Simplification of State Transition Diagrams in Average Unavailability Analysis by Using Generalized Perturbation Theory

Table 2

Derivatives for the edge cutoff criterion.

Case	Failure (𝑗→𝑖)	Failure rate; 𝜆 (hr^−1)	𝜕𝑄𝜕𝑎^′𝑖𝑗	Repair (𝑗→𝑖)	Repair rate; 𝜇 (hr^−1)	𝜕𝑄𝜕𝑎𝑖𝑗	Condition satisfied	Cut
1	2→6	1.0𝐸−4	8.11𝐸−4	19→6; 21→6	1.0𝐸−2; 2.0𝐸−2	−4.03𝐸−8; −7.29𝐸−8	Yes	19→6; 21→6
2	3→7	5.0𝐸−4	1.66𝐸−4	20→7; 18→7	2.0𝐸−2	−5.75𝐸−9; −4.56𝐸−9	Yes	20→7; 18→7
3	2→8	8.0𝐸−5	3.49𝐸−4	17→8	2.0𝐸−2	5.57𝐸−9	Yes	17→8
4	1→3	1.0𝐸−4	3.81𝐸−3	9→3	2.0𝐸−2	−1.20𝐸−7	Yes	9→3
5	1→2	5.0𝐸−4	1.52𝐸−2	10→2	1.0𝐸−2	−8.03𝐸−7	Yes	10→2
6	1→3	1.0𝐸−4	3.81𝐸−3	11→3	1.0𝐸−2	−7.35𝐸−8	Yes	11→3
7	4→12	5.0𝐸−4	5.72𝐸−3	17→12	1.0𝐸−2	−6.25𝐸−9	Yes	17→12
8	1→4	8.0𝐸−5	2.27𝐸−3	13→4	1.0𝐸−2	4.41𝐸−7	Yes	13→4
9	1→5	1.0𝐸−5	3.52𝐸−3	14→5	2.0𝐸−2	−7.60𝐸−9	Yes	14→5