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1-9 Risk Tolerance/Acceptance and Risk Matrix

Risk tolerance or acceptance is defined as “the maximum level of risk of a particular technical process or activity that an individual or organization accepts to acquire the benefits of the process or activity.”6 We cannot eliminate risk entirely—all activities inevitably involve risk. Indeed, people accept risks many times during their daily activities. For instance, simply crossing the street involves a risk assessment as to where and when to cross. People accept risks based on their perceived risk—which may or may not be the actual risk. The risk accepted is voluntary based on the perceived risk, while any additional actual risk not perceived will be involuntary.

Engineers must make every effort to minimize risks within reasonable constraints. No engineer should ever design a process that he or she knows will result in certain human loss or injury. For a chemical plant, at some point in the design stage or at every point in the operation of the plant, the corporation (this decision involves both the workers and management) must determine whether the risks are acceptable. The risk acceptance must be based on more than just perceived risks.

Risk tolerance may also change with time as society, regulatory agencies, and individuals come to expect more from the chemical industry. As a consequence, a risk that was considered tolerable years ago may now be deemed unacceptable.

A risk matrix is a semi-quantitative method to represent risk and to help companies make risk acceptance decisions. A typical risk matrix is shown in Table 1-14. The consequence or severity of the incident is found in columns 1, 2, and 3, and the likelihood of that incident occurring appears in columns 4 through 7. The incident severity is used to estimate the severity category and the safety severity level. The likelihood level is selected based on the frequency of the incident, as shown in columns 4 through 7. The combination of the severity category row and the likelihood column is used to determine the risk level, A through D.

Table 1-14 Risk Matrix for Semi-Quantitative Classification of Incidents

Risk Matrix

  1. Select the severity from the highest box in either of columns 1, 2, or 3. Read the Category and Safety Severity Level from the same row.

  2. Select the likelihood from columns 4 through 7.

  3. Read the Risk Level from the intersection of the severity row and the likelihood column.

TMEF: Target mitigated event frequency (yr–1).

TQ: Threshold quantity—see Table 1-15.




Expected to happen several times over the life of the plant



Expected to happen possibly once over the life of the plant



Expected to happen possibly once in the division over the life of the plant



Not expected to happen anywhere in the division over the life of the plant



Human health impact


Fire, explosion direct cost ($)


Chemical impact



Safety severity level

0–9 years

10–99 years

≥ 100 years

> 1000 years

Public fatality possible, employee fatalities likely

Greater than

$10 million

≥ 20 × TQ




1 × 10–6

Risk level A

Risk level A

Risk level B

Risk level C

Employee fatality possible, major injury likely

$1 million to< $10 million

9 × to< 20 × TQ

Very serious



1 × 10–5

Risk level A

Risk level B

Risk level C

Risk level D

Lost time injury (LTI) likelya

$100,000 to< $1 million

3 × to< 9 × TQ



TMEF =1 × 10–4

Risk level B

Risk level C

Risk level D

Negligible risk

Recordable injuryb

$25,000 to< $100,000

1 × to< 3 × TQ



TMEF =1 × 10–3

Risk level C

Risk level D

Negligible risk

Negligible risk

Risk level A: Unacceptable risk; additional safeguards must be implemented immediately.

Risk level B: Undesirable risk; additional safeguards must be implemented within 3 months.

Risk level C: Acceptable risk, but only if existing safeguards reduces the risk to as low as reasonably practicable (ALARP) levels.

Risk level D: Acceptable risk, no additional safeguards required.

The severity levels are listed under columns 1, 2, and 3 in Table 1-14. They include human health impacts; direct costs of fire and explosion in dollars; and chemical impacts. The chemical impact is based on a chemical release quantity called a threshold quantity (TQ). Table 1-15 lists TQs for a number of common chemicals.

Table 1-15 Threshold Quantities (TQ) for a Variety of Chemicals

2000 kg = 4400 lbm

1000 kg = 2200 lbm

500 kg = 1100 lbm


Acetic anhydride


Ammonium nitrate fertilizer



Amyl acetate


Calcium cyanide

Amyl nitrate


Carbon disulfide


Ammonium perchlorate


Calcium oxide


Diethyl ether or ethyl ether

Carbon dioxide



Carbon, activated






Copper chloride





Hydrazine, anhydrous

Maleic anhydride

Carbon tetrachloride

Hydrogen, compressed


Copper chlorate



Copper cyanide

Methylamine, anhydrous

Nitrogen, compressed



Nitrous oxide


Potassium cyanide



Propylene oxide

Oxygen, compressed






Phosphoric acid

Ethyl acetate

Sodium cyanide

Potassium fluoride

Ethyl benzene

Sodium peroxide

Potassium nitrate




Formic acid




100 kg = 220 lbm



Hydrogen bromide, anhydrous


Methacrylic acid

Hydrogen chloride, anhydrous

200 kg = 440 lbm

Methyl acetate

Hydrogen fluoride, anhydrous

Ammonia, anhydrous


Methyl bromide

Carbon monoxide


Methyl mercaptan



Sulfur dioxide

5 kg = 11 lbm




Phenol, molten or solid

25 kg = 55 lbm







Dinitrogen tetroxide

Silver nitrate


Methyl isocyanate

Sodium permanganate Tetrahydrofuran

Hydrogen sulfide

Nitric oxide, compressed


Nitric acid, red fuming

Nitrogen trioxide


Sulfuric acid, fuming





Vinyl acetate



Zinc peroxide


Source: AICHE/CCPS. Details on how to compute the TQ are available from AICHE/CCPS Process Safety Metrics: Guide for Selecting Leading and Lagging Indicator (New York, NY: American Institute of Chemical Engineers, 2018).

The target mitigated event frequency (TMEF) listed with the safety severity level is the minimum frequency level desired for this level of severity. It defines the frequency for acceptable risk.

Some risk matrixes include a severity column based on environmental impacts. However, the environmental impact is implicitly related to the quantity of chemical released: The greater the chemical release, the greater the environmental impact. Thus, environmental impact is implicit in this risk matrix.

The procedure for using the risk matrix of Table 1-14 is as follows:

  1. Select the severity levels from columns 1, 2, and 3 and select the highest level from any of these columns.

  2. Read the Risk Category and Safety Severity Level from the highest row.

  3. Select the likelihood from columns 4 through 7.

  4. Read the risk level from the intersection of the Safety Severity Level row and the Likelihood column.

The risk levels are identified just below the table and define the risk and the required response. The Safety Severity Level contains the TMEF. The TMEF will be useful for the layer of protection analysis (LOPA) method presented in Chapter 11.

The risk matrix provided in Table 1-14 is one specific example; that is, most companies customize the risk matrix to work for their particular situation. Additional methods for determining risk are presented in Chapter 12 on risk assessment.

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