435 Engineering Statistics

For Whom Intended  An understanding of Statistics is required in the implementation of uncertainty calculations in Metrology such as: statistical and probability concepts in measurements, confidence levels and control charts etc.

Brief Course Description  This TTi course covers all the usual topics in reliability and statistics and explains how the theory is applied in engineering.

Chi-squared distributionIn the study of basic statistics, students encounter equations which are not "user friendly." The volume of statistical formulas and the "number-crunching" has made the true learning and application of statistics difficult for most people. In this course the actual evaluation of statistical formulas is done using programmable calculators such as the TI-82 and TI-83, which simplify the process and save hours of tedious work. When the course is conducted at TTi's headquarters, class exercises in the TTi computer lab teach the use of Microsoft Excel for statistical work. This enables the student to devote more time to the overall understanding of basic statistics and applying the concepts learned.

Diploma Programs  This course may be used as an optional course for any TTi specialist diploma program.

Related Courses  A one-day version of this course is included in the four-day course 132-4, Measurement Uncertainty.

Prerequisites  There are no definite prerequisites for this course. However, prior completion of TTi Distance Learning course 103-2 "Applied Mathematics" would be helpful.

Text  Each student will receive access to the on-line electronic course workbook, including most of the slides used in the course presentation. An initial subscription is included in the price of the course and renewals are available for an additional fee.

Course Hours, Certificate and CEUs  Open courses meet seven hours per day. Upcoming presentation dates can be found on our current open course schedule. Class hours/days for on-site courses can vary from 14-35 hours over 2-5 days as requested by our clients. Upon successful course completion, each participant receives a certificate of completion and one Continuing Education Unit (CEU) for every ten class hours.

Click for a printable course outline (pdf).


Course Outline

Chapter 1 - Introduction

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  • Definitions
  • Populations
  • Data Groups, Variables
  • Class Intervals
  • Frequency Distribution
  • Continuous Distributions
  • Continuous Distributions Histogram
    • Equal Class Size
    • Unequal Class Size
  • Frequency Curves
  • Cumulative Frequency Curve or Ogive

Chapter 2 - Measures of Central Tendency

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  • Central Tendency
  • Arithmetic Mean
  • Median and Mode
  • Frequency Distributions

Chapter 3 - Measures of Dispersion

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  • Dispersion: Mean Deviation
  • Mean Deviation Example
  • Variance
  • Variance: Example
  • Standard Deviation

Chapter 4 - Worked Example

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  • Raw Data
  • Classes
  • Exact Class Limits
  • Frequency Distribution Graph
  • Cumulative Frequency Distribution (cf)
  • Arithmetic Mean for Grouped Data
  • Median for Grouped Data Set
  • Sample Standard Deviation of Grouped Data Set

Chapter 5 - Probability

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  • Probability Exercise
  • Random Data (Tossing Coins)
  • Expressing Probability
  • Venn Diagram
  • Rules of Addition
  • Theory of Intersection
  • Rules of Multiplication
  • Bayes Theorem
  • Hypothesis
  • Test
  • Null Hypothesis (H0)
  • Critical Region
  • Test Statistic
  • Level of Significance

Chapter 6 - Distributions

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  • Binomial Experiment
  • Binomial Population
  • Variables
  • Continuous Distribution
  • Continuous Probability Distribution
  • Normal Distribution
  • Standard Normal Distribution
  • Gaussian (s-Normal) Distribution
  • One-Tailed Test
  • Two-Tailed Test
  • Type I and II Errors
  • Statistical Significance
  • Confidence Intervals
  • Confidence Levels
  • Computing the Standard Deviation-Example

Chapter 7 - More Distributions

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  • Chi-Square (χ2) Distribution
  • Binomial Distribution
  • Binomial Distribution Graph
  • Poisson Distribution
  • Student's t-Distribution
  • Table: t-Distribution
  • F-Distribution
  • Table: Critical Values for the F-test

Chapter 8 - Correlation and Regression

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  • Goodness-of-Fit Tests
  • Correlation
  • Scatter Diagram
  • Regression Analysis
  • Regression
  • Method of Least Squares
  • Linear Regression

Chapter 9-1 - Student Exercise: Designing a Sampling Experiment

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Chapter 9-2 - Student Experiment

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Chapter 9-3 - Student Exercise: Tests Between Two Populations and Samples

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Appendix B - Parameter Estimation and Design of Experiments

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Appendix C - Kolmogorov-Smirnov (K-S) Limits

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Appendix D - Tolerance Analysis

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Appendix E - Markov/State Models

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Appendix F - Statistical Confidence Limits

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Summary, Final Review

Award of certificates for successful completion

Click for a printable course outline (pdf).