Читать книгу System Reliability Theory - Marvin Rausand - Страница 4

1 Chapter 1Figure 1.1 The reliability concept.Figure 1.2 Main drivers for high reliability.Figure 1.3 Main steps of risk analysis, with main methods. The methods cover...Figure 1.4 Reliability as basis of other applications.Figure 1.5 Load and the strength distributions at a specified time .Figure 1.6 Possible realization of the load and the strength of an item.Figure 1.7 The system reliability analysis process.Figure 1.8 The phases of a system development project (example).Figure 1.9 Factors that influence item requirements.

2 Chapter 2Figure 2.1 System breakdown structure (simplified).Figure 2.2 A study object (system) and its boundary.Figure 2.3 A function illustrated as a functional block.Figure 2.4 Function tree (generic).Figure 2.5 SADT diagram for subsea oil and gas stimulation.Figure 2.6 Top‐down approach to establish an SADT model.Figure 2.7 System analysis and synthesis.Figure 2.8 Component function shown as a block.Figure 2.9 Alternative representation of the block in Figure 2.8Figure 2.10 A simple reliability block diagram with three blocks.Figure 2.11 An alternative, and identical, version of the RBD in Figure 2.10...Figure 2.12 RBD for a series structure.Figure 2.13 Parallel structure.Figure 2.14 Voted structure 2oo3, (left) a physical diagram and (right) an R...Figure 2.15 Standby structure.Figure 2.16 RBD for a series–parallel structure.Figure 2.17 Two safety valves in a pipeline: (a) physical layout, (b) RBD fo...Figure 2.18 Construction of the RBD in levels.

3 Chapter 3Figure 3.1 States and transitions for a safety valve.Figure 3.2 Failure as a transition from a functioning state to a failed stat...Figure 3.3 Illustration of the difference between failure and fault for a de...Figure 3.4 Doorbell and associated circuitry.Figure 3.5 Relation between failure causes, failure modes, and failure effec...Figure 3.6 Relationship between failure cause, failure mode, and failure eff...Figure 3.7 Failure classification..Figure 3.8 A primary failure leading to an item fault.Figure 3.9 A secondary failure, caused by an overstress event, leading to an...Figure 3.10 A systematic fault leading to a systematic failure.Figure 3.11 The structure of a security failure.Figure 3.12 Failure causes and mechanisms. A failure mechanism is a specific...Figure 3.13 Cause and effect diagram for the event “car will not start.”Figure 3.14 Repeatedly asking why?

4 Chapter 4Figure 4.1 Deductive versus inductive analysis of a fault or deviation in th...Figure 4.2 Timeline of the development of FMECA variants (not in scale).Figure 4.3 The mains steps of FMECA.Figure 4.4 Example of an FMECA worksheet.Figure 4.5 Risk matrix of the different failure modes.Figure 4.6 A simple fault tree.Figure 4.7 System overview of fire detector system.Figure 4.8 Schematic layout of the fire detector system.Figure 4.9 Fault tree for the fire detector system in Example 4.1.Figure 4.10 Example of a fault tree.Figure 4.11 Sketch of a first stage gas separator.Figure 4.12 Fault tree for the first stage separator in Example 4.2.Figure 4.13 A simple event tree for a dust explosion.Figure 4.14 Presentation of results from ETA.Figure 4.15 Activation pressures for the three protection layers of the proc...Figure 4.16 An event tree for the initiating event “blockage of the gas outl...Figure 4.17 Relationship between some simple RBDs and fault trees.Figure 4.18 RBD for the fire detector system.Figure 4.19 Component 2 is irrelevant.Figure 4.20 Example structure.Figure 4.21 Redundancy at system level.Figure 4.22 Redundancy at component level.Figure 4.23 Bridge structure.Figure 4.24 2oo3 structure represented as a series structure of the minimal ...Figure 4.25 The bridge structure represented as a parallel structure of the ...Figure 4.26 The bridge structure represented as a series structure of the mi...Figure 4.27 The structure of the bridge structure.Figure 4.28 The structure of the bridge structure.Figure 4.29 RBD.Figure 4.30 Structure of modules.Figure 4.31 The three substructures.Figure 4.32 Module II.Figure 4.33 Two prime modules.Figure 4.34 The main BN symbols.Figure 4.35 (a) Linear, (b) converging, and (c) diverging BN with three node...Figure 4.36 BN for a system of two independent components and .Figure 4.37 BN for a 2oo3 structure of three components , , and .Figure 4.38 A simple fault tree and the corresponding BN.Figure 4.39 Hydraulically operated gate valve (Problem 4.2).Figure 4.40 RBD for Problem 4.4.Figure 4.41 RBD for Problem 4.6.Figure 4.42 Lubrication system on a ship engine (Problem 4.7).Figure 4.43 RBD for Problem 4.11.Figure 4.44 Fault tree for Problem 4.12.Figure 4.45 RBD for Problem 12.Figure 4.46 RBD for Problem 4.13.Figure 4.47 RBD for Problem 4.14.

5 Chapter 5Figure 5.1 The state variable and the time‐to‐failure of an item.Figure 5.2 Relative frequency distribution (histogram) (a) and empirical sur...Figure 5.3 Probability density function, for the time‐to‐failure .Figure 5.4 The distribution function (fully drawn line) together with the ...Figure 5.5 Illustration of the integral calculation of the probability to fa...Figure 5.6 The survivor function .Figure 5.7 Empirical bathtub curve.Figure 5.8 The bathtub curve.Figure 5.9 Location of the MTTF, the median lifetime, and the mode of a dist...Figure 5.10 The survivor function , the probability density function , and...Figure 5.11 The residual lifetime of an item that is still functioning at ti...Figure 5.12 The survivor function (fully drawn line), the conditional surv...Figure 5.13 The function (5.38) in Example 5.2.Figure 5.14 Probability density function (fully drawn line) and distributi...Figure 5.15 The failure rate function of the mixture of two exponential dist...Figure 5.16 The failure rate function of an item with stepwise constant fail...Figure 5.17 The gamma probability density for selected values of , .Figure 5.18 Survivor function for the gamma distribution for selected values...Figure 5.19 Failure rate function of the gamma distribution for selected val...Figure 5.20 The probability density function of the Weibull distribution for...Figure 5.21 Failure rate function of the Weibull distribution, and four di...Figure 5.22 The proportionality factor of MTTF as a function of .Figure 5.23 The scaled mean residual lifetime function MRL /MTTF for the W...Figure 5.24 as a function of , the number of independent and identical co...Figure 5.25 The normal distribution with mean and standard deviation .Figure 5.26 Failure rate function of the standard normal distribution wit me...Figure 5.27 Probability density of the lognormal distribution with and . ...Figure 5.28 Failure rate function of the lognormal distribution with and Figure 5.29 Wöhler or – diagram.Figure 5.30 The probability density of .Figure 5.31 The probability density of for some selected values of and Figure 5.32 The binomial distribution ( ).Figure 5.33 Probability density (Problem 5.19 5.19).

6 Chapter 6Figure 6.1 RBD of a simplified automatic alarm system for gas leakage.Figure 6.2 The failure rate function of a series structure of three independ...Figure 6.3 Transition diagram for a parallel structure of independent and ...Figure 6.4 The probability density function of a parallel structure with two...Figure 6.5 The failure rate for a parallel structure of two independent comp...Figure 6.6 Failure rate function for a parallel structure of two independent...Figure 6.7 The failure rate function for a 2oo3 structure of independent a...Figure 6.8 The survivor functions of the three structures in Table 6.1 ( )....Figure 6.9 Standby system with items.Figure 6.10 Standby system with 2 items.Figure 6.11 States of a repairable item.Figure 6.12 The availability of an item with failure rate and repair rat...Figure 6.13 RBD for Example 6.16.Figure 6.14 RBD for Example 6.20, drawn as a series structure of its three M...Figure 6.15 State variables for fault tree AND and OR gates.Figure 6.16 Fault trees with single AND‐gate and single OR‐gate.Figure 6.17 A structure represented as a series structure of the minimal cut...Figure 6.18 RBD for the bridge structure.Figure 6.19 BDD deduced from a truth table.Figure 6.20 Simple BN with two nodes.Figure 6.21 Linear BN with three nodes.Figure 6.22 BN with Three Nodes.Figure 6.23 BN for a simple system of two components.Figure 6.24 Generation of a random variable with distribution .Figure 6.25 System of two production items.Figure 6.26 Simulation of the performance of the production system in Figure...Figure 6.27 RBD for Problem 6.7 6.7.Figure 6.28 Fault tree for Problem 6.9 9.

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).

13 Chapter 13Figure 13.1 Sketch of a simple SIS.Figure 13.2 Failure mode classification.Figure 13.3 The state of a periodically tested item with respect to DU fai...Figure 13.4 The safety unavailability of a periodically tested item.Figure 13.5 PFD of a parallel structure of two items with staggered testing...Figure 13.6 Contributions to safety unavailability.Figure 13.7 Critical situation – fire detector system. is the state of the...Figure 13.8 A 2oo3:G sensor system.Figure 13.9 A process shutdown valve with fail‐safe hydraulic actuator.Figure 13.10 Explicit modeling of a CCF for a system with two pressure senso...Figure 13.11 State transition diagram for the failure process described by H...Figure 13.12 Smoke detector system (simplified).Figure 13.13 Sketch of an emergency shutdown system.

14 Chapter 14Figure 14.1 Main concepts of statistical inference.Figure 14.2 Time‐to‐failure and Observed Survival Time.Figure 14.3 An observed dataset (a), and the same dataset shifted to time 0 ...Figure 14.4 Typical dataset for field data.Figure 14.5 Histogram of the dataset in Table 14.1 with different numbers of...Figure 14.6 A sample density plot of the dataset in Table 14.1.Figure 14.7 Empirical survivor function (survival curve) for the dataset in ...Figure 14.8 Empirical survivor function (survival curve) for the dataset in ...Figure 14.9 Normal Q–Q plot for the dataset in Table 14.1, made with the R f...Figure 14.10 Exponential Q–Q plot for the dataset in Table 14.1, made with t...Figure 14.11 Likelihood function for the binomial distribution ( and ).Figure 14.12 The negative log‐likelihood function for the binomial distribut...Figure 14.13 Likelihood function for the exponential distribution in Example...Figure 14.14 Output from a simple script using WeibullR.Figure 14.15 Kaplan–Meier plot for the data in Example 14.9. Made with R.Figure 14.16 Kaplan–Meier plot of the dataset in Example 14.9 with 90% confi...Figure 14.17 Nelson–Aalen plot (linear scale).Figure 14.18 Nelson–Aalen plot (log 10 scale).Figure 14.19 TTT plot of the data in Example 14.13.Figure 14.20 The TTT transform of the distribution .Figure 14.21 Scaled TTT transform of the exponential distribution (Example 1...Figure 14.22 Scaled TTT transforms of the Weibull distribution for some sele...Figure 14.23 TTT plots indicating (a) increasing failure rate (IFR), (b) dec...Figure 14.24 TTT plot of the ball bearing data in Example 11.11 together wit...Figure 14.25 Determination of the optimal replacement age from the scaled TT...Figure 14.26 Determination of the optimal replacement age from a TTT plot.Figure 14.27 Failure rate function for the PH model. The baseline failure ra...

15 Chapter 15Figure 15.1 The frequentist data analysis process.Figure 15.2 The Bayesian data analysis process.Figure 15.3 Prior beta density with parameters and .Figure 15.4 The gamma distribution with parameters and .Figure 15.5 Loss function.

16 Chapter 16Figure 16.1 Pumps, boundary definition in OREDA.Figure 16.2 Reliability prediction timeline.Figure 16.3 Estimates from field data sources.Figure 16.4 The real failure rate and the erroneously estimated constant fai...Figure 16.5 Average failure rates estimated in two different observation win...Figure 16.6 Estimates and confidence intervals for inhomogeneous samples.Figure 16.7 Example of a reliability data dossier.