Marvin Rausand - System Reliability Theory

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 5.195.19).

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 6.76.7.Figure 6.28 Fault tree for Problem 6.99.