Table 7 Case 2 - Results Monte Carlo simulations (N=1000) in case of three normally distributed uncertain parameters (K _m , λ and k _cat) for robustified terminal constraint and objective function with the number of constraint violations, mean values and variances on the objective function and terminal constraint, respectively

α=1.96

\(\bar {J}\)

6.5268

12.996

12.549

8.7702

9.1358

σ _J

0.57543

1.1893

1.15230

0.78540

0.82107

\(\bar {c_{t}}\)

0.69319

1.0106

1.0106

1.1406

1.2099

\(\sigma _{c_{t}}\)

0.18291

0.17462

0.17752

0.27117

0.28089

c _t violation

477 (47.7 %)

15 (1.5 %)

18 (1.8 %)

23 (2.3 %)

13 (1.3 %)

α=1.65

\(\bar {J}\)

6.5268

10.04

9.6011

8.2477

8.5514

σ _J

0.57543

0.88430

0.83741

0.73621

0.76632

\(\bar {c_{t}}\)

0.69319

1.0143

1.0157

1.0339

1.0933

\(\sigma _{c_{t}}\)

0.18291

0.20620

0.21414

0.25176

0.26120

c _t violation

477 (47.7 %)

31 (3.1 %)

39 (3.9 %)

53 (5.3 %)

34 (3.4 %)