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Table 11 Expected profit in the presence of both Copula and Fault tolerance factor (\(C=0.1)\)

From: Availability and cost–benefit analysis of a fault tolerant series–parallel system with human-robotic operators

Time

\(\boldsymbol{E}_{\boldsymbol{p}}\left(\boldsymbol{t}\right)\)

\(\boldsymbol{{F}_{2}=0.06}\)  

\(\boldsymbol {C=0.1}\)

\(\boldsymbol{E}_{\boldsymbol{p}}\left(\boldsymbol{t}\right)\)

\(\boldsymbol{{F}_{2}=0.05}\)  

\(\boldsymbol {C=0.1}\)

\(\boldsymbol{E}_{\boldsymbol{p}}\left(\boldsymbol{t}\right)\)

\(\boldsymbol{{F}_{2}=0.04}\)  

\(\boldsymbol {C=0.1}\)

\(\boldsymbol{E}_{\boldsymbol{p}}\left(\boldsymbol{t}\right)\)

\(\boldsymbol{{F}_{2}=0.03}\)  

\(\boldsymbol {C=0.1}\)

\(\boldsymbol{E}_{\boldsymbol{p}}\left(\boldsymbol{t}\right)\)

\(\boldsymbol{{F}_{2}=0.02}\)  

\(\boldsymbol{C=0.1}\)

\(\boldsymbol{E}_{\boldsymbol{p}}\left(\boldsymbol{t}\right)\)

\(\boldsymbol{{F}_{2}=0.01}\)  

\(\boldsymbol {C=0.1}\)

0

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1

0.9371

0.9471

0.9571

0.9671

0.9771

0.9871

2

1.8730

1.8930

1.9130

1.9330

1.9530

1.9730

3

2.8089

2.8389

2.8689

2.8989

2.9289

2.9589

4

3.7447

3.7847

3.8247

3.8647

3.9047

3.9447

5

4.6806

4.7306

4.7806

4.8306

4.8806

4.9306

6

5.6164

5.6764

5.7364

5.7964

5.8564

5.9164

7

6.5523

6.6223

6.6923

6.7623

6.8323

6.9023

8

7.4881

7.5681

7.6481

7.7281

7.8081

7.8881

9

8.4161

8.5061

8.5961

8.6861

8.7761

8.8661

10

9.3061

9.4061

9.5061

9.6061

9.7061

9.8061