# How Escalation Factors Work in Bowtie Modelling

Nelson Kho

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

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