Marvin Rausand - System Reliability Theory

7 Chapter 7Figure 7.1 Simple system of three components.Figure 7.2 Illustration of Birnbaum's metric of reliability importance.Figure 7.3 Structure with three components: RBD and associated fault tree re...Figure 7.4 RBD (Problem 3).Figure 7.5 RBD (Problem 6).

8 Chapter 8Figure 8.1 Relationship between independent failures and CCFs of a structure...Figure 8.2 A shared cause combined with coupling factors lead to CCF of a pa...Figure 8.3 Explicit modeling of a CCF in a system of two pressure switches....Figure 8.4 Probabilities of different multiplicities for a voted group of th...Figure 8.5 A component represented as a series structure of two blocks.Figure 8.6 A parallel structure modeled by the beta‐factor model.Figure 8.7 Fractions of different types of failures for a structure of two c...Figure 8.8 RBD for a 2oo3:G structure modeled by the beta‐factor model.Figure 8.9 The MTTF of a 2oo3:G structure modeled as a function of the beta‐...Figure 8.10 Fractions of different types of failures for a system with three...Figure 8.11 Probabilities of failures with different multiplicities.

9 Chapter 9Figure 9.1 Classification of maintenance types.Figure 9.2 Average “behavior” of a repairable item and main time concepts.Figure 9.3 Functional failure analysis (FFA) worksheet.Figure 9.4 RCM‐FMECA worksheet.Figure 9.5 Maintenance task assignment/decision logic.Figure 9.6 Time concepts used in Total productive maintenance.

10 Chapter 10Figure 10.1 Relation between the number of events , the interoccurrence tim...Figure 10.2 The dataset in Example 10.1.Figure 10.3 Number of failures as a function of time for the data in Examp...Figure 10.4 Number of critical compressor failures as a function of time (...Figure 10.5 The forward recurrence time .Figure 10.6 Types of repair and stochastic point processes covered in this b...Figure 10.7 Number of renewals as a function of for a simulated renewal ...Figure 10.8 Illustration of the conditional ROCOF (fully drawn line) for sim...Figure 10.9 Renewal density (fully drawn line) and renewal function (dot...Figure 10.10 The renewal function for Weibull distributed renewal periods wi...Figure 10.11 The age and the remaining lifetime .Figure 10.12 The renewal function of a renewal process with underlying dis...Figure 10.13 Superimposed renewal process.Figure 10.14 Superimposed renewal process. Conditional ROCOF of a series s...Figure 10.15 Alternating renewal process.Figure 10.16 Availability of an item with exponential up‐ and downtimes.Figure 10.17 The availability of an item with exponential uptimes and consta...Figure 10.18 The ROCOF of an NHPP and random failure times.Figure 10.19 An illustration of a possible shape of the conditional ROCOF of...Figure 10.20 The conditional ROCOF of Chan and Shaw's proportional reduction...Figure 10.21 The model for some possible failure times. The “underlying” R...Figure 10.22 Illustration of the transformation of a TRP( ) to a renewal pro...Figure 10.23 Illustration of the conditional ROCOF in Example 10.19 for so...Figure 10.24 Model selection framework.

11 Chapter 11Figure 11.1 Trajectory of a Markov process.Figure 11.2 State transition diagram of the parallel structure in Example 11...Figure 11.3 State transition diagram for the parallel structure in Example 1...Figure 11.4 State transition diagram for a homogeneous Poisson process (HPP)...Figure 11.5 State transition diagram for a single component (function‐repair...Figure 11.6 Availability and survivor function for a single component ( , )...Figure 11.7 State transition diagram of the generators in Example 11.6.Figure 11.8 Partitioning the state transition diagram of a series structure ...Figure 11.9 State transition diagram of a series structure of two components...Figure 11.10 State transition diagram for a parallel structure of two identi...Figure 11.11 State transition diagram for a parallel structure of two compon...Figure 11.12 The of a parallel structure as a function of the common‐cause...Figure 11.13 Parallel structure of two components sharing a common load.Figure 11.14 State transition diagram for the generator system with load‐sha...Figure 11.15 Two‐item standby system.Figure 11.16 State transition diagram of a two‐item parallel structure with ...Figure 11.17 State transition diagram of a two‐item parallel structure with ...Figure 11.18 State transition diagram of a two‐item parallel structure with ...Figure 11.19 State transition diagram of a two‐item parallel structure with ...Figure 11.20 Reliability block diagram (a) and state transition diagram (b) ...Figure 11.21 Example of a Markov's chain simulation – single history.Figure 11.22 Example of a Markov's chain simulation – estimate of MTTF and s...Figure 11.23 RBD for the pitch system in Problem 11.4.Figure 11.24 RBD for the system in Problem 11.5.

12 Chapter 12Figure 12.1 Age replacement strategy and costs.Figure 12.2 The ratio as a function of for the Weibull distribution with...Figure 12.3 The optimal replacement interval in Example 12.2 as a function...Figure 12.4 The average cost per time unit for a block replacement strategy ...Figure 12.5 The average cost per time unit for a block replacement strategy ...Figure 12.6 Average behavior and concepts used in – interval models.Figure 12.7 The asymptotic cost per time unit as a function of for , ...Figure 12.8 Comparison between four different (non‐CBM) maintenance strategi...Figure 12.9 State transition diagram for a single item with degraded states....Figure 12.10 State transition diagram for a single item with degraded states...Figure 12.11 State transition diagram for a single component with degraded s...Figure 12.12 RBD of a safety‐instrumented system (SIS).