Uncertainty  quantification  is a  new  paradigm in industrial  analysis  and  design  as it aims at taking into  account the presence of numerous uncertainties affecting  the behavior  of   physical  systems. Dominating  uncertainties  can be either be operational (such as  boundary conditions) and//or  geometrical  resulting   from  unknown  properties,  such  as  tip  clearances  of  rotating fan blades  or from manufacturing tolerances.   Other uncertainties are related to models, such  as turbulence or combustion should also be  considered,  or to numerical related errors. Whether bringing  a  new   product  from  conception  into  production  or  operating  complex  plant   and production processes  ,  commercial success rests on careful management and control of risk in the face of many interacting uncertainties.
Historically,  chief   engineers and   project  managers   have estimated and managed risk using mostly human  judgment founded  upon years of experience and heritage.  As the  21st  century begins to  unfold,  the design and  engineering  of  products  as well  as the  control of plant and process are increasingly relying on computer models and simulation.

This  era  of  virtual  design and  prototyping  opens  the  opportunity   to  deal   with  uncertainty in a systematic formal way by which sensitivities to various uncertainties can  be  quantified and  understood, and designs and processes optimized so as to be robust against such uncertainties.

After several successful  Courses on  the applications of UQ,  ERCOFTAC  decided,  based   on requests  from   many    participants,   to   focus   the   present   Course   on   the   mathematical methodologies  of  UQ,   enabling  the   participants  to develop an in-depth understanding of the main methods such as: spectral, including polynomial chaos methods; methods of moments and Monte-Carlo methodologies.