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
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 