face of uncertainty”
Introduction

6. The Big Picture Data Set Question Descriptive Statistics Set & Model
Tool
Description
Set
Data Set
Model
Results
Question
Introduction

7. Main Topics Probability Distributions Samples of Distributions
Discrete
Continuous
Samples of Distributions
Process Control
Hypothesis Testing
Chi Squared
Analysis of Variance
Regression Analysis
Design of Experiment
Introduction

8. If I tell you that in a biomedical study of a new drug,
85% of patients benefited from the new drug
75% benefited from the old drug
how confident do you feel that the new drug is better, if
the study included 20 people?
the study included 2000 people?
the study included 200,000 people?
How can we quantify that confidence?
Introduction

9. Relationship of Population and Sample
Observation -- a single data unit
Population
“A Statistical population is the collection of all possible observations of a specified characteristic of interest” Lapin p. 6
Sample
“A sample is a collection of observations representing only a portion of the population.” Lapin p. 7
Introduction

10. What is the probability of getting a head in a coin toss?
Does that mean that if all of you toss 10 coins, each of you will get 5 heads?
How do we quantify the probability that you will get 5? or 4? or 0?
What can we predict in advance?
For now, we don’t have the math, so let’s do an experiment.
coin toss.xls
We will come back to these results in the next few chapters.
Introduction

11. Now, for Some Ground Rules
No Cheating
Read the Honor Code.
Book
Probability & Statistics for Engineers and Scientists, 8th Ed.
Walpole, Meyers, Myers, & Ye
Pearson Prentice Hall, 2007
ISBN
Bring to class
Syllabus
Posted on Blackboard
Schedule
Posted on Blackboard, subject to change!
Homework (Weekly)
Posted on Blackboard
Calculator
Bring to class, and to exams.
Introduction

12. Assessment Exams (68%) 2 midterms (22% each), 1 final (24%)
Homework (10%)
every week (1% each)
graded for effort, not answers
Quizzes (22%)
5 scheduled. (drop 1)
On the reading, as in Dr. Smela class
Project (22%) Optional
Assignments spread throughout the semester
Introduction

13. Prof. David Bigio Where to Find Me 2184 Martin Hall dbigio@umd.edu
x5-5258
Office Hours
Tuesday after class: 12:30-1:30pm
Thursday afternoon: 2 pm – 3 pm
or by appointment
Introduction

14. 2nd Section Prof. Elizabeth Smela
Tu, Th :30am - 10:45AM (GLM 0110)
KEB = bldg 225 = Kim Engineering Buildingß
If you think you might really struggle in this class (and some of you will), attend those lectures, too.
Introduction

15. Introduction and basic concepts.
Chapter 1
Introduction and basic concepts.
Introduction

16. From an engineering perspective.
Chapter 1
From an engineering perspective.
Products have variation.
batch 1
batch 2
Too much is not good.
 How do we achieve a desired level of quality?
1. Measure every widget at every step of the process, reject the bad ones.
 Usually impractical.
2. Take samples from the total population of widgets and use inferential statistics to draw conclusions about the rest.
This course will deal with:
how to take those samples
how many to take
what the samples tell you about those you didn’t measure.
Introduction

17. From a descriptive perspective.
Chapter 1
From a descriptive perspective.
Products have variation.
batch 1
batch 2
How, and by how much, do those in batch 1 differ from those in batch 2?
1. Provide a table with all the data on each.
 Doesn’t see the forest for the trees – hard to grasp.
2. Quantify the key points.
This course will deal with:
means, medians, standard deviations
histograms and other plots
Introduction

18. Everybody’s favorite subject: Probability.
Chapter 1
Everybody’s favorite subject: Probability.
Without understanding probability, statistics can only be learned as empty plug-and-chug formulas. You will not understand what the numbers you get actually mean.
probability
population
sample
statistical inference
Figure adapted from Walpole.
Introduction

19. Topics Addition Rule Multiplication Rule Compound Events
Union
Multiplication Rule
Intersection
Compound Events
Conditional Probability
Probability Trees
Permutations
Combinations
Reliability
Introduction

20. Chapter 1 Random Sampling
Why is it important that samples be chosen randomly?
If I chose students from the front row of this classroom, would that represent a random sample, or would it be biased?
Introduction

21. Chapter 1 Non-Homogeneity
If I’m trying to determine the heights of 6-year-olds, what happens if I measure children from all over the world?
Introduction

22. Chapter 1 Mean vs. Median How is a mean, or average, defined?
How is the median defined?
The data are arranged in order of increasing magnitude, x1, x2, ... xn
n odd
n even
How do they differ?
EX 1.7, 2.2, 3.9,3.11, 14.7
Introduction

23. Measures of Variability
Chapter 1
Measures of Variability
How is the standard deviation defined?
Why the square root?
Why n – 1?
The variance is s2.
Introduction

24. Discrete vs. Continuous Distributions
Chapter 1
Discrete vs. Continuous Distributions
Give an example of a discrete distribution.
Give an example of a continuous distribution.
What do we mean by a “skewed” distribution?
Introduction

25. Chapter 1
Interactions
What do we mean when we say there is an interaction between variables? Examples?
Introduction

26. Statistical Displays Frequency Distribution Histogram Stem & Leaf
Box and Whisker Plot
Relative Frequency Distribution
Cumulative Frequency Distribution
Introduction