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Reliability Statistics Testing 3-Day Course

Course Description

The Reliability Statistics Training Course is a three-day, applications-oriented course on statistical methods. Designed for the practitioner, this course covers the main statistical methods used in reliability and life data analysis. The course starts with an overview of the main results of probability and reliability theory. Then, the main discrete and continuous distributions used in reliability data analysis are overviewed. This review of reliability principles prepares the participants to address the main problems of estimating, testing, and modeling system reliability data.

Who Should Take the Course

Statistics have, at least, three consumers. Data collectors need to know how data will be used to gather their task efficiently. Otherwise, the inefficient GIGO model (garbage-in, garbage-out) takes over. Data analysts need to be proficient in the correct implementation of statistical methods. Managers need to understand the usefulness of statistical procedures in enhancing reliability and quality work, so they can seriously support such kind of activity. Finally, anyone preparing to take the Professional Engineering Certification Exams in Reliability, Quality, Logistics, etc., which are heavily based on statistical procedures, will benefit greatly from taking this course, as the material reinforces the statistical material required for those certifications.

What the Student Will Learn

Statistics can be divided, in broad terms, into descriptive statistics (calculation of basic statistics, tables and graphs), and inferential statistics (implementation of tests and confidence intervals and statistical modeling, such as regression and analysis of variance). Each day, out of the three-day course, will be dedicated to one of these three topics: descriptive, testing/CI and modeling. Most importantly, however, the concept of "statistical thinking" will be reinforced. Statistics is not about memorizing some formulas; statistics is a complete data analysis philosophy that uses these formulas to obtain clearer, more valid analyses results.

Included Materials

Course materials include the course manual, a selection of RIAC's START sheets, and the RIAC publication "Practical Statistical Tools for the Reliability Engineer."

Required Materials

Attendees are encouraged to bring their laptops so they can take class work and other examples and materials developed during the course with them. Attendees are also encouraged to bring their own data to be used as class examples with the procedures developed in the course.

Course Outline

Day 1:
Review of Probability and Reliability Concepts

1. Scope and Course Content and Objectives
• Statistical Thinking v. Statistical Mechanics
2. Overview of Probability and Reliability Definitions
• Reliability as a Product Performance Measure
• Distribution, Density Hazard Functions
• Increasing, Decreasing and Constant Failure Rates
• The Bathtub Curve and its Implications
3. Basic Probability and Descriptive Statistics Concepts
• Coin tossing and dice rolling
• Mean, median, variance, range, etc
• Tabulation and graphing of the data

Statistical Distributions Frequently Used in Reliability Engineering

1. Discrete Distributions, their Properties and their Parameters
• Hypergeometric, Binomial, Geometric and Poisson
2. Continuous Distributions, their Properties and their Parameters
• Exponential, Normal, Log-normal, and Weibull
3. Some Sampling Distributions and their Practical Uses
• Student t, Fisher's F, Chi-Square
• Use of statistical tables
4. Some Graphical Methods of Distribution Identification
• Normal Scores, Probability, and Other Plots
• Implementation, Interpretation, and Uses
• Interpretation of Models and Their Parameters

Day 2:
Derivation of Confidence Intervals

1. Distribution of the Average of a Large Sample
• The Central Limit Theorem and its Applications
2. Confidence Intervals (C.I.) for the Population Mean
• From Large and Small Samples
• From the Normal and Exponential Distributions
3. C.I. for the Difference of Two Population Means
• From Two, Large and Small Samples
• From the Normal and the Exponential Distributions
4. C.I. for the Population Proportion
• And for the Difference of Two Population Proportions

Hypothesis Testing

1. Testing for the Population Mean
• From Large and Small Samples
• From the Normal and Exponential Distributions
2. Testing for the Difference of Two Population Means
• From Large and Small Samples
• From the Normal and Exponential Distributions
3. Testing for the Population Proportion
• And for the Difference of Two Population Proportions

Testing the Goodness of Fit (GoF)

1. Reasons and Uses of GoF Testing
2. The Chi-Square Goodness of Fit Test
• For Large Samples and Arbitrary Distributions
3. The Anderson-Darling Goodness of Fit Test
• For Small Samples and Normal Distributions
4. Graphical and Computer-based GoF Tests

Day 3:
Introduction to Regression Modeling

1. Reasons and Benefits of Implementing a Regression
2. The Simple Linear Regression Model
3. Model Checking via Residual Analysis
4. Other Regression Models
5. Reliability Application Examples

Introduction to Analysis of Variance (ANOVA)

1. Reasons and Benefits of Performing ANOVAs
2. Design and Planning of an Experiment
3. One-way Analysis of Variance
4. Residual Analysis and Model Checks
5. Reliability Application Examples

The Road Ahead

1. Reliability Case Studies
2. Industrial Applications
3. Where Do We Go From Here?