### How Escalation Factors Work in Bowtie Modelling

Escalation Factors are conditions that lead to increased risk by defeating or reducing the effectiveness of safeguards.

– The integrity (I) of Risk Control 1 is 99 %, i.e. I = 0.99

– The gap of Risk Control 1 is the amount that can come through the Risk Control, i.e. 1 – I = 1 – 0.99 = 0.01

– The Risk Reduction Factor (RRF) of Risk Control 1 is the reciprocal of the gap,

– i.e. RRF = 1/gap = 1/0.01 = 100

– The ‘Outgoing Frequency’ of Risk Control 1 is therefore = 1.0 × 0.01 = 0.01

#### Examples of different integrity values:

– If I = 0, Outgoing frequency = 1.0 × (1-0) = 1.0

– If I = 1, Outgoing frequency = 1.0 × (1-1) = 0

– If I = 0.25, Outgoing frequency = 1.0 × (1-0.25) = 0.75

An ‘escalation factor’ can be added to a risk control. This escalation factor undermines the effectiveness of the risk control, and therefore causes its integrity to be reduced.

For example:

– Baseline integrity of Risk Control 1 = 0.99

– New effective integrity of Risk Control 1 = 0.99 × (1 – Escalation Factor Severity) = 0.99 × (1 – 0.7) = 0.297

– The gap of Risk Control 1 is now: 1 – 0.297 = 0.703

– The Outgoing Frequency of Risk Control 1 is therefore = 1.0 × 0.703 = 0.703

– With the RRF = 1/0.703 = 1.42

#### Examples of different ‘Esc Factor Freq.’ values:

– If Escalation Factor Severity = 0, effective integrity of Risk Control 1 = 0.99 × (1-0) = 0.99 (i.e. escalation factor has no effect on Risk Control 1).

– If Escalation Factor Severity = 0.25, effective integrity of Risk Control 1 = 0.99 × (1-0.25) = 0.7425 (i.e. the escalation factor slightly undermines the integrity of Risk Control 1).

– If Escalation Factor Severity = 1, effective integrity of Risk Control 1 = 0.99 × (1-1) = 0 (i.e. the escalation factor completely undermines the integrity of Risk Control 1).

– Another escalation factor can be added in parallel to Risk Control 1.

The amount by which the two escalation factors undermine Risk Control 1 is the combination of the two effects.

i.e. Baseline integrity of Risk Control 1 = 0.99

– New effective integrity of Risk Control 1 = 0.99 × ((1 – Escalation Factor 1 Severity) × (1 – Escalation Factor 2 Severity)) = 0.99 × ((1 – 0.7) × (1 – 0.5)) = 0.99 × 0.15 = 0.1485

– The gap of Risk Control 1 is now: 1 – 0.1485 = 0.8515

– The Outgoing Frequency of Risk Control 1 is therefore = 1.0 × 0.8515 = 0.8515

– With the RRF = 1/0.8515 = 1.17 – the RRF is reduced when the two escalation factors are both undermining the Risk Control.

– Escalation Controls can also be present on escalation factors.

This Escalation Control 1 will reduce the extent to which Risk Control 1 is undermined by Escalation Factor 1.

The severity of Escalation Factor 1 will be modified as follows:

– Baseline Escalation Factor 1 Severity = 0.7

– Modified Escalation Factor 1 Severity = 0.7 × (1-0.7) = 0.21 (since the integrity of Escalation Control 1 is 70 %, the severity here has been reduced compared to the previous example – this is due to the Escalation Control).

– New effective integrity of Risk Control 1 = 0.99 × ((1 – Modified Escalation Factor 1 Severity) × (1 – Escalation Factor 2 Severity)) = 0.99 × ((1 – 0.21) × (1 – 0.5)) = 0.99 × 0.395 = 0.391

– The gap of Risk Control 1 is now: 1 – 0.391 = 0.609

– The Outgoing Frequency of Risk Control 1 is therefore = 1.0 × 0.609 = 0.609

– With the RRF = 1/0.609 = 1.64

Finally, escalation factors can be added on the escalation controls to escalation factors. For example:

– The severity of Escalation Factor 3 will undermine the integrity of Escalation Control 1.

– The severity of the Escalation Factor 1 will be modified as follows:

– Baseline Escalation Factor 1 Severity = 0.7

– New effective Escalation Control 1 Integrity = (0.7 × (1-0.2)) = 0.56

– Modified Escalation Factor 1 Severity = 0.7 × (1 – Effective Escalation Control 1 Integrity) = 0.7 × (1 – 0.56) = 0.308 (i.e. the severity has been increased compared to the previous example – this is due to the escalation factor).

– New effective integrity of Risk Control 1 = 0.99 × ((1 – Modified Escalation Factor 1 Severity) × (1 – Escalation Factor 2 Severity)) = 0.99 × ((1 – 0.308) × (1 – 0.5)) = 0.99 × 0.346 = 0.343

– The gap of Risk Control 1 is now: 1 – 0.343 = 0.657

– The Outgoing Frequency of Risk Control 1 is therefore = 1.0 × 0.657 = 0.657

– With the RRF = 1/0.657 = 1.52