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Professor Philip Scarf

Professor Philip Scarf

Honorary Professor


Phil is Professor of Management Mathematics at Cardiff Business School, Cardiff University. He holds visiting professorships in Industrial Engineering at the Federal University of Pernambuco, Brazil, and in Statistics at King Saud University, Riyadh, Saudi Arabia. He has wide ranging interests in the application of Statistics and Operational Research in reliability and maintenance, manufacturing informatics, autonomous systems, corrosion science, and sport. He has published 87 articles in refereed journals and graduated 20 PhD students as first supervisor.

He organizes conferences on Maintenance Modelling ( and Mathematics in Sport (

He has advised the FA Premier League regarding football player rating, having developed the EA Sports Player Performance Index with Ian McHale, and has held EPSRC grants relating to development of optimum strategy in track cycling (EP/F005792/1), modelling of the training process (EP/F006136/1), Bayesian calculations in maintenance modelling (GR/L92716), and  condition based maintenance of production plant (GR/L20801). He was co-investigator on the EPRSC project “HEAD: Holistic evidence and design (HEAD): sensory impacts, practical outcomes”(EP/J015709/1), and on the EU FP7 Marie Curie ITN: “SMART-E: Sustainable Manufacturing through Advanced Robotics Training – Europe” (€3.9m, 2013-17), supervising an early-stage researcher in “Mathematical modelling for a self-healing robotic cell (maintenance robot)”.

Phil is co-editor-in-chief of the IMA Journal of Management Mathematics (

Outside academia, Phil’s primary hobby is sport. He is an adventure racer with Team Endurancelife and competes all over the world in expedition races. He is World Champion in Rogaining (ultra-orienteering) in the mixed-super-veterans class.



  • Ph.D. (Manchester), ‘Statistical Models in Metallic Corrosion’, NRC sponsored,1989
  • B.Sc. (Sheffield), First Class Honours in ‘Probability and Statistics’, 1984 (final year prize)

Editorial work

  • Co-Editor-in-Chief, IMA Journal of Management Mathematics, 2009→
  • Editorial Board member, Reliability Engineering and System Safety, 2013→
  • Associate Editor, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2016-2019
  • Associate Editor, Journal of Quantitative Analysis in Sports (an American Statistical Society journal), 2014-17

Conferences organised

  • Chair at 4th (2001), 5th (2004), 6th (2007), 7th (2011), 8th (2014), 9th (2016), 10th (2018)  IMA conferences on “Modelling in Industrial Maintenance and Reliability”.
  • Chair at 1st (2007), 2nd (2009), 3rd (2011), 4th (2013), 5th (2015), 6th (2017) “Mathematics in Sport” conferences.
  • Member of local organising committee for RSS 2004 conference.
  • Co-organiser of 11th EURO Summer Institute on “OR Models in Maintenance”, 1995


  • Institute for Mathematics and its Application (Fellow)
  • Operational Research Society
  • Royal Statistical Society (Fellow)
  • Mathsport International (Chair and founding member)
  • EURO Working Group on OR in Sports (founding member)










Industry 4.0 is connected, reconfigurable, and automated. Maintenance must become the same, not least because maintenance costs typically account for 15-60% of the total value of services. Therefore, maintenance must be dynamically planned, it must respond in real time to signals about system state, and it must be able to handle the interactions that exist between sub-systems, and between agents in the maintenance supply chain. In short, maintenance must move towards its automation.

There exist significant challenges for the automation of maintenance. Engineered objects are complex and characterised by structural, economic and wear-related dependencies between sub-systems and components. Thus, both the state and actions taken to improve the state of one component affects other components in the system, and the mathematical models that adequately describe these interactions and the data required to test relevant models are lacking. Furthermore, algorithms for automating decision-making for complex systems that integrates system prognosis with maintenance planning and execution must be developed. Conceptually, such algorithms will form the basis of a maintenance “robot” that will plan maintenance interventions dynamically, just-in-time, and with minimum human intervention. Then, one can then imagine a self-healing system: a system possessing its own maintenance robot that plans replacement, repair and routine maintenance and adjustment, considers operational demand within the planning process, orders and obtains spare parts and tools, and directs maintenance interventions that are safe, economically justified, ‘just-in-time’ and ‘just enough’ to ensure continuity of operation.

My research is focused on solving this “maintenance automation” problem, through collaborations with colleagues at Cardiff University (on joint modelling of spare-parts inventory and maintenance planning), at Federal University of Pernambuco, Brazil (on learning-algorithms for decision-making for maintenance planning), at University of Lorraine, France (on mathematical modelling of interacting wear processes in multi-component systems), and at IDE-Americas, California (on membrane replacement and renovation in reverse-osmosis desalination).

Currently, collaboratively, we have developed a digital twin (DT) of a reverse-osmosis (RO) desalination train, using a multivariate model of wear, calibrated using five years of daily data about the state of membranes of 14 RO trains in a state-of-the-art plant. This DT is being used to plan maintenance interventions in RO trains (cleaning, replacement of membranes). The next steps are to refine the multivariate wear-model, to use the DT as an environment in which to train learning-algorithms, so that maintenance planning (membrane replacement at least) can be automated in the plant and at similar plant worldwide, and to integrate inventory planning with maintenance automation, so that spare-parts ordering can be automated.