**4. Research framework: Human reliability model based on AHP**

In this section, a human reliability model is proposed to analyze the human reliability in emergency conditions, based on failure modes and effects analysis. Here, below is a brief description of the phases and steps characterizing the model.

#### **4.1. The rationale**

As reported in the previous sections, a quantitative method was developed to prioritize failure modes and human errors using AHP technique. The logic model is depicted in **Figure 6**. Each model phase is discussed in brief, as follows:

**Figure 6.** Methodological approach.

*Phase #1: Preliminary analysis.* The aim of the first phase was to identify scenario under study defining failure modes and human errors characterizing the accident. This phase represents the most critical phase because an incorrect assessment could determine the inappropriateness of the overall model. Three main steps were identified, as follows:


*Phase #2: Multicriteria analysis.* One of the crucial elements in measuring the effectiveness of a decision model is to obtain consistent results according to common standards. Thus, the aim of the second phase was to define the AHP model according to prioritize failure modes (FMs) and human errors (HRs), when there is a disagreement in ranking scale for severity, occur‐ rence, detection, human errors, and PSFs. The final purpose of this phase was to define the final score for each criteria and subcriteria according to the AHP model and according to the expert team.

Four main steps were identified, as follows:


**4.1. The rationale**

**Figure 6.** Methodological approach.

Step #1: Identify of risk factors

expert team.

Step #2: Identify failure modes (FMs)

Step #3: Identify human errors (HRs)

model phase is discussed in brief, as follows:

As reported in the previous sections, a quantitative method was developed to prioritize failure modes and human errors using AHP technique. The logic model is depicted in **Figure 6**. Each

152 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

*Phase #1: Preliminary analysis.* The aim of the first phase was to identify scenario under study defining failure modes and human errors characterizing the accident. This phase represents the most critical phase because an incorrect assessment could determine the inappropriateness

*Phase #2: Multicriteria analysis.* One of the crucial elements in measuring the effectiveness of a decision model is to obtain consistent results according to common standards. Thus, the aim of the second phase was to define the AHP model according to prioritize failure modes (FMs) and human errors (HRs), when there is a disagreement in ranking scale for severity, occur‐ rence, detection, human errors, and PSFs. The final purpose of this phase was to define the final score for each criteria and subcriteria according to the AHP model and according to the

of the overall model. Three main steps were identified, as follows:

*Phase #3: Synthesis.* The aim of the last phase was to define the final assessment for RPN according to the expert team. One step was identified to carry out the phase, as follows:

Step #9: Final assessment

#### **4.2. Case study: the model validation**

To demonstrate the proposed approach, a real-world application is employed in this section. The example is related to an emergency shutdown valve (ESDV) in a petrochemical plant. Of course, reliability is crucial to safety (**Figure 7**). An emergency shutdown valve is an actuated valve designed to stop the flow of a hazardous fluid upon the detection of a dangerous condition, protecting people, equipment, or the environment.

**Figure 7.** Example of emergency shutdown valve.

#### *4.2.1. Phase #1: preliminary analysis*

According to Step #1, the identification of risk factors were carried out. In detail, an expert team, composed by five engineers, was selected to develop the model.

According to Step #2, the main failure modes characterizing the malfunction of an ESDV were identified: valve open (FM1), partially open (FM2), closed (FM3), partially closed (FM4), and wobble (FM5). The main failure causes were identified in broken and corrosion.

Scales for S, O, and D were defined by each expert, as is shown in **Table 3**.


**Table 3.** Failure mode – for each experts.

The aggregation of values expressed by each experts was made *computing the mode* or in other words identifying the value that appeared most often in the set of data. For instance, if we


consider the set data for FM1 related to the severity scale, the most frequent value or the mode value is 3. The final set of data used is shown in **Table 4**.

**Table 4.** Calculation of the mode values for the five experts

Frequently, human errors are overlooked. Because the FMEA examines individual faults of system elements taken singly, the combined effects of coexisting failures are not considered. Thus, according to Step #3, the human errors (HR) were identified by the expert team. For the scenario under study, three HRs and three PSFs were selected, as is shown in **Tables 5** and **6**.


**Table 5.** Human errors selection.

**Failure mode S O D RPN**

154 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

FM1 2 4 7 56 FM2 3 5 6 90 FM3 2 6 4 48 FM4 4 7 5 140 FM5 4 7 2 56

FM1 3 5 7 105 FM2 2 4 8 64 FM3 3 7 6 126 FM4 6 3 8 144 FM5 7 7 1 49

FM1 1 8 3 24 FM2 4 4 6 96 FM3 5 8 7 280 FM4 3 3 5 45 FM5 2 4 5 40

FM1 3 8 7 168 FM2 4 2 6 48 FM3 5 7 6 210 FM4 6 3 5 90 FM5 2 4 5 40

FM1 3 8 7 168 FM2 1 4 4 16 FM3 5 4 6 120 FM4 6 4 2 48 FM5 2 4 5 40

The aggregation of values expressed by each experts was made *computing the mode* or in other words identifying the value that appeared most often in the set of data. For instance, if we

**Expert#1**

**Expert#2**

**Expert#3**

**Expert#4**

**Expert#5**

**Table 3.** Failure mode – for each experts.


**Table 6.** PSFs scale.


Scales for PSFs were defined by each expert. In **Table 7**, a synthesis is shown.

**Table 7.** PSF scale—experts—synthesis.

#### *4.2.2. Phase #2: AHP model*

According to Step #4, the AHP model was built to determine the criteria and subcriteria weights. The model consists of eight criteria and six subcriteria. In **Figure 8**, the AHP model is shown.

**Figure 8.** R-AHP model.


**Table 8.** Example of pairwise comparison for potential failure modes criteria.

In this phase, according to Step #5, pairwise comparison matrices were filled out by the expert team to define the weights of criteria and subcriteria. It is worth noting that the same impor‐ tance was attributed to the main criteria or 50 % potential failure mode and 50 % potential human errors. **Tables 8** and **9** show two examples of pairwise comparison. For each pairwise comparison, according to Step #6, consistency analysis was carried out.


Consistency: 0.051 < 0.10.

Scales for PSFs were defined by each expert. In **Table 7**, a synthesis is shown.

156 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

**Table 7.** PSF scale—experts—synthesis.

*4.2.2. Phase #2: AHP model*

is shown.

**Figure 8.** R-AHP model.

Consistency: 0.078 < 0.10.

**Human error PS1 PS2 PS3** HR1 10 1 1 HR2 1 5 1 HR3 5 1 2

According to Step #4, the AHP model was built to determine the criteria and subcriteria weights. The model consists of eight criteria and six subcriteria. In **Figure 8**, the AHP model

**FM1 FM2 FM3 FM4 FM5 Weight**

In this phase, according to Step #5, pairwise comparison matrices were filled out by the expert team to define the weights of criteria and subcriteria. It is worth noting that the same impor‐

FM1 1 5 5 6 6 0.547 FM2 1/5 1 3 4 4 0.215 FM3 1/5 1/3 1 3 3 0.121 FM4 1/6 1/4 1/3 1 2 0.065 FM5 1/6 1/4 1/3 1/2 1 0.050

**Table 8.** Example of pairwise comparison for potential failure modes criteria.

**Table 9.** Example of pairwise comparison for potential error criteria.

**Figure 9.** Final weights.

**Figure 10.** Example of initial and revised severity scale for Expert #1.

The determination of relative weights in AHP model is based on the pairwise comparison conducted with respect to their relative importance toward their control criterion. In detail, evaluation expressed in **Tables 4**–**7** was used. Furthermore, Saaty's semantic scale was used for the comparison.


**Table 10.** Revised failure mode—for each expert.

Furthermore, according to Step #7, the *geometric mean* was used to synthesize the set of judgments given by the expert team.

According to Step #8, the ranking was obtained. The aim of the present step was to define the final score for each criteria and subcriteria according to the AHP model and according to the expert team. One step was identified to carry out the phase, as follows. The scores of these each weighted criteria and subcriteria are shown in **Figure 9**.

Results pointed out that, according to expert judgments, the occurrence is the most important parameter with a score of 46.4 % than the other (severity with a score of 32.4 % and detectability with a score of 21.2 %). Furthermore, the most critical failure mode is FM1 with a score of 54.7 %, the most critical human error is HR3 with a score 52.7 %, and the most important performance shape factor is PS3 with a score of 47.9 %.

#### *4.2.3. Phase #3: a new approach for prioritizing human errors and failure modes*

evaluation expressed in **Tables 4**–**7** was used. Furthermore, Saaty's semantic scale was used

**Failure mode S O D RPN revised**

158 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

FM1 5 7 3 105 FM2 4 5 4 80 FM3 3 5 4 60 FM4 2 5 4 40 FM5 2 5 2 20

FM1 4 5 7 140 FM2 3 6 5 90 FM3 3 6 5 90 FM4 6 3 4 72 FM5 6 7 1 42

FM1 5 8 3 120 FM2 5 5 4 100 FM3 5 5 4 100 FM4 4 4 3 48 FM5 4 4 3 48

5 8 3 120 5 4 5 4 80 4 5 7 2 70 5 4 3 2 24 4 2 4 4 32 2

3 8 5 120 3 5 5 4 100 5 5 4 5 100 5 5 5 2 50 5 2 4 4 32 2

**Table 10.** Revised failure mode—for each expert.

for the comparison.

Expert #1

Expert #2

Expert #3

Expert #4

Expert #5

Phase #3 is a crucial phase in the proposed methodological approach. In fact, it is important to note that, for instance, for Expert #1, FM1 and FM 5 had the same RPN (56) with different ranking values for occurrence, severity, and detection. For determining the most significant failure mode H-RPN, the weights defined through AHP model were used, as is shown in **Table 9**.

In detail, according to the final weights obtained with AHP, each expert expressed a reassess‐ ment judgments for S, O, and D scales. **Figure 10** shows an example of revised severity scale for Expert #1.

In a similar way, revised scales for occurrence and detectability were obtained by each expert, as shown in **Table 10**.

The aggregation of values expressed by each expert was made computing the mode, as shown in **Table 11**.


**Table 11.** Revised calculation of the mode values of five experts.

**Table 12** shows an example of new RPN.


**Table 12.** Example of calculation of RPN.

**Figure 11** shows a comparison between initial and revised RPNs, highlighting the *RPN reduction* for each FM. It is significant to point out that in general **Figure 11** shows, for the specific case study, a reduction of the RPN because usually the expert team have overestimated one parameter. But an *increase of RPN* could happen also.

**Figure 11.** Comparison between initial and revised RPN.

Of course, in our opinion, the above assessment allows to evaluate the RPN more precisely and objectively with respect to the traditional approach.

#### **5. Conclusion**

This paper proposes a novel approach to prioritize failure modes taking into account human errors. The final aim was to improve the evaluation of risk priority number integrating human errors in the calculation. The goal was achieved through a multicriteria model, based on AHP. The method allowed us to weigh the failure modes integrating with human errors and to prioritize failure modes. The model can be applied when there is a disagreement in ranking scale for severity, occurrence, and detection. The novelty of the method is because there is no evidence in literature of this kind of approach using AHP. In our opinion, the proposed method ensures several benefits, as detailed follows: (1) it is a generic method that can be applied in several industrial processes; (2) it can be used to identify human errors that can become single points of failure; and (3) it can be used to define potential human errors that are the most critical by revealing the severity and probability of occurrence. Future research will investigate a great number of failure modes and human errors. Furthermore, several scenarios will be taken into account to compare results.
