# Sensitivity and Uncertainty Analyses of Human and Organizational Risks in Fire Safety Systems for High-Rise Residential Buildings with Probabilistic T-H-O-Risk Methodology

^{*}

## Abstract

**:**

## 1. Introduction

- Develop an improved PRA methodology to address concerns that deterministic, fire engineering approaches significantly underestimate safety levels that lead to inaccurate fire safety levels.
- Enhance existing verification methods by incorporating probabilistic risk approach and HOEs for (i) a more inclusive view of risk, and (ii) to overcome the deterministic nature of Australian verification method.
- Perform comprehensive sensitivity and uncertainty analyses to address uncertainties in numerical estimates used in fault tree/event trees (FT/ET), BN and SD and their propagation in T-H-O-Risk model.
- Quantification of human and organizational risks for high-rise residential buildings which contributes towards Australia’s agenda that is moving in the direction of a sustainable, risk-based regulatory approach.

## 2. Materials and Methods

#### 2.1. Characteristic Overview

- Fully comply with the NCC DTS provisions;
- Comply with other relevant regulations;
- Have the same footprint, floor area and volume as the proposed building;
- Be of the same NCC classes as the proposed building;
- Have the same effective height;
- Have the same occupant load and occupant characteristics;
- Have the same fire load and design fire.

#### 2.2. Methodology

#### 2.3. FSVM

#### 2.4. T-H-O-Risk Framework

- Calculation of the frequency of ignition: the calculation is based on [32]. The resulting value is then multiplied by the probability of a fire located in a sole-occupancy unit (SOU), in other words an apartment fire, or in the corridor (corridor fire).
- Deployment of the accident scenarios and calculation of the associated probability using ETA: starting from the initiating event, the possible scenarios are derived by assuming a set of events that could or could not happen. The events are related to the effectiveness of the safety countermeasures (detection, notification, sprinkler, smoke management system) hat is linked to the type of fire (flaming or smouldering). FTA, a top-down failure analysis tool, is used to estimate the effectiveness of the safety measures.
- Calculation of the consequences for each scenario using ASET/RSET analysis: as described elsewhere, consequences are estimated by comparison of the ASET and the RSET. The first parameter is obtained from the B-Risk fire modelling simulation by determination of the time available before untenable conditions occur; the second is obtained as the sum of the time to complete different evacuation phases (detection, notification, pre-movement, and movement). Those times are derived partly from analytical calculations (hydraulic model), and partly via B-Risk simulation.
- Introduction of HOEs through a BN: a static evaluation of the effects of human and organisational failures is performed through a BN. The ET structure of the model is converted into the more flexible BN which allows the description of multiple relationships between variables.
- Calculation of the individual and societal risk for different contexts (level of organization): the impact on the risk of a good or bad safety organisation is investigated using two different indicators. The first indicator is a single risk value, the Expected Risk to Life (ERL), which expresses the risk in deaths/year*building; the second risk indicator, the SR is represented using the Frequency—Consequences (F-N) curves. F-N curves allow a comparison of the different solutions on Societal Risk which reflects average risk, in terms of death that a whole group of occupants is exposed to a fire scenario instead of looking at individual occupant. This second indicator is helpful in the decision-making process, introducing the possibility of adopting human-related countermeasures.
- Dynamic modelling of risk variations in the system using SD: to include future changes of the various components of a complex system, the evolution along its entire life cycle should be investigated. The analysis incorporating changes over time is performed with SD: each parameter of the system is checked along a period of ten years and hypotheses are made on the evolution of their values in relationships with all other parameters. A ‘societal’ loop is created which enables the modelling of HOEs in response to changes in the perception of the risk in the system.
- Calculation of the time—risk curve for the entire lifecycle of the building.
- Sensitivity and uncertainty analyses using a Monte Carlo approach. Uncertainties in point estimates of ERL values are propagated through probability distributions with Monte Carlo simulations while a family of F-N curves and confidence intervals propagate epistemic uncertainty on SRs. Sensitivity and uncertainty analyses are also performed on key variables in the SD model to assess model robustness and to explore how uncertainty affects the assessment of different safety systems and reliability of model outputs.

#### 2.5. Sensitivity and Uncertainty Analysis

## 3. Case Studies

#### 3.1. Objectives and Performance Requirements

- BE—Blocked Exit, a fire blocks the evacuation route; it is necessary to demonstrate through ASET/RSET and ERL analysis that the level of safety is at least equivalent to the DTS provisions.
- CS—Concealed Space, a fire starts in a concealed space that can spread and harm several people in a room. The solution might include fire suppression or automatic detection.
- SF—Smouldering Fire, a fire is smouldering close to a sleeping area. The solution may provide a detection and alarm system.
- IS—Internal Surfaces, interior surfaces are exposed to a growing fire that potentially endangers occupants.
- CF—Challenging Fire, the worst credible fire in an occupied space.
- RC—Robustness Check, failure of a critical part of the fire safety system will not result in the design not meeting objectives of the NCC (modified ASET/RSET analysis to demonstrate that the remaining floors or fire compartments are robust).

#### 3.2. Probability Analysis of Human and Organizational Errors

#### 3.3. Event and Fault Tree

_{1}(A) is the ignition frequency of a building with floor area A/year, c

_{1}, c

_{2}, s and r constants based on [32] (refer Appendix A).

#### 3.4. Bayesian Network

#### 3.5. System Dynamics

#### 3.6. Consequence Analysis & Design Scenarios

#### 3.7. Fire Safety Verification Methods—Applicable Design Scenarios

#### 3.7.1. Exit Blocked by a Fire

#### 3.7.2. Concealed Space

^{2}). It is assumed that the initial fire is in the bedroom and the fire develops to engulf the mattresses (data from fire test from mattresses re-reported in SFPE Handbook [8] to be around 2 MW).

#### 3.7.3. Smouldering Fire

#### 3.7.4. Internal Surfaces

^{2}). This scenario affects fire growth and fuel load in a fire compartment and is addressed in the consequence modelling.

#### 3.7.5. Challenging Fire

#### 3.7.6. Robustness Check

#### 3.8. PRA—ASET/RSET Analysis

- A smouldering fire yields no casualties as the fire is limited in size and generally its extinction is performed by occupants before the fire develops into flashover.
- When suppression systems work as expected, the fire is controlled, and there are no victims.
- When the egress protection system is working as expected, untenable conditions do not arise in the corridor, hence the ASET is infinite and there are no victims (all scenarios identified with an odd number).

- The fire starts in the corridor/stairs; exit doors are not closed due to door blockade or due to failure of the self-closing mechanism. Smoke leakage through SOU doors.
- The fire starts in SOU; SOU doors remain open after the people have left the apartment (the self-closing mechanism is not working). Exit doors remain open due to door blockade or due to the failure of the self-closing mechanism.

## 4. Analysis

#### 4.1. Verification Method Incorporating T-H-O-Risk to Compare ERL and HOEs

#### 4.2. Sensitivity and Uncertainty Analyses of HOE Variables and ERL

#### 4.2.1. Sensitivity Analysis of HOE Variables and ERL

#### 4.2.2. Uncertainty Analysis of HOE and ERL

^{−}

^{5}deaths/year while the maximum ERL value is 4.38 × 10

^{−}

^{5}deaths/year. The mean value is 4.21 × 10

^{−}

^{5}deaths/year and the standard deviation is 7.57 × 10

^{−}

^{7}. The 5% and 95% confidence interval range for uncertainty is between 4.09 × 10

^{−}

^{5}and 4.34 × 10

^{−}

^{5}.

^{−}

^{5}and 4.32 × 10

^{−}

^{5}as shown in Figure 10b. This indicates that a beta or triangular distribution does not alter the uncertainty range significantly while the beta distribution produces a smoother curve.

^{−}

^{7}with 5% and 95% uncertainty ranges from 4.15 × 10

^{−}

^{5}to 4.30 × 10

^{−}

^{5}. The cumulative probability distribution of the single-run curve (S-curve) for Case #4 is presented in Figure 11b where the mean ERL is 4.25 × 10

^{−}

^{5}.

^{−}

^{7}. (Refer to Appendix C for detailed calculations). As expected, the HOE variable ‘not comply with instructions’ has the greatest influence on the outcome with a sensitivity of 5% followed by ‘deficient training’ at 4% and ‘inefficient emergency plan’ at 3%.

- For Case#1 ERL values for the performance solution with HOEs for 5% and 95% bounds are 4.21 × 10
^{−}^{5}and 4.58 × 10^{−}^{5}, respectively. ERL values for the DTS solution for 5% and 95% bounds are 3.10 × 10^{−5}and 3.37 × 10^{−}^{5}, respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 2.94 × 10^{−}^{5}and 3.18 × 10^{−}^{5}, respectively. From the average value, the ERL for the performance solution with HOEs is higher by 35% compared to the DTS solution and by about 44% as compared to performance solution. - For Case#2 ERL values for the performance solution with HOEs for 5% and 95% bounds are 4.40 × 10
^{−}^{5}and 4.63 × 10^{−}^{5}, respectively. ERL values for the DTS solution for 5% and 95% bounds are 3.91 × 10^{−}^{5}and 4.10 × 10^{−}^{5}, respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 3.78 × 10^{−}^{5}and 3.97 × 10^{−}^{5}, respectively. From the average value, the ERL for the performance solution with HOEs is higher by 13% as compared to the DTS solution and by about 16% as compared to performance solution. - For Case#3 ERL values for the performance solution with HOEs for 5% and 95% bounds are 3.01 × 10
^{−}^{5}and 3.15 × 10^{−}^{5}, respectively. ERL values for the DTS solution for 5% and 95% bounds are 2.58 × 10^{−}^{5}and 2.72 × 10^{−}^{5}, respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 2.10 × 10^{−}^{5}and 2.22 × 10^{−}^{5}, respectively. From the average value, the ERL for the performance solution with HOEs is higher by 16% as compared to the DTS solution and by about 41% as compared to performance solution. - For Case#4 ERL values for the performance solution with HOEs for 5% and 95% bounds are 4.15 × 10
^{−}^{5}and 4.30 × 10^{−}^{5}, respectively. ERL values for the DTS solution for 5% and 95% bounds are 3.83 × 10^{−}^{5}and 4.02 × 10^{−}^{5}, respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 2.92 × 10^{−}^{5}and 3.03 × 10^{−}^{5}, respectively. From the average value, the ERL for the performance solution with HOEs is higher by 7% as compared to the DTS solution and by about 42% as compared to the performance solution.

- For the DTS solution, the ERL value is highest for Case #2 followed by Case #4, #1 and #3 in descending order.
- For the performance solutions, the ERL value is highest for Case #2 followed by Case #1, #4 and #3 in descending order.
- When HOEs are considered, the ERL value is highest for Case #2 followed by Case #1, #4 and #3 in descending order.
- The average across different cases shows that the performance solution gives the lowest ERL with an average value of 3.02 × 10
^{−}^{5}whereas for DTS solution it is 3.48 × 10^{−}^{5}.

^{−}

^{5}, considering it is average value across different cases. Thus, across different cases, HOEs can increase the ERL value by as much as 42% compared to the performance solution. Further, the performance solution gives a lower value of ERL by much as 33% as compared to DTS solution.

#### 4.3. Societal Risk Assessment and Uncertainty Analysis

#### 4.4. System Dynamics Risk Modelling, Sensitivity and Uncertainty Analysis

- X, ${x}_{t},{x}_{t-1}$ are state variables; Y, ${y}_{t},{y}_{t-1}$ are observable variables;
- $P\left({x}_{t}|{x}_{t-1}\right)$ gives time dependencies between states;
- $P\left({y}_{t}|{x}_{t}\right)$ gives state dependencies between the variables;
- $P\left({x}_{0}\right)$ is initial state distribution.

#### 4.5. Assessment of Robustness of SD Model Outputs

_{i,t}of the target variables was calculated for ten years based on the following equation:

_{i,t}is relative variation of target variable I with respect to the mean using 95% CI; OM95

_{i,t}and Om95

_{i,t}are max. & min. values of the ith target variable at time t, using the 95% CI; and O

_{i}

^{m}is mean value of target variable i. There are 3 categories of response: low where VCi is less than 50%, moderate where variation coefficient is between 50–100% and high where variation coefficient is higher than 100%

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A T-H-O-Risk Methodology

- In the current study, the variation of the risk over time is considered along with technical, human, and organizational risks.
- Hazards and potential risk factors are identified in the first step which can cause damage to buildings or harm to humans.

- o
- Frequency analysis: conventional event and fault tree techniques are used to compute risk. In addition to technical errors, HOEs are included in the risk analysis using the BN. BNs are based on the Bayesian statistical decision theory [41] according to which uncertainties originate from real-world situations along with subjective analyses are intended to help aimed engineers in the decision-making process. Some common HOEs are listed later.
- o
- Consequence analysis: ASET/RSET method is employed to check whether building design is safe or not. In both approaches, if the risk is found to be higher than the acceptable level, risk control is done in the analysis framework. The steps are iterated until the risk is acceptable.

#### Appendix A.1. Step 1—Hazard Identification

- Ignition source;
- Fuel (such as waste products and textiles);
- Oxygen.

#### Appendix A.2. Step 2—Event Tree

- The probabilities are defined for each successive event through fault tree analysis and some typical events.
- Based on the logical structure of the events, the overall risk is then estimated for the building design related to fire safety. The overall risk is presented as ERL.

- It can identify critical events that result in higher risk;
- It can determine cause and effect relationship;
- It can be automated.

- (1)
- Initiating event;
- (2)
- Location of fire, e.g., apartment or corridor, concealed space or in a room;
- (3)
- Challenging fire or smouldering fire
- (4)
- Detection failure;
- (5)
- Alarm failure;
- (6)
- Sprinklers failure;
- (7)
- Egress protection where an emergency exit is blocked.

_{1}(A) is the ignition frequency of a building with floor area A during one year and c

_{1}, c

_{2}, s, and r are constants that are derived empirically, computed through fire statistics available from different countries.

#### Appendix A.3. Step 3a—Identification of Human and Organizational Errors

Basic Events | Probability (10^{6} h) |
---|---|

Poor safety supervision | 4.60 × 10^{−4} |

Deficient training | 1.89 × 10^{−3} |

Not following procedures | 1.70 × 10^{−4} |

Deficient risk assessment | 1.80 × 10^{−4} |

Deficient knowledge | 1.89 × 10^{−3} |

Inexperience | 1.10 × 10^{−3} |

Insufficient technical handover | 6.30 × 10^{−3} |

Insufficient safety check | 2.50 × 10^{−2} |

Inadequate periodic inspection | 2.50 × 10^{−2} |

Invalid daily record | 5.60 × 10^{−3} |

Inadequate emergency plan | 5.00 × 10^{−4} |

Failure to read monitoring data correctly | 2.50 × 10^{−3} |

Design error of operator | 2.20 × 10^{−3} |

Failure to follow technical requirements | 1.92 × 10^{−4} |

Not following technical requirements | 1.92 × 10^{−4} |

#### Appendix A.4. Step 3b—Bayesian Network

- Multi-state variables;
- Dependent failures;
- Expert opinions that cannot be performed using standard FTA.

- For the incorporation of HOEs, ET is mapped into a BN.
- In the first instance, the BN inserts observations in the nodes that are observable and then utilizes the rules of probabilistic calculations forward and backward from the nodes that are observable to the target node via an intermediate node, if exists.
- The extended BN model incorporating HOEs, determines a more precise estimate for the probability of occurrence of the top event if a specific configuration of critical HOEs is given.
- The critical parameters are revised based on prior probability, posterior probability, and mutual information (i.e., entropy reduction) computed for each given HOEs.
- The BN scheme is essential when the system state depends on more than one event. Since ETs are only capable of representing single input in a node, multiple inputs are ensured by adopting a Bayesian approach [50]. This is the case when human errors are considered.

- To incorporate case files;
- To provide sensitivity analysis;
- To operate in batch mode.

- FY: fire ignition.
- FN: no fire ignition.
- DY: detection ON.
- DN: detection OFF.
- SuY: Suppression ON.
- SuN: Suppression OFF.
- SpY: fire and smoke spreads outside AOF
- SpN: fire and smoke does not spread outside AOF.
- NY: alarm/notification ON.
- NN: alarm/notification OFF.
- EY: egress protection ON.
- EN: egress protection OFF.

#### Appendix A.5. Step 4—System Dynamics

- ‘Deficient training’;
- ‘Inefficient emergency plan’;
- ‘Not comply with the instruction’.

Deficient Training | Inefficient Emergency Plan | Not comply with the Instruction | Inefficient Timely Control |
---|---|---|---|

yes | yes | yes | yes |

yes | yes | no | yes |

yes | no | yes | yes |

yes | no | no | yes |

no | yes | yes | yes |

no | yes | no | yes |

no | no | yes | yes |

no | no | no | no |

- Fire;
- Inefficient timely control;
- Deficient check;
- Equipment aging.

- FY DY (fire yes, detection yes);
- FY DN (fire yes, detection no);
- FN (fire no).

**Table A3.**CPT for the four parent nodes, i.e., fire, inefficient timely control, deficient check, and equipment aging.

Fire | Inefficient Timely Control | Deficient Check | Equipment Aging | FYDY | FYDN | FN |
---|---|---|---|---|---|---|

yes | yes | yes | yes | 70 | 30 | 0 |

yes | yes | yes | no | 70 | 30 | 0 |

yes | yes | no | yes | 70 | 30 | 0 |

yes | yes | no | no | 70 | 30 | 0 |

yes | no | yes | yes | 80 | 20 | 0 |

yes | no | yes | no | 80 | 20 | 0 |

yes | no | no | yes | 80 | 20 | 0 |

yes | no | no | no | 90 | 10 | 0 |

no | yes | yes | yes | 0 | 0 | 100 |

no | yes | yes | no | 0 | 0 | 100 |

no | yes | no | yes | 0 | 0 | 100 |

no | yes | no | no | 0 | 0 | 100 |

no | no | yes | yes | 0 | 0 | 100 |

no | no | yes | no | 0 | 0 | 100 |

no | no | no | yes | 0 | 0 | 100 |

no | no | no | no | 0 | 0 | 100 |

- Deficient training;
- Inefficient emergency plan;
- Not comply with the instruction;
- No check rules;
- Deficient maintenance;
- Incorrect risk assessment;
- Not following standards;
- Improper safety organization.

#### Appendix A.6. Step 5—Probabilities

- o
- Different estimates for ignition frequency could be obtained through literature. Ignition frequency is considered one of the most influencing parameters.
- o
- For the reliability of detection and sprinkler, the estimates are similar to the literature, as discussed above in Step 2.
- o
- For HOEs, a review and assessment of selected incident data and maintenance databases were performed to obtain average probabilities/ frequencies of HOEs in industry, which are assigned to initiate events and basic events in the model to further carry out a quantitative analysis of the occurrence frequency.

#### Appendix A.7. Step 6—Available Safe Egress Time (ASET)

- Temperature;
- Visibility;
- Fractional effective doses.

#### Appendix A.8. Step 7—Required Safe Egress Time (RSET)

_{d}+ T

_{p}+ T

_{m}

- T
_{d}is detection time; - T
_{p}is pre-movement time; - T
_{m}is movement time.

#### Appendix A.9. Step 8—ASET-RSET Analysis

#### Appendix A.10. Step 9—Risk Evaluation

_{i}is the probability of each scenario and C

_{i}are the consequences for the same scenario.

#### Appendix A.11. Step 10—Risk Reduction

## Appendix B

Safety System Failure | Critical Component | Low | Expected | High | Reference |
---|---|---|---|---|---|

Challenging Fire | 0.25 | 0.35 | 0.45 | Hall [54] | |

Emergency Exit is Blocked | Human error | 0.15 | 0.20 | 0.25 | Magnusson et al. [55] |

Fire in Concealed Space | Non-combustible partition ceiling/wall | 0.15 | 0.20 | 0.25 | N.A. |

Sprinkler system | Main valve shut off, Human errors | 0.02 | 0.05 | 0.15 | Moinuddin & Thomas [43] |

Smoke detection | Poor maintenance | 0.05 | 0.10 | 0.15 | Bukowski [56] |

Alarm system | Shut-off after maintenance | 0.05 | 0.10 | 0.15 | PD7974−7 [6] |

Manual detection | Human errors | 0.30 | 0.48 | 0.60 | Holborn et al. [57] |

Smoke Control/Mechanical ventilation | Fire damper failure | 0.20 | 0.30 | 0.50 | Zhao [58] |

Smoke barrier | Door seal failure | 0.05 | 0.20 | 0.50 | PD7974−7 [6] |

Fire department response | Human and organizational errors | 0.02 | 0.05 | 0.30 | USFA [59] |

Management strategy | Human errors | 0.05 | 0.15 | 0.30 | Sabapathy et al. [40] |

Distribution | Graph | Probability Density Function | Properties | Framework |
---|---|---|---|---|

Uniform | $f\left(x\right)=\frac{1}{max-min}$ | Close-ended with same probability | Same likelihood of either overestimating or underestimating (+/− 10%) | |

Triangular | $f\left(x\right)=\frac{2\left(x-\mathrm{min}\right)}{\left(mode-\mathrm{min}\right)\left(\mathrm{max}-\mathrm{min}\right)}$ $ifmin\le x\le mode$ $f\left(x\right)=\frac{2\left(max-\mathrm{x}\right)}{\left(max-\mathrm{min}\right)\left(\mathrm{max}-\mathrm{mode}\right)}$ $ifmodex\le max$ | Close-ended With possible skewness | Possible under-estimation of ML is [−10%; ML: +50% | |

Beta | $f\left(x\right)=\frac{{\left(x\right)}^{\alpha -1}{\left(1-x\right)}^{\beta -1}}{B\left(\alpha ,\beta \right)}$ $\mathrm{Where}B\left(\alpha ,\beta \right)\mathrm{is}\mathrm{a}\mathrm{Beta}\mathrm{funtion}$ | Close-ended with possible skewness | Possible under-estimation of ML is [−10%; ML: +50% | |

Normal | $f\left(x\right)=\frac{1}{\sqrt{2\pi {\sigma}^{2}}}exp\left(-\frac{{\left(x-\mu \right)}^{2}}{2{\sigma}^{2}}\right)$ | Close-ended With no skewness | The most likely value is set to first-year impact, std. dev. is set to 15% | |

Gamma | $f\left(x\right)=\frac{{\beta}^{-\alpha}{x}^{\alpha -1}exp\left(-\frac{x}{\beta}\right)}{\mathsf{\Gamma}\left(\alpha \right)}$ | Semi-close-ended Possible right skewness | k-value setting is 5, calculated based on mean from Lichtenberg [−25%; ML: +100%] |

## Appendix C Sensitivity Calculations of HOE Variables

## Appendix D Uncertainty—Confidence-Level Based Societal Risk in F-N Curves

## Appendix E Sensitivity Analysis for System Dynamics

## Appendix F

Parameters | Model Value (Units) | Definition/Equation | Range of Variation (Multi) |
---|---|---|---|

adopt unsuitable equipment | dimensionless | 1 − (improper safety organisation yes) × (1 − dump1 × not obey standards) | 0.0028–0.0048 |

fire probability | dimensionless | ignition frequency + RANDOM UNIFORM(−default Change/4, default Change/4, 1) × ignition frequency | 0.0023–0.0038 |

inefficient emergency control plan | dimensionless | 1 − (1 − deficient training yes) × (1 − dump2 × not comp w instr yes) × (1 − control2 × inefficient emergency plan yes) | 0.0053–0088 |

not obey standards | dimensionless | 1.05 − Level of organisation/4 | 0.16–0.28 |

wrong risk assessment | dimensionless | 1.3 − Level of organisation/4 | 0.48–0.58 |

deficient check | dimensionless | 1 − deficient check no | 0.23–0.45 |

deficient maintenance | dimensionless | deficient maintenance = RANDOM UNIFORM(− default Change, default Change, 1) × deficient maintenance yes | 0.06–0.10 |

deficient training | dimensionless | 1 − Level of organization | 0.0645–0.1075 |

electrical failure | dimensionless | 1 − (1 − component faulty connection) × (1 − no battery) | 0.0375–0.0625 |

equipment aging | dimensionless | 1 − (deficient maintenance yes a)*(1 − wrong risk assessment) | 0.2325–0.3875 |

improper safety organisation | dimensionless | 1.3 − control4 × Level of organisation/4 | 0.075–0.125 |

inefficient timely control | dimensionless | 1 − (deficient training yes) × (1 − dump2 × not comp w instr yes) × (1 − control3 × inefficient emergency plan) | 0.315–0.525 |

inefficient emergency plan | dimensionless | 1.25 − Level of organisation*dump5/4 | 0.092–0.154 |

Level of organisation | dimensionless | rate of change | 1 to 4 |

n° of accidents | dimensionless | INTEG(accident rate) | 15–25 |

no check rules | dimensionless | 1.3 − Level of organisation*dump6/4 | 0.1065–0.1775 |

not comply with instructions | dimensionless | 0.3 + deficient training | 0.3045–0.5075 |

Number of checks | number per year | INTEG(rate of change) | 23.25–38.75 |

perceived safety | dimensionless | gap in no of accidents × perception | 2.175–3.625 |

ProbCheckFailure | dimensionless | 0.4 × deficient training + 0.1 | 0.0825–0.1375 |

ProbValveClosed | dimensionless | ProbValveClosed = 0.01 + RAMP(0.05,1,20) | 0.0075–0125 |

reliability | days/year | 1 − (((ProbCheckFailure × 19) + 1)/20) + ProbValveClosed a + (1/N° of checks) | 9 to 15 |

smoke alarm failure | dimensionless | 1 − (1 − panel failure) × 1 − zone isolated) | 0.675–0.925 |

notification failure | dimensionless | 1 − (1 − bell failure) × (1 − bulb failure) | 0.75–0.95 |

panel failure | dimensionless | 1 − (1 − electronic failure)*(1 − notification failure) | 0.011175–0.018625 |

sprinkler failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.85–0.95 |

sprinkler head failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.00225–0.0375 |

water supply failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.099–0.165 |

downfeed failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.019725–0.032875 |

pressure valve failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.00093–0.00155 |

outlet valve failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.000465–0.000775 |

isolation closed | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0174–0.029 |

water valve closed | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.001425–0.002375 |

pressure valve closed | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.000472–000788 |

tank failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.08175–0.13625 |

pump failure | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0423–0.0705 |

return valve closed | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0009–0.0015 |

operator fails | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0009–0.0015 |

flow probability | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.70–0.90 |

valve left closed | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0009–0015 |

alarm valve | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.00141–00235 |

ordinary stop valve | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.000465–000775 |

non-return valve | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0008925–001488 |

alarm bell | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.02175–0.03625 |

storage tank | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0054225–0.009038 |

mains power | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0002745–0.000458 |

pressure switch | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.0059175–0.009863 |

diesel pump | dimensionless | Probability of Failure on Demand (PFD) [43,48] | 0.069–0.115 |

## References

- Wang, Y.F.; Roohi, S.F.; Hu, X.M.; Xie, M. Investigations of Human and Organizational Factors in hazardous vapor accidents. J. Hazard. Mater.
**2011**, 191, 69–82. [Google Scholar] [CrossRef] - Tan, S.; Moinuddin, K. Systematic review of human and organizational risks for probabilistic risk analysis in high-rise buildings. Reliab. Eng. Syst. Saf.
**2019**, 188, 233–250. [Google Scholar] [CrossRef] - Sun, X.-Q.; Luo, M.-C. Fire Risk Assessment for Super High-rise Buildings. Procedia Eng.
**2014**, 71, 492–501. [Google Scholar] [CrossRef] [Green Version] - Kodur, V.; Kumar, P.; Rafi, M.M. Fire hazard in buildings: review, assessment and strategies for improving fire safety. PSU Res. Rev.
**2019**, 4, 1–23. [Google Scholar] [CrossRef] - Hackitt, J. Building a Safer Future—Independent Review of Building Regulations and Fire Safety: Final Report, Cm 9607; APS Group: London, UK, 2018. [Google Scholar]
- Hurley, M.J. (Ed.) SFPE Handbook of Fire Protection Engineering, 5th ed.; SFPE: Gaithersburg, MD, USA, 2016. [Google Scholar] [CrossRef]
- Pence, J.; Sakurahara, T.; Zhu, X.; Mohaghegh, Z.; Ertem, M.; Ostroff, C.; Kee, E. Data-theoretic methodology and computational platform to quantify organizational factors in socio-technical risk analysis. Reliab. Eng. Syst. Saf.
**2019**, 185, 240–260. [Google Scholar] [CrossRef] - Mohaghegh, Z.; Mosleh, A. Incorporating organizational factors into probabilistic risk assessment of complex socio-technical systems: Principles and theoretical foundations. Saf. Sci.
**2009**, 47, 1139–1158. [Google Scholar] [CrossRef] - Mohaghegh, Z. Combining System Dynamics and Bayesian Belief Networks for Socio-Technical Risk Analysis. In Proceedings of the 2010 IEEE International Conference on Intelligence and Security Informatics, Vancouver, BC, Canada, 23–26 May 2010; pp. 196–201. [Google Scholar]
- Groth, K.M.; Smith, R.; Moradi, R. A hybrid algorithm for developing third generation HRA methods using simulator data, causal models, and cognitive science. Reliab. Eng. Syst. Saf.
**2019**, 191, 106507. [Google Scholar] [CrossRef] - Lin, P.; Hale, A.; Van Gulijk, C. A paired comparison approach to improve the quantification of management influences in air transportation. Reliab. Eng. Syst. Saf.
**2013**, 113, 52–60. [Google Scholar] [CrossRef] - Wang, Y.F.; Li, Y.L.; Zhang, B.; Na Yan, P.; Zhang, L. Quantitative Risk Analysis of Offshore Fire and Explosion Based on the Analysis of Human and Organizational Factors. Math. Probl. Eng.
**2015**, 2015, 1–10. [Google Scholar] [CrossRef] [Green Version] - Meacham, B.J.; Stromgren, M.; Van Hees, P. A holistic framework for development and assessment of risk-informed performance-based building regulation. Fire Mater.
**2020**. [Google Scholar] [CrossRef] - Meacham, B.J.; Van Straalen, I.J. A socio-technical system framework for risk-informed performance-based building regulation. Build. Res. Inf.
**2017**, 46, 444–462. [Google Scholar] [CrossRef] - Blewett, V.; Rainbird, S.; Dorrian, J.; Paterson, J.; Cattani, M. Keeping rail on track: preliminary findings on safety culture in Australian rail. Work.
**2012**, 41, 4230–4236. [Google Scholar] [CrossRef] [Green Version] - Penney, G.; Habibi, D.; Cattani, M. The Handbook of Wildfire Engineering; Bushfire & Natural Hazards CRC: Melbourne, Australia, 2020; ISBN 978-0-6482756-8-8. [Google Scholar]
- Van Coile, R.; Hopkin, D.; Lange, D.; Jomaas, G.; Bisby, L. The Need for Hierarchies of Acceptance Criteria for Probabilistic Risk Assessments in Fire Engineering. Fire Technol.
**2019**, 55, 1111–1146. [Google Scholar] [CrossRef] - British Standards Institution; PD 7974-7:2003. Application of Fire Safety Engineering Principles to the Design of Buildings—Part 7; Probabilistic Risk Assessment: London, UK, 2003.
- Meacham, B.J.; Tubbs, B.; Bergeron, D.; Szigeti, F. Performance System Model—A Framework for Describing the Totality of Building Performance. In Proceedings of the CIB-CTBUH International Conference on Tall Buildings: Strategies for Performance in the Aftermath of the World Trade Center, CIB and CTBUH, Kuala Lumpur, Malaysia, 20–23 October 2003; pp. 361–372. [Google Scholar]
- Johnson, P.; Lobel, N. Fire Safety Verification Method—The Australia Research Experience. J. Phys. Conf. Ser.
**2018**, 1107, 042033. [Google Scholar] [CrossRef] - Fire Safety Verification Method—Handbook; Australian Building Codes Board: Canberra, Australia, 2019.
- Verification Method: Framework for Fire Safety Design: For New Zealand Building Code Clauses C1-C6 Protection from Fire; New Zealand Government: Wellington, Malaysia, 2014.
- Meacham, B. Feasibility of a Centralized Hub for Verification of Complex Fire Engineered Solutions in Scotland; Scottish Government: Edinburgh, Scotland, 2018.
- Baker, G.; Utstrand, J.; Norén, J. Probabilistic Method to Verify Fire Safety Design in Buildings; SP Technical Research Institute of Sweden: Boras, Sweden, 2016. [Google Scholar]
- Society of Fire Safety (Engineers Australia). SFS Fire Safety Verification Method Investigation; Engineers Australia, Society of Fire Safety: Barton, Australia, 2020. [Google Scholar]
- Pau, D.; Duncan, C.; Fleischmann, C. Pau Performance-Based Fire Engineering Design of a Heritage Building: McDougall House Case Study. Safety
**2019**, 5, 45. [Google Scholar] [CrossRef] [Green Version] - Tan, S.; Weinert, D.; Joseph, P.; Moinuddin, K.A.M. Incorporation of technical, human and organizational risks in a dynamic probabilistic fire risk model for high-rise residential buildings. Fire Mater.
**2020**, 2872. [Google Scholar] [CrossRef] - Tan, S.; Weinert, D.; Joseph, P.; Moinuddin, K.A.M. A dynamic probabilistic fire risk model incorporating technical, human and organizational risks for high-rise residential buildings. In Proceedings of the Interflam 2019—Fire Science and Engineering Conference, Egham, UK, 1–3 July 2019. [Google Scholar]
- Tan, S.; Weinert, D.; Joseph, P.; Moinuddin, K. Impact of Technical, Human, and Organizational Risks on Reliability of Fire Safety Systems in High-Rise Residential Buildings—Applications of an Integrated Probabilistic Risk Assessment Model. Appl. Sci.
**2020**, 10, 8918. [Google Scholar] [CrossRef] - Rao, K.D.; Kushwaha, H.S.; Verma, A.K.; Srividya, A. Epistemic Uncertainty Propagation in Reliability Assessment of Complex Systems. Int. J. Perform. Eng
**2008**, 4, 71–84. [Google Scholar] - Paté-Cornell, M. Uncertainties in risk analysis: Six levels of treatment. Reliab. Eng. Syst. Saf.
**1996**, 54, 95–111. [Google Scholar] [CrossRef] - Tillander, K.; Keski-Rahkonen, O. The Ignition Frequency of Structural Fires in Fin-land 1996–1999. In Proceedings of the Seventh International Symposium on Fire Safety Science, Worcester, MA, USA, 16–21 June 2003; pp. 1051–1062. [Google Scholar]
- Groth, K.; Wang, C.; Mosleh, A. Hybrid causal methodology and software platform for probabilistic risk assessment and safety monitoring of socio-technical systems. Reliab. Eng. Syst. Saf.
**2010**, 95, 1276–1285. [Google Scholar] [CrossRef] - NPFA72 National Fire Alarm Code; National Fire Protection Association: Quincy, MA, USA, 2019.
- Wade, C.; Baker, G.; Frank, K.; Robbins, A.; Harrison, R.; Spearpoint, M.; Fleischmann, C. B-RISK User Guide and Technical Manual; BRANZ study Report No 282; BRANZ: Judgeford, New Zealand, 2013. [Google Scholar]
- Steijn, W.; Van Kampen, J.; Van Der Beek, D.; Groeneweg, J.; Van Gelder, P. An integration of human factors into quantitative risk analysis using Bayesian Belief Networks towards developing a ‘QRA+’. Saf. Sci.
**2020**, 122, 104514. [Google Scholar] [CrossRef] - BSI; PD 7974-7:2019. Application of Fire Safety Engineering Principles to the Design of Buildings—Part 7: Probabilistic Risk Assessment; British Standards Published Document: London, UK, 2019. [Google Scholar]
- Sun, M.; Zheng, Z.; Gang, L. Uncertainty Analysis of the Estimated Risk in Formal Safety Assessment. Sustain. J. Rec.
**2018**, 10, 321. [Google Scholar] [CrossRef] [Green Version] - Ford, A.; Flynn, H. Statistical screening of system dynamics models. Syst. Dyn. Rev.
**2005**, 21, 273–303. [Google Scholar] [CrossRef] - Sabapathy, P.; DePetro, A.; Moinuddin, K. Probabilistic Risk Assessment of Life Safety for a Six-Storey Commercial Building with an Open Stair Interconnecting Four Storeys: A Case Study. Fire Technol.
**2019**, 55, 1405–1445. [Google Scholar] [CrossRef] - Kupper, L.L. Probability, Statistics, and Decision for Civil Engineers. Technometrics
**1971**, 13, 211. [Google Scholar] [CrossRef] - Swain, A.D.; Guttman, H.E. Handbook of Human Reliability Analysis with Emphasis on Nuclear Power Plant Applications (NUREG CR-1278); NRC: Washington, DC, USA, 1982.
- Moinuddin, K.; Thomas, I. Reliability of sprinkler system in Australian high rise office buildings. Fire Saf. J.
**2014**, 63, 52–68. [Google Scholar] [CrossRef] - Moinuddin, K.A.M.; Innocent, J.; Keshavarz, K. Reliability of Sprinkler System in Australian Shopping Centres—A Fault Tree Approach. Fire Saf. J.
**2019**, 105, 204–215. [Google Scholar] [CrossRef] - Det Norske Veritas. OREDA-Offshore & Onshore Reliability Data Handbook, 6th ed.; Det Norske Veritas: Høvik, Norway, 2015. [Google Scholar]
- HSE. The Implementation of CORE-DATA, a Computerised Human Error Probability Database. HSE Books: Merseyside, UK, 1999. [Google Scholar]
- Bhandari, J.; Abbassi, R.; Garaniya, V.; Khan, F. Risk analysis of deepwater drilling operations using Bayesian network. J. Loss Prev. Process. Ind.
**2015**, 38, 11–23. [Google Scholar] [CrossRef] - MacLeod, J.; Tan, S.; Moinuddin, K. Reliability of fire (point) detection system in office buildings in Australia—A fault tree analysis. Fire Saf. J.
**2020**, 115, 103150. [Google Scholar] [CrossRef] - Benjamin, J.R.; Cornell, C.A. Probability, Statistics and Decisions for Civil Engineers; McGraw-Hill: New York, NY, USA, 1970. [Google Scholar]
- Hanea, D.; Ale, B. Risk of human fatality in building fires: A decision tool using Bayesian networks. Fire Saf. J.
**2009**, 44, 704–710. [Google Scholar] [CrossRef] - Unnikrishnan, G.; Siddiqui, N.A. Application of Bayesian methods to event trees with case studies. Reliab. Theory Appl.
**2014**, 9, 32–45. [Google Scholar] - Dulac, N.; Leveson, N.; Zipkin, D.; Friedenthal, S.; Cutcher-Gershenfeld, J.; Carroll, J.; Barrett, B. Using System Dynamics for Safety and Risk Management in Complex Engineering Systems. In Proceedings of the Winter Simulation Conference, Orlando, FL, USA, 4–7 December 2005; p. 10. [Google Scholar]
- Basirat, P.; Fazlollahtabar, H.; Mahdavi, I. System dynamics meta-modelling for reliability considerations in maintenance. Int. J. Process. Manag. Benchmarking
**2013**, 3, 136. [Google Scholar] [CrossRef] - Hall, J.R. US Experience with Sprinklers and Other Automatic Fire Extinguishing Equipment; National Fire Protection Association: Quincy, MA, USA, 2010. [Google Scholar]
- Magnusson, S.E.; Frantzich, H.; Harada, K. Fire safety design based on calculations: Uncertainty analysis and safety verification. Fire Saf. J.
**1996**, 27, 305–334. [Google Scholar] [CrossRef] [Green Version] - Bukowski, R.; Budnick, E.; Schemel, C. Estimates of the Operational Reliability of Fire Protection Systems. In Proceedings of the third International Conference on Fire Research and Engineering, Gaithersburg, MD, USA, 22–26 July 2002; pp. 111–124. [Google Scholar]
- Holborn, P.; Nolan, P.; Golt, J. An analysis of fire sizes, fire growth rates and times between events using data from fire investigations. Fire Saf. J.
**2004**, 39, 481–524. [Google Scholar] [CrossRef] - Zhao, L. Reliability of Stair Pressurisation and Zoned Smoke Control Systems; Victoria University of Technology: Melbourne, Australia, 1998. [Google Scholar]
- U.S Fire Administration. Structure Fire Response Times. Trop. Fire Res. Ser.
**2006**, 5, 5–10. [Google Scholar]

**Figure 1.**Technical-Human-Organizational Risk (T-H-O-Risk) FSVM (fire safety verification method) process flow chart. NCC: National Construction Code.

**Figure 2.**Two solutions for Case #1 Australian Building Codes Board (ABCB) model residential building.

**Figure 7.**ERL for design scenarios for Case #1 to #4. Note: CS—Concealed Space, CF—Challenging Fire, RC1—Robustness Check Detection Failure, RC2—Robustness Check Sprinkler Failure, RC3—Robustness Check Building Alarm Failure, BE—Blocked Exit, SOU—Sole Occupancy Unit (not CS), BEN—Exit is NOT Blocked.

**Figure 10.**Case #4: Uncertainty analysis for ‘not complying with instructions’. (

**a**) ERL uncertainty analysis for Case #4 with beta distribution. (

**b**) ERL uncertainty analysis for Case #4 with triangular distribution.

**Figure 11.**(

**a**) Uncertainty analysis of 3 main HOE variables -Case #4. (

**b**) Single Cumulative probability plot of ERL Case #4 HOE. (

**c**) Probability plots of significant HOEs for Case #4 (

**d**) Cumulative distribution plots for significant HOEs –Case #4.

**Figure 12.**Cumulative Probability Distribution for Case #1 to #4—DTS, Performance & Performance with HOE.

**Figure 20.**SD sensitivity trace range under multivariate uncertainty—ERL over 10 years for Case #1 to #4.

**Figure 21.**SD sensitivity trace range under multivariate uncertainty—global risk over 10-year period for Case #1 to #4.

**Figure 28.**SD sensitivity analysis of ‘not comply with instructions’ and ‘inefficient timely control’ variables.

**Table 1.**Characteristics of Case #1- Australian Building Codes Board (ABCB) Deemed-to-Satisfy (DTS) and Performance solutions.

Building Characteristics | ABCB DTS | ABCB Performance |
---|---|---|

Occupants per floor | 36 | 36 |

Number of floors | 20 | 20 |

Floorplate area (m^{2}) | 702 | 702 |

Number of units per floor | 12 | 12 |

Building | Case #2 | Case #3 | Case #4 | |||
---|---|---|---|---|---|---|

Characteristics | Performance | DTS | Performance | DTS | Performance | DTS |

Occupants per floor | 24 | 24 | 54 | 54 | 58 | 58 |

Number of floors | 24 | 24 | 23 | 23 | 21 | 21 |

Floorplate area (m^{2}) | 484 | 484 | 1099 | 1099 | 1343 | 1343 |

Number of units/floor | 6 | 6 | 15 | 15 | 20 | 20 |

Design Scenario | Numerical Experiment # | Solution | Fire Spread |
---|---|---|---|

Fire blocks evacuation route | BE1 | Performance | Yes |

BE2 | Performance | No | |

BE3 | DTS | Yes | |

BE4 | DTS | No | |

Fire starts in concealed space | CS1 | Performance | Yes |

CS2 | Performance | No | |

CS3 | DTS | Yes | |

CS4 | DTS | No | |

Robustness Check | RC1 | Performance | Yes |

RC2 | Performance | No | |

RC3 | DTS | Yes | |

RC4 | DTS | No | |

Challenging fire | CF1 | Performance | Yes |

CF2 | Performance | No | |

CF3 | DTS | Yes | |

CF4 | DTS | No | |

Fire in a normally unoccupied room threatens occupants of other rooms | UT | Not required | |

Smouldering fire | SF | Not required | |

Internal surfaces | IS | Not required | |

Structural stability and other properties | SS | Not required | |

Horizontal fire spread | HS | Not required | |

Vertical fire spread involving cladding or arrangement of openings in walls | VS | Not required | |

Fire brigade intervention | FI | Not required | |

Unexpected catastrophic failure | UF | Not required |

Tenability Criteria | Sole Occupant Unit | Corridor | Stairway |
---|---|---|---|

Upper Layer temperature | n | n | 150 s |

Lower layer temperature | n | n | 90 s |

Visibility | 240 s | 150 s | 59 s |

FED thermal | n | n | 135 s |

FED asphyxiant | n | n | 1011 s |

**Table 5.**ERL results of design scenarios for Case #1 to #4 (DTS, Performance, HOE (human and organizational errors)).

Design | Case #1 | Case #2 | Case #3 | Case #4 |
---|---|---|---|---|

DTS | 3.21 × 10^{−5} | 4.02 × 10^{−5} | 2.64 × 10^{−5} | 3.98 × 10^{−5} |

Performance | 3.03 × 10^{−5} | 3.91 × 10^{−5} | 2.18 × 10^{−5} | 2.98 × 10^{−5} |

Performance HOE | 4.36 × 10^{−5} | 4.55 × 10^{−5} | 3.14 × 10^{−5} | 4.27 × 10^{−5} |

PSF | Modal Level | Modal Multiplier | Best Case Multiplier | Worst Case Multiplier |
---|---|---|---|---|

Available time | Nominal | 1 | 1 | 1 |

Stress and stressors | Nominal | 1 | 1 | 2 |

Complexity | Nominal | 1 | 1 | 1 |

Experience and training | Nominal | 1 | 0.1 | 1 |

Procedures | Nominal | 1 | 0.5 | 1 |

Ergonomics | Nominal | 1 | 1 | 1 |

Fitness for duty | Nominal | 1 | 1 | 1 |

Work processes | Nominal | 1 | 0.8 | 2 |

Multipliers | 1 | 0.04 | 4 |

Design | Sampling | Case #1 | Case #2 | Case #3 | Case #4 |
---|---|---|---|---|---|

DTS | Mean | 3.25 × 10^{−5} | 4.02 × 10^{−5} | 2.66 × 10^{−5} | 3.97 × 10^{−5} |

5%CI | 3.10 × 10^{−5} | 3.91 × 10^{−5} | 2.58 × 10^{−5} | 3.83 × 10^{−5} | |

95%CI | 3.37 × 10^{−5} | 4.11 × 10^{−5} | 2.72 × 10^{−5} | 4.02 × 10^{−5} | |

Standard deviation | 7.66 × 10^{−7} | 5.87 × 10^{−7} | 4.37 × 10^{−7} | 5.43 × 10^{−7} | |

Performance | Mean | 3.05 × 10^{−5} | 3.89 × 10^{−5} | 2.17 × 10^{−5} | 2.98 × 10^{−5} |

5%CI | 2.94 × 10^{−5} | 3.78 × 10^{−5} | 2.10 × 10^{−5} | 2.92 × 10^{−5} | |

95%CI | 3.18 × 10^{−5} | 3.97 × 10^{−5} | 2.22 × 10^{−5} | 3.03 × 10^{−5} | |

Standard deviation | 7.78 × 10^{−7} | 5.27 × 10^{−7} | 3.56 × 10^{−7} | 3.79 × 10^{−7} | |

HOE | Mean | 4.39 × 10^{−5} | 4.56 × 10^{−5} | 3.09 × 10^{−5} | 4.25 × 10^{−5} |

5%CI | 4.21 × 10^{−5} | 4.40 × 10^{−5} | 3.01 × 10^{−5} | 4.15 × 10^{−5} | |

95%CI | 4.58 × 10^{−5} | 4.63 × 10^{−5} | 3.15 × 10^{−5} | 4.30 × 10^{−5} | |

Standard deviation | 1.14 × 10^{−6} | 6.90 × 10^{−7} | 4.18 × 10^{−7} | 5.40 × 10^{−7} |

Target Model Variables | Responsive Parameters | Sensitivity Results 95% Confidence Interval |
---|---|---|

Adopt unsuitable equipment: | Perception, Max number of accidents, Probability Valve Closed | 0.92 ± 0.004 (dimensionless) |

Improper safety organisation | Perception, Max number of accidents, Probability Valve Closed | 1.29 ± 0.233 (dimensionless) |

Inefficient timely control | Perception, Max number of accidents, Probability Valve Closed | 0.25 ± 0.212 (dimensionless) |

Inefficient emergency plan | Perception, Max number of accidents, Probability Valve Closed | 1.24 ± 0.226 (dimensionless) |

No check rules | Perception, Max number of accidents, Probability Valve Closed | 0.29 ± 0.211 (dimensionless) |

Not comply with instructions | Perception, Max number of accidents, Probability Valve Closed | 0.30 ± 0.219 (dimensionless) |

Not obey standards | Perception, Max number of accidents, Probability Valve Closed | 1.29 ± 0.236 (dimensionless) |

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**MDPI and ACS Style**

Tan, S.; Weinert, D.; Joseph, P.; Moinuddin, K.
Sensitivity and Uncertainty Analyses of Human and Organizational Risks in Fire Safety Systems for High-Rise Residential Buildings with Probabilistic T-H-O-Risk Methodology. *Appl. Sci.* **2021**, *11*, 2590.
https://doi.org/10.3390/app11062590

**AMA Style**

Tan S, Weinert D, Joseph P, Moinuddin K.
Sensitivity and Uncertainty Analyses of Human and Organizational Risks in Fire Safety Systems for High-Rise Residential Buildings with Probabilistic T-H-O-Risk Methodology. *Applied Sciences*. 2021; 11(6):2590.
https://doi.org/10.3390/app11062590

**Chicago/Turabian Style**

Tan, Samson, Darryl Weinert, Paul Joseph, and Khalid Moinuddin.
2021. "Sensitivity and Uncertainty Analyses of Human and Organizational Risks in Fire Safety Systems for High-Rise Residential Buildings with Probabilistic T-H-O-Risk Methodology" *Applied Sciences* 11, no. 6: 2590.
https://doi.org/10.3390/app11062590