Table 1 Evaluation of the probability of the corresponding individual SN states for a given WSN state=X s , X t , X p , X b }, where “true” and “false” are denoted by 1 and 0, respectively, and \( {\lambda}_s^i, \) \( {\lambda}_t^i, \) \( {\lambda}_p^i \), \( {\lambda}_b^i \) are the probabilities of failure of the four main components of SN s i
s i ∈ X s | s i ∈ X t | s i ∈ X p | s i ∈ X b | Prob( x i (π)) |
|---|---|---|---|---|
0 | 0 | 0 | 0 | (1 − \( {\lambda}_s^i \)) (1 − \( {\lambda}_t^i \)) (1 − \( {\lambda}_p^i \)) (1 − \( {\lambda}_b^i \)) |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | (1 − \( {\lambda}_s^i \)) \( {\lambda}_t^i \) (1 − \( {\lambda}_p^i \)) (1 − \( {\lambda}_b^i \)) |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | \( {\lambda}_s^i \) (1 − \( {\lambda}_t^i \)) (1 − \( {\lambda}_p^i \)) (1 − \( {\lambda}_b^i \)) |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | \( {\lambda}_s^i{\lambda}_t^i \) (1 − \( {\lambda}_p^i \)) (1 − \( {\lambda}_b^i \)) |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | \( {\lambda}_p^i \) (1 − \( {\lambda}_b^i \)) |
1 | 1 | 1 | 1 | \( {\lambda}_b^i \) |