Introduction to Markov Modeling for Reliability

 

 

1 Introduction

 

2 Markov Model Fundamentals

2.1       What Is A Markov Model?

2.2       A Simple Markov Model for a Two-Unit System  

2.3       Matrix Notation

2.4       Delayed Repair of Total Failures

2.5       Transient Analysis

2.6       Discussion

 

3 Considerations for More Complex Systems

3.1       Modeling Infrequent Periodic Repairs for First-Order States

3.2       Simplifying Higher-Order Models By State Aggregation

3.3       Iterative Solution of Steady-State Models

3.4       Modeling Periodic Repairs for Higher-Order States

3.5       Exact Solution of Complex Models with Infrequent Periodic Repair

3.6       Exact Solution With Multiple Distinct Periodic Repair Intervals

3.7       Model Truncation and Completeness

3.8       Models with Variable Transition Rates

3.9       Phased Mission Analysis

 

4 Examples

4.1       Active/Backup System with Internal/External Fault Monitoring

4.2       Two-Unit System with Latent Failures of Protective Elements

4.3       Three-Unit System with Latent Failures of Protective Elements

 

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