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.
