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

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 http://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics Introduction

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

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

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

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

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

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

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

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

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 0-13-187711-9 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

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

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

2nd Section Prof. Elizabeth Smela Tu, Th......9:30am - 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

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

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

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

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

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

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

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

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

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

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

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

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