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Probability and Statistics for Reliability and Reliability Growth

Reliability is heavily dependent on Probability and Statistics for measuring and describing its characteristics.

To further explore this topic, there are certain terms you need to understand such as:

  • Failure Distribution: This is a representation of the occurrence failures over time usually called the probability density function, PDF, or f(t)
  • Cumulative Failure Distribution: The cumulative version of the PDF called the CDF, or F(t)
  • Reliability: If we can call the CDF the unreliability of a product, then 1-F(t) must be the reliability.

An important part of reliability is identifying, understanding, and optimizing the type of statistical distribution that represents the product.

Binomial Distribution, for example, is used to represent situations where there are two possible outcomes, success or failure and the probability of one of the types of outcomes is known, whereas, Normal Distribution usually represents wear out situations.

Another type of distribution, Weibull Distribution, can be used to represent a number of other distributions such as the Normal, the Exponential, and others (usually 2 parameter but can be 3 parameter).

The concept of reliability growth is not just theoretical or absolute.

Reliability growth is related to factors such as the management strategy toward taking corrective actions, effectiveness of the fixes, reliability requirements, the initial reliability level, reliability funding and competitive factors.

A good example of this might be when one management team takes corrective actions for 90% of the failures seen during testing, while another management team with the same design and test information may take corrective actions on only 65% of the failures seen during testing.

Different management strategies may attain different reliability values with the same basic design. The effectiveness of the corrective actions is also relative when compared to the initial reliability at the beginning of testing.

Several important factors for an effective reliability growth program are:

  • Management strategy:decisions to correct problems or not correct problems and the effectiveness of the corrective actions
  • Testing:provides opportunities to identify the weaknesses and failure modes in the design and manufacturing process
  • Failure mode root cause identification:funding, personnel and procedures are provided to analyze, isolate and identify the cause of failures
  • Corrective action effectiveness:design resources to implement corrective actions that are effective and support attainment of the reliability goals
  • Valid reliability assessments

Probability and Statistics for Reliability and Reliability Growth Course by Tonex

Probability and Statistics for Reliability and Reliability Growth is a 3-day hands-on course. Probability and Statistics for Reliability and Reliability Growth training bootcamp helps facilitate the foundation for engineers, designers, product managers, project managers, technicians and other professionals. Our multi-tier bootcamp curriculum guides participants through foundational industry knowledge to in-depth, hands-on experiential learning.

Reliability growth is dependent on Probability and Statistics for measuring and describing its characteristics.

Failure Distribution is a representation of the occurrence failures over time usually called the probability density function, PDF, or f(t). Cumulative Failure Distribution (CDF) is the cumulative version of the PDF.

If the CDF is unreliability of a product, then 1-F(t) must be the reliability. The most common distribution usually representing wearout situations, Normal Distribution.

Course Agenda

Principles of Reliability and Reliability Growth

  • Principles of Reliability
  • Reliability Key Concepts & Terminology
  • Design for Reliability
  • Probability and Statistics
  • Physics of Failure
  • High Accelerated Life Testing (HALT)
  • High Accelerated Stress Screening (HASS)
  • Reliability Scorecard
  • Operational Availability
  • Operational Mode
  • Mission Profile
  • Reliability Growth Analysis
  • Reliability Test Program Planning

Application of Reliability Growth

  • Repairable System Theory
  • Reliability Growth Planning and Management
  • Reliability Growth Planning
  • Reliability Data Analysis
  • Reliability Growth Tracking
  • Reliability Growth Projection
  • Software Reliability Overview
  • Example Reliability Growth Application
  • Reliability Growth Lessons Learned
  • Repairable System Analysis

Reliability Growth Models

  • Introduction
  • The Exponential Model
  • Reliability Growth Models
  • Modeling Process
  • Identifying Trends in Failure Data
  • Laplace Trend Test

Probability and Statistics

  • Basic Process
  • Normal Distribution
  • Exponential Distribution
  • Weibull Distribution
  • Binomial Distribution
  • Poisson Distribution
  • Hypergeometric
  • Classifying the Failure Model

Decreasing the Failure Rate

  • Attaining the Requirement
  • Factors Influencing the Growth Rate
  • Reliability Growth Management Control Processes
  • Assessment Approach
  • Monitoring Approach
  • Factors Influencing the Growth Curve’s Shape
  • Stages of the Development Program
  • Test Phases
  • Test Phase Reliability Growth
  • Timing of Fixes
  • Growth Curve Re-initialization
  • Shape Changes Due to Calendar Time
  • Reliability Growth Programmatic Concepts
  • Levels of Consideration for Planning and Controlling Growth
  • Analysis of Previous Programs
  • Reliability Growth Planning Concepts
  • Planned Growth vs.

Idealized Growth Curve

  • Other Planning Considerations
  • Threshold
  • Reliability Growth Tracking Concepts
  • Demonstrated Reliability
  • Reliability Growth Tracking Curve
  • Reliability Growth Projection Concepts
  • Extrapolated Reliability
  • Projected Reliability
  • Models Covered in this Handbook
  • Sources for Models Covered in this Handbook

Principals of Reliability Growth Planning and Management

  • Repair vs. Fix
  • Analysis of Failure Modes
  • Fix Effectiveness Factor (FEF)
  • Growth Potential (GP)
  • Growth Management Strategy (MS)
  • Growth Rate
  • Poisson Process
  • Homogeneous Poisson Process (HPP)
  • Non-Homogeneous Poisson Process (NHPP)
  • Idealized Growth vs. Planned Growth Curve
  • Reliability Growth Tracking Curve
  • Reliability Growth Projection
  • Exit Criterion (Milestone Threshold)
  • Basic Model Approaches Covered
  • Planning Models Covered
  • Planning Model Limitations
  • Demonstrating Reliability Requirements with Statistical Confidence
  • Planning Areas
  • Reliability Growth Planning Checklist

Planning Models and Tools

  • Planning Models
  • United States Army Materiel Systems Analysis Activity (AMSAA)
  • Planning Model based on Projection Methodology (PM2) Continuous
  • Planning Model based on Projection Methodology (PM2) Discrete
  • Subsystem Level Planning Model (SSPLAN)
  • Tracking Models
  • Reliability Growth Tracking Model (RGTM) Continuous
  • Projection Models
  • System Level Planning Model (SPLAN)
  • Planning Factors
  • Reliability Growth OC Curve Analysis

Planning Model Based on Projection Methodology (PM2)

  • Overview of PM Continuous Approach
  • Equations and Metrics
  • Plausibility Metrics for Planning Parameters
  • PM Continuous Example
  • Planning Model Based on Projection Methodology (PM)-Discrete
  • Equations and Metrics
  • PM-Discrete Example
  • Failure Mode Preclusion Considerations
  • Threshold Program

Reliability Growth Analysis and Assessment Tools

  • Reliability Growth Assessment
  • Managing Reliability Growth
  • Commitment and Involvement
  • Controlling Reliability Growth
  • Management’s Role
  • Basic Reliability Activities
  • Benefits of Reliability Growth Planning Assessment
  • Finding Unforeseen Deficiencies
  • Designing-in Improvement through Surfaced Problems
  • Reducing the Risks Associated with Final Demonstration
  • Increasing the Probability of Meeting Objectives
  • Practical Data Analysis Considerations
  • Reliability Growth Tracking
  • AMSAA Reliability Growth Tracking Model – Continuous (RGTMC)
  • Estimation Procedures for the Option for Grouped Data
  • AMSAA Reliability Growth Tracking Model – Discrete (RGTMD)
  • Subsystem Level Tracking Model (SSTRACK)
  • Reliability Growth Projection
  • Introduction
  • AMSAA-Crow Projection Model (ACPM)
  • Crow Extended Reliability Projection Model
  • AMSAA Maturity Projection Model (AMPM)
  • AMSAA Maturity Projection Model based on Stein Estimation (AMPM-Stein)
  • AMSAA Discrete Projection Model based on Stein Estimation (ADPM-Stein)

 

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