# Reliability and risk research

New concepts and models in reliability and risk

### Research highlights

- Creating the foundations of the theory of repairable flow networks and networks with disturbed flows. High-speed algorithms for analysis, optimisation and control in real time of repairable flow networks.
- Discovering the existence of closed and dominated flow loops in real networks and developing algorithms for their removal.
- Revealing the drawbacks of the successive shortest-path strategy for minimising the transportation cost from multiple interchangeable origins to multiple destinations and developing the correct alternative.
- Creating the foundations of risk-based reliability analysis – driven by the cost of system failure. Formulation of the principle of risk-based design.
- Creating the theoretical foundations of the maximum risk reduction attained within limited risk-reduction resources.
- Creating the theoretical foundations for evaluating the risk of unsatisfied random demand on a time interval.
- A new reliability measure based on rolling failure-free operation periods.
- Formulation and proof of the upper bound variance theorem regarding the exact upper bound of properties from sampling multiple sources.
- Formulation and proof of the damage factorisation theorem – the necessary and sufficient condition for the validity of the Palmgren-Miner rule.
- An equation for the probability of fracture controlled by random flaws for components with complex shape.
- Theoretical and experimental proof that the Weibull distribution does not describe correctly the probability of failure of materials with flaws and a derivation of the correct alternative.
- A general equation related to reliability dependent on the relative configurations of random variables.
- Revealing the drawbacks of the maximum expected profit criterion in the case of risky prospects containing a limited number of risk-reward bets.
- Formulation and proof of the damage factorisation theorem – the necessary and sufficient condition for the validity of the Palmgren-Miner rule.
- An equation for the probability of fracture controlled by random flaws for components with complex shape.
- Theoretical and experimental proof that the Weibull distribution does not describe correctly the probability of failure of materials with flaws and a derivation of the correct alternative.
- A general equation related to reliability dependent on the relative configurations of random variables.
- Revealing the drawbacks of the maximum expected profit criterion in the case of risky prospects containing a limited number of risk-reward bets.