Sensitivity of OPI rankings to alternative component weightings (cell entries are ranks; OPIk = Fkα × Nkβ × Vkγ)
| Failure cluster | Equal (1/1/1) | Freq.↑ (2/1/1) | Neg.↑ (1/2/1) | Vis.↑ (1/1/2) | Freq.↓ (0.5/1/1) | Sev. (0.5/2/1) |
|---|---|---|---|---|---|---|
| Comfort & Cleanliness | 1 | 1 | 1 | 1 | 1 | 4 |
| Staff & Communication | 2 | 3 | 2 | 2 | 3 | 3 |
| Ticketing & Refunds | 3 | 2 | 5 | 3 | 5 | 5 |
| Delay & Disruption | 4 | 4 | 3 | 5 | 4 | 2 |
| Safety & Security | 5 | 5 | 4 | 4 | 2 | 1 |
| Crowding & Capacity | 6 | 6 | 6 | 6 | 6 | 6 |
| Accessibility | 7 | 7 | 7 | 7 | 7 | 7 |
| Spearman ρ vs. baseline | 1.000 | 0.964 | 0.893 | 0.964 | 0.750 | 0.393 |
| Failure cluster | Equal (1/1/1) | Freq.↑ (2/1/1) | Neg.↑ (1/2/1) | Vis.↑ (1/1/2) | Freq.↓ (0.5/1/1) | Sev. (0.5/2/1) |
|---|---|---|---|---|---|---|
| Comfort & Cleanliness | 1 | 1 | 1 | 1 | 1 | 4 |
| Staff & Communication | 2 | 3 | 2 | 2 | 3 | 3 |
| Ticketing & Refunds | 3 | 2 | 5 | 3 | 5 | 5 |
| Delay & Disruption | 4 | 4 | 3 | 5 | 4 | 2 |
| Safety & Security | 5 | 5 | 4 | 4 | 2 | 1 |
| Crowding & Capacity | 6 | 6 | 6 | 6 | 6 | 6 |
| Accessibility | 7 | 7 | 7 | 7 | 7 | 7 |
Note(s): Cell entries are ranks. Column headings denote the exponent vector (α/β/γ): Equal = equal weighting; Freq.↑ = frequency-weighted; Neg.↑ = negativity-weighted; Vis.↑ = visibility-weighted; Freq.↓ = frequency-discounted; Sev. = severity-oriented. Ranks are derived from the max-normalized components reported in Table 6. ρ is the Spearman rank correlation between the continuous index values under each specification and those under the equal-weight baseline.
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