1 Introduction
2 Relationship of this Special Report to Other
Bellcore Documents
3 Definitions
4 Guidelines for the Requesting Organization
4.1 Identify Intent of the Analysis
4.2 Define a Failure in the System
4.3 Define the Reliability Objectives
4.4 Provide the Necessary Parameters
4.5 Verify the Results
5 Guidelines for System Reliability Prediction
5.1 Steps in System Reliability Modeling and Analysis
5.2 Elements of a System Reliability Model
6 Graphical Methods for Representing the System
Architecture
6.1 Functional Block Diagrams
6.2 Reliability Block Diagrams
6.3 State Transition Diagrams
6.4 Comparison of Reliability Block and State Transition
Diagrams
7 Basic Concepts
7.1 The Exponential Distribution
7.2 Renewal Theory Results
8 Analyzing Reliability Block Diagrams
8.1 The Combinatorial Method
8.2 Difficulties and Assumptions
9 State Space Methods
9.1 Creating State Transition Diagrams
9.2 Solution of the Markov Model
9.3 Nonexponential Times to Events
9.4 Examples of Markov Modeling
9.5 Difficulties and Assumptions of Markov Models
10 Comparison of Combinatorial and State Space
Methods
10.1 Both Methods Applicable
10.2 Neither Method Applicable
11 Measures of System Reliability
11.1 Unavailability and Availability
11.2 Limiting Frequencies
11.3 Other Measures of Reliability
11.4 Other Common Measures of RAM
12 Failure Modes and Effects Analysis*
12.1 System Reliability Measures
13 Glossary of Terms
REFERENCES
LIST OF FIGURES
Figure 6.1 Example of a Functional Block Diagram
Figure 6.2 Functional Block Diagram of a Digital Switch
Figure 6.3 Reliability Block Diagram of a Series System
Figure 6.4 Reliability Block Diagram of a Parallel System
Figure 6.5 Reliability Block Diagram of a Hypothetical
Billing Module
Figure 6.6 State Transition Diagram of a Two Component
System
Figure 6.7 State Transition Diagram of a Duplicated
Component System
Figure 6.8 State Transition Diagram with Transition Rates
Figure 9.1 State Transition Diagram for Configuration of
Three Components
Figure 9.2 Equivalent State Transition Diagram
Figure 9.3 Reliability Block Diagram for System
Figure 9.4 State Transition Diagram for System
Figure 9.5 State Transition Diagram for Instantaneous
Failure
Figure 9.6 Comparison of Repair Strategies
Figure 9.7 State Transition Diagram for Travel and Repair
Figure 9.8 Fragment with Nonexponential Times
Figure 9.9 Equivalent Markov Fragment
Figure 9.10 Functional Block Diagram for Optical
Transmission System
Figure 9.11 State Transition Diagram for Optical
Transmission System
Figure 9.12 First Markov Model
Figure 9.13 State Transition Diagram for Travel and Repair
Figure 9.14 Equivalent State Transition Diagram for Travel
and Repair
Figure 12.1 Reliability Block Diagram for Example
Figure 12.2 State Transition Diagram for Example
Figure 12.3 FMEA State Transition Diagram for Subsystem
LIST OF TABLES
Table 9.1 Approximations for Exact Equivalent Transition
Rates
Table 9.2 Parameters of Fiber Optic Transmission System
Markov Model
Table 9.3 Definitions of States in Fiber Optic Transmission
System Markov Model
Table 12.1 Example Failure Modes and Effects Table
Table 12.2 Published RAM Objectives for Switching Systems
Table 12.3 Definitions used in Cutoff Call Calculations
Table 12.4 Equations for p, and k, in Cutoff Call Calculations
Table 12.5 Example Cutoff Call Calculation
Table 12.6 Definitions used in RRIMA Calculations
Table 12.7 Values of k, for RRIMA
Table 12.8 Example RRIMA Calculations