II. A. 3. Discrete and Continuous Probability Distributions

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About Fred Schenkelberg

I am the reliability expert at FMS Reliability, a reliability engineering and management consulting firm I founded in 2004. I left Hewlett Packard (HP)’s Reliability Team, where I helped create a culture of reliability across the corporation, to assist other organizations.

CRE Preparation Course
- Course Introduction
  - Welcome
  - Introduction
  - Thank You for Your Interest in the Course
  - Exam Day
  - Preparation Approach
  - Discussion Forums Introduction
  - CRE Sample Quiz
  - Terms Glossary
  - Math Quiz
  - Body of Knowledge 2009 version
  - Body of Knowledge 2018 version
- Reliability Management
  - Reliability Management Introduction
- I. A. Strategic Management
  - Strategic Management Introduction
  - I. A. 1. Benefits of Reliability Engineering
  - I. A. 2. Interrelationship of Safety, Quality, and Reliability
  - I. A. 3. Role of the Reliability Function
  - I. A. 4. Product and Process Development
  - I. A. 5. Failure Consequences and Liability Management
  - I. A. 6. Warranty Management
  - I. A. 7. Customer Needs Assessment
  - I. A. 8. Supplier Reliability
  - I. A. Strategic Management Quiz
  - I. A. Bonus — Building Influence
- I. B. Reliability Program Management
  - Reliability Program Management Introduction
  - I. B. 1. Terminology
  - I. B. 2. Elements of a Reliability Program
  - I. B. 3. Types of Risk
  - I. B. 4. Product Lifecycle Engineering
  - I. B. 5. Design Evaluation
  - I. B. 6. Systems Engineering and Integration
  - I. B. Reliability Program Management Quiz
- I. C. Ethics, Safety, and Liability
  - Ethics, Safety, and Liability Introduction
  - I. C. 1. Ethical Issues
  - I. C. 2. Roles and Responsibilities
  - I. C. 3. System Safety
  - I. C. Ethics, Safety, and Liability Quiz
- II. Probability and Statistics for Reliability
  - Probability and Statistics for Reliability Introduction
- II. A. Basic Concepts
  - Basic Concepts Introduction
  - II. A. I. Statistical Terms
    - II. A. I. a. Basic Statistical Terms
    - II. A. I. b. Measures of Central Tendency
    - II. A. I. c. Central Limit Theorem
    - II. A. I. d. Measures of Dispersion
    - II. A. 1. e. COV and a Couple of Laws
  - II. A. 2. Basic Probability Concepts
    - II. A. 2. a. Probability
    - II. A. 2. b. Laws and Counting
    - II. A. 2. c. Expectation
  - II. A. 3. Discrete and Continuous Probability Distributions
    - II. A. 3. a. The Four Functions
    - II. A. 3. b. Continuous Distributions
    - II. A. 3. c. Discrete Distributions
    - II. A. 3. d. Bathtub Curve
  - II. A. 4. Poisson Process Models
    - Poisson Process Models Introduction
    - II. A. 4. a. Homogeneous Poisson Process
    - II. A. 4. b. Repair System Terminology
    - II. A. 4. c. Non-Homogenous Poisson Process
    - II. A. 4. d. Mann Reverse Arrangement Test
    - II. A. 4. e. Laplace’s Trend Test
    - II. A. 4. f. Fisher’s Composite Test
  - II. A. 5. Non-Parametric Statistical Methods
    - II. A. 5. a. The Approach
    - II. A. 5. b. Ranking
    - II. A. 5. c. Reliability and Comparisons
    - Non-Parametric Statistical Methods Introduction
  - II. A. 6. Sample Size Determination
    - II. A. 6. Sample Size Determination
  - II. A. 7. Statistical Process Control and Process Capability
    - II. A. 7. a. Control Charts Introduction
    - II. A. 7. b. X-bar and R charts
    - II. A. 7. c. Selecting Control Charts
    - II. A. 7. d. Individual and Moving Range Charts
    - II. A. 7. e. Attribute Charts
    - II. A. 7. f. The Analysis
    - II. A. 7. g. Process Capability
    - II. A. 7. h. Standard Normal and z-values
    - II. A. 7. i. Capability and Charts
    - II. A. 7. j. Pre-Control Charts
    - Statistical Process Control and Process Capability Introduction
  - II. A. Basic Concepts Quiz
- II. B. Statistical Inference
  - Statistical Inference Introduction
  - II. B. 1. Point Estimates of Parameters
  - II. B. 2. a. Statistical Intervals – Point Estimates
  - II. B. 2. b. Statistical Intervals – MTBF Estimates
  - II. B. 3. a. Hypothesis Testing – The Process
  - II. B. 3. b. Hypothesis Testing – Means
  - II. B. 3. c. Hypothesis Testing – Variance
  - II. B. 3. d. Hypothesis Testing – Comparisons
  - II. B. Statistical Inference Quiz
- III. Reliability in Design and Development
  - Reliability in Design and Development Introduction
- III. A. Reliability Design Techniques
  - Reliability Design Techniques Introduction
  - III. A. 1. Environmental and Use Factors
  - III. A. 2. Stress-Strength Analysis
  - III. A. 3. FMEA and FMECA
  - III. A. 4. Common Mode Failure Analysis
  - III. A. 5. Fault and Success Tree Analysis
  - III. A. 6. Tolerance and Worst-Case Analysis
- III. A. 7. Design of Experiments
  - Design of Experiments Introduction
  - III. A. 7. a. How We Experiment
  - III. A. 7. b. Differences and Approaches
  - III. A. 7. c. Language of DOE
  - III. A. 7. d. Only the Right Experiments
  - III. A. 7. e. Steps to Accomplish
  - III. A. 7. f. Dealing with Measurements
  - III. A. 7. g. Interactions and Confounding
  - III. A. 7. h. Adjusting the Design
  - III. A. 7. i. Classical DOE
  - III. A. 7. j. Various Designs
  - III. A. 7. k. A Simple Taguchi Example
  - III. A. 7. l. Robust Design
- III. A. more Reliability Design Techniques
  - III. A. 8. Fault Tolerance
  - III. A. 9. Reliability Optimization
  - III. A. 10. Human Factors
  - III. A. 11. Design for X – DFX
  - III. A. 12. Reliability Apportionment or Allocation Techniques
  - III. A. Reliability Design Techniques Quiz
- III. B. Parts and Systems Management
  - Parts and Systems Management Introduction
  - III. B. 1. a. Selection, Standardization, and Reuse – Parts
  - III. B. 1. b. Selection, Standardization, and Reuse – Software
  - III. B. 2. Derating Methods and Principles
  - III. B. 3. Parts Obsolescence Management
  - III. B. 4. Establishing Specifications
  - III. B. Parts and Systems Management Quiz
- IV. Reliability Modeling and Predictions
  - Reliability Modeling and Predictions Introduction
- IV. A. Reliability Modeling
  - Reliability Modeling Introduction
  - IV. A. 1. Sources and Uses of Reliability Data
  - IV. A. 2. a. Reliability Block Diagrams and Models – Series Systems
  - IV. A. 2. b. Reliability Block Diagrams and Models – Parallel Systems
  - IV. A. 2. c. Reliability Block Diagrams and Models – Redundancy
  - IV. A. 2. d. Reliability Block Diagrams and Models – Complex
  - IV. A. 2. e. Reliability Block Diagrams and Models – Keynote
  - IV. A. 3. Physics of Failure Models
  - IV. A. 4. a. Simulation Techniques – Markov Models
  - IV. A. 4. b. Simulation Techniques – Monte Carlo
  - IV. A. 5. Dynamic Reliability
  - IV. A. Reliability Modeling quiz
- IV. B. Reliability Predictions
  - Reliability Predictions Introduction
  - IV. B. 1. Parts Count Predictions and Parts Stress Analysis
  - IV. B. 2. a. Reliability Prediction Models – Considerations
  - IV. B. 2. b. Reliability Prediction Models – Uncertainty
  - IV. B. 2. c. Reliability Prediction Models – Tolerance Intervals
  - IV. B. Reliability Predictions quiz
- V. Reliability Testing
  - Reliability Testing Introduction
- V. A. Reliability Testing Planning
  - Reliability Testing Planning Introduction
  - V. A. 1. a. Reliability Test Strategies – Types of Testing
  - V. A. 1. b. Reliability Test Strategies – Human Factors Testing
  - V. A. 2. Test Environment
  - V. A. Reliability Test Planning quiz
- V. B. Testing During Development
  - Testing During Development Introduction
  - V. B. 1. Accelerated Life Tests
  - V. B. Bonus – A Few Models
  - V. B. 2. Discovery Testing
  - V. B. 3. Reliability Growth Testing
  - V. B. 4. Software Testing
  - V. B. Testing During Development quiz
- V. C. Product Testing
  - Product Testing Introduction
  - V. C. 1. a. Qualification Demonstration Testing – PRST
  - V. C. 1. b. Qualification Demonstration Testing – Success Testing
  - V. C. 2. Product Reliability Acceptance Testing – PRAT
  - V. C. 3. Ongoing Reliability Testing
  - V. C. 4. Stress Screening
  - V. C. 5. Attribute Testing
  - V. C. 6. Degradation Testing
  - V. C. Bonus – Acceleration Factors
  - V. C. Product Testing quiz
- VI. Maintainability and Availability
  - Maintainability and Availability Introduction
- VI. A. Management Strategies
  - Management Strategies Introduction
  - VI. A. 1. a. Planning
  - VI. A. 1. b. Planning – System Effectiveness
  - VI. A. 1. c. Planning – Reliability Time
  - VI. A. 2. a. Maintenance Strategies – RCM
  - VI. A. 2. b. Maintenance Strategies – TPM
  - VI. A. 2. c. Maintenance Strategies – Allocation
  - VI. A. 3. Availability Tradeoffs
  - VI. A. Management Strategies quiz
- VI. B. Maintenance and Testing Analysis
  - Maintenance and Testing Analysis Introduction
  - VI. B. 1. Preventative Maintenance Analysis
  - VI. B. 2. Corrective Maintenance Analysis
  - VI. B. 3. Non-Destructive Evaluation
  - VI. B. 4. Testability
  - VI. B. 5. Spare Parts Analysis
  - VI. B. Maintenance and Testing Analysis quiz
- VII. Data Collection and Use
  - Data Collection and Use Introduction
- VII. A. Data Collection
  - Data Collection Introduction
  - VII. A. 1. a. Types of Data
  - VII. A. 1. b. Types of Data – Censored Data
  - VII. A. 2. Collection Methods
  - VII. A. 3. Data Management
  - VII. A. Data Collection quiz
- VII. B. Data Use
  - Data Use Introduction
  - VII. B. 1. Data Summary and Reporting
  - VII. B. 2. Preventive and Corrective Actions
  - VII. B. 3. Measures of Effectiveness
  - VII. B. Data Use quiz
- VII. C. Failure Analysis and Correction
  - Failure Analysis and Correction Introduction
  - VII. C. 1. Failure Analysis Methods
  - VII. C. 2. Failure Reporting, Analysis, and Corrective Action System
  - Exam Day Bonus
  - VII. C. Failure Analysis and Correction quiz