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In greater detail, Sij represents the likelihood that the target unit j can sustain the chain of accidents by involving a generic further unit k in its secondary accident. The value of Sij may range between 0 and 1. When Sij = 0, the chain of accidents gets blocked at unit j because a secondary accident occurring in that unit cannot extend its effects beyond those already generated by the primary accident. The interaction between units i and j remains thus confined within the damage to those units, and the domino effect does not propagate any further. When Sij > 0, the secondary event may instead continue the chain of accidents by affecting further process units. To determine the value of Sij, two cases should be analyzed.
Figure 3 — Effect Amplification Factor Schematization.
Case 1: The damage area of unit j is entirely within the damage area of unit i. In this case, shown in Figure 3a), Sij = 0 when there is no other unit k within the damage area of unit j or when the probability of direct damage to unit k from the primary accident in unit i is greater than the probability of damaging unit k as a result of the secondary accident in unit j, i.e., when pik > pij pjk. If instead pik < pij pjk, then Sij = 1.
Case 2: The damage area of unit j is partly outside the damage area of unit i. In this case, Sij = 1 if there is some other unit k outside the damage area of unit i, but within the damage area of unit j, as shown in Figure 3 b). Sij = 0 if there is no other unit k outside the damage area of unit i but within the damage area of unit j, as shown in Figure 3c). When the damage area of unit j extends outside the damage area of unit i, but additional units k are within the damage area of both units, then Case 1 applies.
In general, Sij is a weighted average of the values it may assume when considering the different accidental events
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(25)
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The damage magnitude coefficient for unit j relates to the magnitude of effects of the secondary accident. The higher this magnitude, the higher the likelihood that the secondary accident triggers a tertiary accident, and so on. The magnitude of a secondary accident is intuitively correlated to the kind and amount of hazardous substance contained in unit j, and its process conditions (temperature, pressure, etc.). Therefore, for the sake of simplicity we will assume Mj equal to the DOW Fire and Explosion Index [Ref. 24] computed for unit j. In the present method, it is not necessary to explicitly consider the whole chain of events triggered from unit i. The effects of a tertiary event caused by the secondary event in unit j are covered by the case when unit j is assumed to be the source unit instead of a target unit, and so on. The mitigation factor accounts for any protective measure that has been applied to unit j to reduce the consequences of the secondary event. It may be computed as
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(26)
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The Ck coefficients adopted by the DOW Fire and Explosion Index procedure can be utilized here.
The overall Domino Source Index DSIi for the generic source unit i is then
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(27)
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Instead, the Domino Target Index DTIj is
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(28)
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The indices DSIi and DTIj enable one to assess the criticality of a process unit with respect to its dangerousness or vulnerability so that specific preventive or protective mitigation measures may be taken.
Finally, the overall Domino Effect Potential (DEP) Index for the entire plant is computed as
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(29)
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where NS is the number of source units having DSI  0.
It should also be pointed out that while the chain of accidents is an intrinsically dynamic phenomenon, the proposed analysis approach, which does not attempt to model the time-dependent sequence of accidents along each singular potential chain, nor the absolute probability of a chain of accidents to occur, gives instead a static assessment of the overall plant-related or process unit-related domino risk.
In order to define a meaningful, although empirical, ranking scale, the minimum and maximum score values were selected to span from a low domino risk condition to a high one. A low-risk situation was considered as the best case, where only two units are involved by the primary accident, having Pij = 0.1, a low value of the damage magnitude coefficient (M = 90) and only one target unit sustaining the chain of accidents. A high risk was considered as the worst case where up to six target units are involved with Pij = 1, M = 140 and three units sustaining the chain of accidents. The resulting ranking scale is shown in Table 1.
Table 1 — Process Unit Risk Ranking Scale.
| DSIi, DTIj, DEP Score |
Risk Level |
| 1-70 |
Low |
| 71-225 |
Moderate |
| 226-392 |
Medium |
| 393-630 |
High |
| > 630 |
Severe |
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