This advanced course introduces probabilistic design, risk-informed decision making, structural reliability and maintenance under uncertainty for offshore engineering learners. Engineering decisions in offshore and civil applications must account for uncertainty in loads, resistance, failure progression and consequences, and probabilistic methods provide a structured way to do so. The course builds from the definition of risk and the steps of a risk analysis through probability calculus and random variables, decision models and safety criteria, element reliability with Level III, Level II and FORM methods, time-dependent failure and Level I design logic. It then extends to system reliability, fault and event trees, availability and Markov models, inspection and reliability updating, maintenance scheduling and wider applications, finishing with worked practice problems and a problem-solving strategy.
Course at a glance: Duration 20 hours · Self-paced online · 12 sections, 45 lessons, a 198-page downloadable course book
What you will learn
- Define risk and describe the steps of a structured risk analysis.
- Apply probability concepts, random variables, moments and estimation methods to engineering uncertainty.
- Explain decision models under uncertainty, risk perception and societal safety criteria.
- Calculate element reliability using limit states, Level III methods, mean-value methods and FORM.
- Explain time-dependent failure probability, load combinations and Level I partial factor design.
- Analyse system reliability using series and parallel models, bounds, FMEA, event trees and fault trees.
- Apply availability, Markov, inspection-updating and maintenance scheduling concepts to correctable systems.
Inside the course: a high-level summary, section by section.
Defining risk
The course starts with what risk means: a combination of the probability of an undesired event and its consequences. A risk analysis is not just about computing a number; it is a structured process for moving from a physical system to a defensible decision about tolerability. The steps include system description, hazard identification, estimating probabilities and consequences, evaluating risk against criteria and deciding on measures.
Probability foundations
The probability section reviews the axioms of probability, conditional probability and Bayes’ theorem, before introducing random variables and their distributions. Moments, including the expected value, variance, standard deviation, coefficient of variation, skewness and kurtosis, summarise the behaviour of uncertain quantities. Dependence between variables is described through covariance and correlation in random vectors, and functions of random variables show how uncertainty propagates through engineering models. Estimation methods include expert judgement, frequentist approaches such as the method of moments, maximum likelihood and least squares, and Bayesian updating.
Decisions and safety criteria
Decision models under uncertainty compare alternatives using expected costs and utilities. Risk perception explains why society treats voluntary and involuntary risks, and frequent small accidents versus rare large disasters, differently. Safety criteria include individual risk limits and societal risk criteria expressed as frequency-number of fatalities curves, which often penalise large-consequence events more heavily. The Dutch approach to standards for flood defences and hazardous installations is used to show how such criteria are applied in practice.
Element reliability methods
A limit state function separates safe and failure domains, typically expressed as resistance minus load. Level III methods compute the failure probability exactly or by numerical integration and Monte Carlo simulation. Level II methods approximate the problem: the mean-value first-order second-moment method uses only means and variances, which makes it practical when full distribution data are unavailable, and introduces the reliability index. The first-order reliability method transforms variables into standard normal space, locates the design point as the most probable failure point and uses the reliability index and sensitivity factors to show which variables matter most.
Time dependence and Level I design
Failure probability over time depends on how loads and resistance change, for instance through extreme storm events or degradation. Load combinations and life span consider how several time-varying loads act together over a design life. Level I design logic shows how partial safety factors and characteristic values used in codes can be calibrated from reliability analysis, linking everyday design calculations to target reliability levels.
System reliability
Real structures and installations are systems of components. Series systems fail when any component fails, and parallel systems fail only when all components fail; bounds and approximations estimate system reliability when components are correlated. Failure mode and effects analysis provides a systematic qualitative review, while event trees trace how an initiating event can develop, and fault trees break down a top event into combinations of basic failures. Consequence analysis completes the picture.
Time dependence and maintenance theory
For correctable systems, life span, availability and downtime matter as much as failure probability. Markov models describe systems that move between working and failed states with repair. Inspection and reliability updating show how inspection results, including the probability of detecting a defect, can be used with Bayesian methods to update estimates of structural condition.
Scheduling and maintenance
Scheduling under uncertainty considers how to plan maintenance when deterioration rates are uncertain. Corrective measures and cost balance the cost of inspection, repair and failure, and maintenance strategy explains the choice between corrective, time-based, condition-based and risk-based approaches.
Application areas and practice
Applications span structural safety, offshore installations, flood defences, management and quality systems and broader technical domains. Worked practice problems cover decision and safety analysis, FORM and element reliability, and system and maintenance problems, ending with a problem-solving strategy that helps learners structure unfamiliar reliability problems.
Why this matters in practice
Offshore and coastal infrastructure must be safe, economical and defensible to regulators and the public. Probabilistic design gives engineers a rational basis for choosing safety factors, comparing designs, justifying life extension and planning inspection and maintenance. It also helps engineers communicate risk transparently. As industry moves towards risk-based inspection and performance-based standards, reliability methods are increasingly part of everyday engineering practice rather than a specialist niche. Engineers who understand where partial factors come from are better able to judge when a code applies, when a site-specific assessment is justified and how much benefit can be gained from better data. Reliability thinking also encourages honest treatment of uncertainty, helping project teams focus investigation and monitoring on the variables that genuinely drive risk.
Key takeaways
You leave able to structure a risk analysis, model uncertainty with random variables, apply Level I, II and III reliability methods including FORM, analyse system reliability with fault and event trees and use reliability concepts to plan inspection and maintenance.
How you study
The course is delivered fully online and is self-paced, so you can fit roughly 20 hours of study around professional commitments. Lessons combine clear explanation with examples, diagrams and short interactive checks, and the main sections end with graded quizzes (9 in total) so you can confirm you can apply each method before moving on. A 198-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Risk Analysis Foundations: Why Probabilistic Design Matters; Defining Risk; Steps in a Risk Analysis
- Probability Calculus: Probability Models and Axioms; Random Variables and Moments; Dependence and Random Vectors; Functions and Estimation
- Decision Making and Safety Standards: Decision Models Under Uncertainty; Risk Perception and Safety Criteria; Dutch Standards and Case Decisions
- Element Reliability Methods: Limit States and Failure Domains; Level III Methods; MVFOSM and Reliability Index; FORM and Design Point Analysis
- Level I and Time Dependence: Failure Probability Over Time; Load Combinations and Life Span; Level I Design Logic
- System Reliability: Serial and Parallel Systems; Bounds and Approximation; FMEA and Event Trees; Fault Trees and Consequences
- System Time Dependence and Maintenance Theory: System Life Span and Availability; Markov Models for Correctable Systems; Inspection and Reliability Updating
- Scheduling and Maintenance of Correctable Systems: Scheduling Under Uncertainty; Corrective Measures and Cost; Maintenance Strategy and Inspections
- Application Areas: Structural Safety Applications; Management and Quality Applications; Broader Technical Domains
- Worked Exam Practice: Decision and Safety Practice; FORM and Element Practice; System and Maintenance Practice; Exam Strategy and Review
- Summary: Key Takeaways
Who this course is for
This advanced course is for engineering graduates and practising engineers in offshore, structural, coastal and marine engineering, risk and integrity management, and asset management. A background in engineering mathematics and basic statistics is assumed.
Frequently asked questions
How long does Probabilistic Design take?
The course is designed for about 20 hours of study. It is self-paced and fully online, so you can spread it over a few weeks or complete it more quickly.
What is covered?
The course is organised into 12 sections with 45 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 198-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (9 in total, with a pass mark of 80%). The quizzes test understanding of the concepts and methods explained in the lessons rather than memorisation, and you can review the relevant lessons before attempting them.
Can I record this study for my own professional development?
Yes. The course notebook includes a self-assessment of the course objectives before and after study, a reflection page and a learning log, which you can use to keep your own record of professional development.
Duration: 20 hours
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