Prof Michael Todinov

Professor of Mechanical Engineering


Michael Todinov leads the research and teaching in the area of Engineering Reliability and Risk Management. From the University of Birmingham, he holds a PhD related to mathematical modelling of thermal and residual stresses and a higher doctorate Doctor of Engineering (DEng) which is the engineering equivalent of Doctor of Science (DSc). The higher doctorate was awarded for fundamental contributions in the area of new probabilistic concepts and models in Engineering.

M.Todinov's name is associated with creating the foundations of risk-based reliability analysis (driven by the cost of failure) and the theory of repairable flow networks and networks with disturbed flows. M.Todinov also pioneered research on reliability dependent on the relative configurations of random variables, optimal allocation of fixed budgets to achieve a maximal reduction of technical risk, formulation of generic principles for reduction of technical risk and evaluating the risk of unsatisfied random demand on a time interval.

A sample of M.Todinov's results includes: the discovery of closed and dominated parasitic flow loops in real networks; the proof that the Weibull distribution is an incorrect model for the distribution of breaking strength of materials and deriving the correct alternative of the Weibull model; a theorem regarding the exact upper bound of properties from random sampling of multiple sources; a general equation for the probability of failure of brittle components with complex shape, the formulation and proof of the necessary and sufficient conditions of the Palmgren-Miner rule and Scheil's additivity rule; deriving the correct alternative of the Johnson-Mehl-Avrami-Kolmogorov equation; formulating the dual network theorems for static flows networks and networks with disturbed flows.

M.Todinov’s research has been funded by the automotive industry, nuclear industry, the oil and gas industry and research councils.


Reliability and risk research

Selected publications


  • Todinov M.T.Reliability and Risk Models: Setting quantitative reliability requirements 2nd.ed.,Wiley, (2016).
  • Todinov M.T.Flow Networks: Analysis and optimisation of repairable flow networks, networks with disturbed flows and reliability networks, Elsevier, (2013).
  • Todinov M.T.Risk-based reliability analysis and generic principles for risk reduction, Elsevier, (2007).

Book chapters

  • Todinov M.T., Virtual accelerated life testing of complex systems, In Intelligent Decision Systems in Large-Scale Distributed Environment, Bouvry, Pascal; González-Vélez, Horacio; Kolodziej, Joanna (Eds.), Springer, (2011), pp.293-314.

Journal papers

  • Todinov M., Evaluating the risk of unsatisfied demand on a time interval, Artificial Intelligence Research 5(1) (2016), pp.67-77.
  • Todinov M., The same sign local effects principle and its application to technical risk reduction, accepted by the International Journal of Safety and Reliability (2015).
  • Todinov M.T., Reducing risk through segmentation, permutations, time and space exposure, inverse states, and separation, International Journal of Risk and Contingency Management, 4(3), pp.1-21, (2015).
  • Todinov M.T and S.Same, A fracture condition incorporating the most unfavourable orientation of the crack, International Journal of Mechanics and Materials in Design, 11, pp.243-252 (2015).
  • Todinov M.T., Dominated parasitic flow loops in networks, International Journal of Operations Research, v.11(1), (2014), pp.1-17.
  • Todinov M.T., The Throughput Flow Constraint Theorem and its Applications, International Journal of Advanced Computer Science and Applications, v.5 (3), (2014), pp.11-24.
  • Todinov M.T., Optimal allocation of limited resources among discrete risk-reduction options, Artificial Intelligence Research v.3 (4), (2014), pp.15-27.
  • Todinov M.T., New models for optimal reduction of technical risks, Engineering Optimisation, v.45(6), (2013), pp.719-743.
  • Todinov M., Parasitic flow loops in networks, International Journal of Operations Research, v.10(3), (2013), pp.109-122.
  • Todinov M.T., Fast augmentation algorithms for maximising the output flow in repairable flow networks after edge failures, International Journal of Systems Science, v.44 (10), pp.1807-1830, (2013), Published online 29.03.2012.
  • Todinov M.T., The dual network theorem for static flow networks and its application for maximising the throughput Flow, Artificial Intelligence Research, 2 (1) (2013) pp.81-106.
  • Todinov M.T., Topology optimisation of repairable flow networks for a maximum average availability, Computers and Mathematics with Applications, v.64, (2012), pp.3729-3746.
  • Todinov M.T., Algorithms for minimising the lost flow due to failed components in repairable flow networks with complex topology, International Journal of Reliability and Safety (2012) 6 (4) pp.283-310.
  • Todinov M.T., Topology Optimization of Repairable Flow Networks and Reliability Networks, International Journal of Simulation Systems, Science & Technology, v.11(3), (2011), pp.75-84.
  • Todinov M.T., The cumulative stress hazard density as an alternative of the Weibull model, International journal of Solids and Structures, v.47, (2010), pp.3286-3296.
  • Todinov M.T., Is Weibull distribution the correct model for predicting probability of failure initiated by non-interacting flaws, International Journal of Solids and Structures, v.46, (2009), pp.887-901.
  • Todinov M.T., Robust design using variance upper bound theorem, International Journal of Performability Engineering, v.5(4), (2009), pp.403-420.
  • Todinov M.T., A comparative method for improving the reliability of components, Nuclear Engineering and Design, v.239, (2009), pp.214-220.
  • Todinov M.T., Efficient algorithm and discrete-event solver for stochastic flow networks with converging flaws, International Journal of Reliability and Safety, v.2(4), (2008), pp.286-308.
  • Todinov M.T., Risk-based design based on limiting the probability of system failure at a minimum total cost, International Journal of Risk Management, v.10(2), (2008), pp.104-121.
  • Todinov M.T., Potential benefit, potential loss and potential gain from competing opportunity and failure events, International Journal of Risk Assessment and Management, v.10(1/2), (2008), pp.1-30.
  • Todinov M.T., Selecting designs with high resistance to overstress failure initiated by flaws, Computational Materials Science, v.42, (2008), pp.306-315.
  • Todinov M.T., An equation and a fast algorithm for determining the probability of failure initiated by flaws, Probabilistic Engineering Mechanics v.22, (2007), pp.12-21.
  • Todinov M.T., Reliability analysis based on the losses from failures, Risk Analysis v.26(2), (2006), pp.311-335.
  • Todinov M.T., Reliability value analysis of complex production systems based on the losses from failures, International Journal of Quality, and Reliability Management, v.23(6), (2006), pp.696-718.
  • Todinov M.T., Reliability analysis of complex systems based on the losses from failures, International Journal of Reliability, Quality and Safety Engineering, v.13(2), (2006), pp.127-148.
  • Todinov M.T., Limiting the probability of failure for components containing flaws, Computational Materials Science, v.32, (2005), pp.156-166.
  • Todinov M.T., Reliability analysis and setting reliability requirements based on the cost of failure, International Journal of Reliability, Quality and Safety Engineering,v.11(3), (2004), pp.1-27.
  • Todinov M.T., Uncertainty and risk associated with the Charpy impact energy of multi-run welds, Nuclear Engineering and Design, v.231, (2004), pp.27-38.
  • Todinov M.T., Setting reliability requirements based on minimum failure-free operating periods, Quality and Reliability Engineering International, v.20, (2004), pp.273-287.
  • Todinov M.T., A new reliability measure based on specified minimum distances before the locations of random variables in a finite interval, Reliability Engineering and System Safety, v.86, (2004), pp.95-103.
  • Todinov M.T., Reliability governed by the relative locations of random variables in a finite interval, IEEE Transactions on Reliability, v.53(2), (2004), pp.226-237.
  • Todinov M.T., On Coolen's comments related to statistics of defects in one-dimensional components, Computational Materials Science, v.29, (2004), pp.253-258.
  • Todinov M.T., Statistics of inhomogeneous media formed by nucleation and growth, Probabilistic Engineering Mechanics, v.18, (2003), pp.139-149.
  • Todinov M.T., Modelling consequences from failure and material properties by distribution mixtures, Nuclear Engineering and Design, v.224, (2003), pp.233-244.
  • Todinov M.T., Distribution mixtures from sampling of inhomogeneous microstructures: variance and probability bounds of the properties, Nuclear Engineering and Design, v.214, (2002), pp.195-204.
  • Todinov M.T., Statistics of defects in one-dimensional components, Computational Materials Science, v.24 (2002), pp.430-442.
  • Todinov M.T., Distribution of properties from sampling inhomogeneous materials by line transects, Probabilistic Engineering Mechanics, v.17, (2002), pp.131-141.
  • Todinov M.T., An efficient method for estimating from sparse data the parameters of the impact energy variation in the ductile-to-brittle transition region, International Journal of Fracture v.111, (2001), pp.131-150.
  • Todinov M.T., Estimating the probabilities of triggering brittle fracture associated with the defects in the materials, Materials Science and Engineering A, v.302(2), (2001), pp.235-245.
  • Todinov M.T., Estimating the parameters of the impact energy variation in the ductile-brittle transition region from complete and sparse data sets, Computational Materials Science, v.21, (2001), pp.111-123.
  • Todinov M.T., Probability distribution of fatigue life controlled by defects, Computers and Structures, v.79, (2001), pp.313-318.
  • Todinov M.T., Necessary and sufficient condition for additivity in the sense of the Palmgren-Miner rule, Computational Materials Science, v.21, (2001), pp.101-110.
  • Todinov M.T., On some limitations of the Johnson-Mehl-Avrami-Kolmogorov equation, Acta Materialia, 48 (2000) 4217-4224.
  • Todinov M.T., Probability of fracture initiated by defects, Materials Science and Engineering A A276, (2000), pp.39-47.
  • Todinov M.T., M.Novovic, P.Bowen and J.F.Knott. Modelling the impact energy in the ductile/brittle transition region of C-Mn multi-run welds, Materials Science and Engineering A, A287, (2000), pp.116-124.
  • Todinov M.T., Residual stresses at the surface of automotive suspension springs, Journal of Materials Science, v.35, (2000), pp.3313-3320.
  • Todinov M.T., On some applications of the random transects, Modelling and Simulation in Materials Science and Engineering, v.7, (1999), pp.525-539.
  • Todinov M.T., Fitting impact fracture toughness data in the transition region, Materials Science and Engineering A, A265, (1999), pp.1-6.
  • Todinov M.T., Influence of some parameters on the residual stresses from quenching, Modelling and Simulation in Materials Science and Engineering, v.7, (1999), pp.25-41.
  • Todinov M.T., Maximum principal tensile stress and fatigue crack origin for compression springs, International Journal of Mechanical Sciences, v.41, (1999), pp.357-370.
  • Todinov M.T., Alternative Approach to the problem of additivity, Metallurgical and Materials Transactions B, 29B, (1998), pp.269-273.
  • Todinov M.T., A probabilistic method for predicting fatigue life controlled by defects, Materials Science and Engineering A, A255, (1998), pp.117-123.
  • Todinov M.T., Mechanism for the formation of the residual stresses from quenching, Modelling and Simulation in Materials Science and Engineering, v.6, (1998), pp.273-291.
  • Todinov M.T., A new approach to the kinetics of a phase transformation with constant radial growth rate, Acta Materialia, v.44, (1996), pp.4697-4703.
  • Todinov M.T., J.F.Knott and M.Strangwood. An assessment of the influence of complex stress states on martensite start temperature, Acta Materialia, v.44, (1996), pp.4909-4915.

Michael Todinov


Department of Mechanical Engineering and Mathematical Sciences

Oxford Brookes University
Wheatley Campus
United Kingdom
Tel: +44 (0)1865 483546
Room: R2.19