Introduction
      
        Sensitivity Analysis = the study 
        of how uncertainty in the output 
        of a model can be apportioned to 
        different input parameters
      
        Local sensitivity = focus on 
        sensitivity at a particular set of 
        input parameters, usually using 
        gradients or partial derivatives
      
        Global or domain-wide sensitivity 
        = consider entire range of inputs
               Typical Approach
               
                  Consider a Point Reactor Kinetics 
                  problem
                                        1.8                                      
                                                                     =0.08
   dP                              1.7                           increased by 50%
        0          P(t)C(t)
   dt                                1.6
                  
   dC                                  1.5
        P(t) C(t)                   )
                                       t1.4
                                       (
   dt                                 P
  P(0) P 1                            1.3
            0                           1.2
            P
  C(0)        0                        1.1
                                       1 
                                         0     0.5    1     1.5    2     2.5    3
                                                           time (s)
                       Results
                        
                             P(t) normalized to P0
                        
                             Mean lifetime normalized to 
                                                                      -3
                            baseline value (0.001 s)
                                                                 3 x 10
                        
                             t=3 s
                                                                 2
                                                               ) 1
                                                               t
                                                               (
                                                               P
                                                                
                                                               n
                                                               i
                                                                
                                                               e
                                                               g
                                                               n 0
                                                               a
                                                               h
                                                               c
                                                                
                                                               e
                                                               v
                                                               i
                                                               t
                                                               a
                                                               l-1
                                                               e
                                                               r
                                                                -2
                                                                -3
                                                                 -0.1       -0.05         0          0.05         0.1        0.15
                                                                                         relative change in 
             Results
              
                P(t) normalized to P0
              
                Mean lifetime normalized to 
                baseline value (0.001 s)
                                   0.02
                                 0.015
                t=0.1 s
                                   0.01
                                 )
                                 t
                                 (
                                 P
                                  
                                 n
                                 i
                                  0.005
                                 e
                                 g
                                 n
                                 a
                                 h
                                 c
                                    0
                                 e
                                 v
                                 i
                                 t
                                 a
                                 l
                                 e
                                 r-0.005
                                  -0.01
                                  -0.015
                                    -0.1  -0.05   0     0.05   0.1    0.15
                                                 relative change in 
                 Putting all on one chart – 
                 t=0.1 s
                         0.025                                            
                                                                       
                          0.02                                         
                         0.015                                         
                       )                                               0
                       t
                       (  0.01
                       P
                        
                       n
                       i
                        
                       n
                       o 0.005
                       i
                       t
                       a
                       i
                       r
                       a
                       v    0
                        
                       s
                       s
                       e
                       l -0.005
                       n
                       o
                       i
                       s
                       n
                       e -0.01
                       m
                       i
                       d
                         -0.015
                         -0.02
                         -0.025 
                           -0.2  -0.15  -0.1  -0.05   0    0.05   0.1   0.15
                                       dimensionless variation in input variable