**3. Methods**

of documents by year. Results point out that there is a growing interest on emergency

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

A depth analysis shows that the majority of the researches are developed in the USA (**Figure 4**).

In recent literature, several approaches and models have been proposed to manage emergency conditions. For instance, Pérez et al. [10] in their study proposed a fleet assignment model for the Santiago Fire Department to maximize the number of incidents successfully attended. Omidvari et al. [11] developed a model based on analytical hierarchy process and failure modes and effects analysis logic to determine the factors influencing the fire risk of an education center. Bariha et al. [12] proposed the analysis of hazards associated with accidental release of high pressure from gas-pipeline transportation system. A probabilistic risk assess‐ ment from potential exposures to the public applied for innovative nuclear installations has been analyzed by Dvorzhak et al. [13]. While Shi et al. [14] used a technique plan repository and evaluation system based on AHP group decision-making for emergency treatment and disposal in chemical pollution accidents, Ergu et al. [15] applied the analytic network process, a generalization of the AHP, in risk assessment a decision analysis. Liu et al. [16] present a

novel approach for FMEA based on AHP and fuzzy VIKOR method.

management issue.

**Figure 3.** Documents by year.

**Figure 4.** Documents by country/territory.

To design the model, a novel approach including HRA, FMEA, and AHP is defined. In this section, a short description of these methods is given.

#### **3.1. The failure modes and effects analysis (FMEA): the traditional approach**

According to the American Society for Quality [17], FMEA is a procedure that is performed after a failure modes and effects analysis to classify each potential failure effect according to its severity and probability of occurrence. Traditional FMEA method is based on risk priority number (RPN) for analyzing the risk associated with potential problems. RPN is calculated by multiplying the scores of severity (S), occurrence (O), and detection (D). In details:

 Occurrence (O) represents the probability that a particular cause for the occurrence of a failure mode occurs (1–10). The range of occurrence scale is from score 1 (failure is unlikely) to score 10 (failure is very high and inevitable).

 Severity (S) represents the severity of the effect on the final process outcome resulting from the failure mode if it is not detected or corrected. The severity scale is from score 1 (none effect) to score 10 (hazardous without warning).

 Lack of detectability (D) represents the probability that the failure will not be detected. The detectability scale is from score 1 (detection almost certain) to score 10 (absolute uncertainty).

Generally, it will give more importance to the failure modes with higher RPNs. The RPN method has been criticized due to its limitations, among which are:


 They are ordinal type of scale (not cardinal). Thus, no arithmetic operation among them is permitted.

To avoid some of the drawbacks mentioned above, some different approaches have been proposed in literature. For instance, Narayanagounder and Gurusami [18] used analysis of variance (ANOVA) to prioritize failure modes or using additional characteristic indexes to define the order to analyze (from a design point of view) the failure mode. However, this proposal are very complex, and it is not simple to apply it in industrial context. For this reason, our study aims to propose a simple application using AHP technique according to human reliability analysis that is explained in the next sections.

#### **3.2. The human reliability analysis (HRA)**

The development of human reliability methods occurred over time in three stages [19]: (1) the first stage (1970–1990), known as the *first human reliability method generation*; (2) the second phase (1990–2005), known as *the second human reliability method generation*; and (3) finally, the *third generation*, started in 2005 and still in progress [20, 21].

Among the several approaches that have been proposed and developed for error classification, we remember the Systematic Human Error Reduction and Prediction Approach (*SHERPA*) [22], the Cognitive Reliability Error Analysis Method (*CREAM*) [23], the Human Error Identification in Systems Tool (*HEIST*) and Human Error Assessment and Reduction Techni‐ que (*HEART*) [24], and the Human Factors Analysis and Classification System (*HFACS*) [25], among others.

**Figure 5.** The Weibull function.

The common basis for all techniques is the assessment of the human error probability (HEP) representing the index of human error and its variation according to PSFs. The analysis of human error starts with a definition of HEP. Obviously, the probability of error is a growing function of the time. The HEP value can be calculated as:

$$HEP\_{now} = 1 - e^{-ar'} \tag{1}$$

The above formula can be changed in relation to the working hours. Since the operator's reliability is highest in the first hour of work and descending gradually, it gets closer to the eighth hour, and the unreliability decreases with the time (**Figure 5**).

$$\begin{cases} \textit{HEP}\_{\textit{now}}\left(\boldsymbol{t}\right) = \boldsymbol{l} - \boldsymbol{k} \, \ast \, \boldsymbol{e}^{-a\left(\boldsymbol{l} - \boldsymbol{t}\right)^{\boldsymbol{\theta}}} \, \forall \, \boldsymbol{t} \in \left[0; 1\right] \\ \textit{HEP}\_{\textit{now}}\left(\boldsymbol{t}\right) = \boldsymbol{l} - \boldsymbol{k} \, \ast \, \boldsymbol{e}^{-a\left(\boldsymbol{t} - \boldsymbol{l}\right)^{\boldsymbol{\theta}}} \, \forall \, \boldsymbol{t} \in \left[\boldsymbol{l}; \infty\right] \end{cases} \tag{2}$$

where α is the scale parameter and β is the shape parameter. The β parameter is defined as 1.5 by the scientific literature of the HEART method.

The α parameter is calculated by the following formula:

$$\alpha = \frac{-\ln\left[\frac{k\left(t=8\right)}{k\left(t=1\right)}\right]}{\left(t=1\right)^{\beta}}\tag{3}$$

Using (Eq. 2), it is possible to define the trend of reliability associated to specific generic task or human errors, as it is shown in **Table 1**.


**Table 1.** Human errors scale.

our study aims to propose a simple application using AHP technique according to human

The development of human reliability methods occurred over time in three stages [19]: (1) the first stage (1970–1990), known as the *first human reliability method generation*; (2) the second phase (1990–2005), known as *the second human reliability method generation*; and (3) finally, the

Among the several approaches that have been proposed and developed for error classification, we remember the Systematic Human Error Reduction and Prediction Approach (*SHERPA*) [22], the Cognitive Reliability Error Analysis Method (*CREAM*) [23], the Human Error Identification in Systems Tool (*HEIST*) and Human Error Assessment and Reduction Techni‐ que (*HEART*) [24], and the Human Factors Analysis and Classification System (*HFACS*) [25],

The common basis for all techniques is the assessment of the human error probability (HEP) representing the index of human error and its variation according to PSFs. The analysis of human error starts with a definition of HEP. Obviously, the probability of error is a growing

reliability analysis that is explained in the next sections.

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

*third generation*, started in 2005 and still in progress [20, 21].

**3.2. The human reliability analysis (HRA)**

among others.

**Figure 5.** The Weibull function.

function of the time. The HEP value can be calculated as:

One of the most important aspects is the study of factor interactions that increase the proba‐ bility of error and interdependencies of performance shaping factors (PSFs). Specifically, the context in which humans make errors is analyzed. The PSFs allow the inclusion, in the model, of all the environmental and behavioral factors that influence the decision and actions of man [26]. In particular, the use of PSFs allows to simulate different scenarios. Analytically, the PSFs are modifying the value of the error probability because they introduce external factors that strain and distract the decision maker [27]. The PSF and their values are obtained from the literature, as is shown in **Table 2**. The PSFs considered are (1) *available time, (2) stress/stressor, (3) complexity, (4) experience and training, (5) procedures, (6) ergonomics, (7) fitness for duty, and (8) work processes.*


**Table 2.** PSFs scale.

It is important to note that four main sources of deficiencies can be identified in current HRA methods:


are modifying the value of the error probability because they introduce external factors that strain and distract the decision maker [27]. The PSF and their values are obtained from the literature, as is shown in **Table 2**. The PSFs considered are (1) *available time, (2) stress/stressor, (3) complexity, (4) experience and training, (5) procedures, (6) ergonomics, (7) fitness for duty, and (8)*

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

**# PSFs Levels Values** 1 Available time Inadequate time 1

2 Stress Extreme 5

3 Complexity Highly complex 5

4 Experience/training Low 3

5 Procedures Not available 50

6 Ergonomics Missing 50

7 Fitness for duty Unfit 1

8 Work processes Nominal 1

Time available = time required adequate time 10 Nominal time 1 Time available > 5 time required (extra time) 0.1 Time available > 50 time required 0.01

High 2 Nominal 1

Moderately complex 2 Nominal 1

Nominal 1 High 0.5

Incomplete 20 Available, but poor 5 Nominal 1

Poor 10 Nominal 1 good 0.5

Degraded fitness 5 Nominal 1

Good 0.5

*work processes.*

**Table 2.** PSFs scale.

Large variability in implementation

 Heavy reliance on expert judgment in selecting PSFs and the use of these PSFs to obtain the HEP in human reliability analysis

The limitations characterizing the FMEA and HRA methods are the motivation under our study and provide the reason to integrate them with AHP technique.

#### **3.3. The analytic hierarchy process (AHP)**

AHP uses mathematical objectives to process the inescapable, subjective, and personal preferences of an individual or a group making a decision [28]. In the AHP process, firstly, the hierarchy is defined. Secondly, judgments on pairs of elements with respect to a controlling element are expressed to derive ratio scales that are then synthesized throughout the structure used to select the best alternative [29]. The modeling process can be divided into different phases; to provide a better understanding of the main phases, they are described as follows:

1. *Pairwise comparison and relative weight estimation.* Pairwise comparisons of the elements in each level are conducted with respect to their relative importance toward their control criteria. Saaty suggested a scale of 1–9 when comparing two components. For example, a score of 9 represents an extreme importance over another element, while a score of 8 represents an intermediate importance between "very strong importance" and "extreme importance" over another element. The pairwise comparisons can be represented in the form of a matrix. Score 1 represents equal importance of two components, and score 9 represents extreme importance of the component i over the component j.

2. *Priority vector.* After all pairwise comparisons are completed, the priority weight vector (w) is obtained.

3. *Consistency index estimation*. The consistency index (CI) of the derived weights could then be calculated by CI = (λmax − n)/n − 1., where λmax is the largest eigenvalue of the judgment matrix A and n is the rank of the matrix. In general, if CI is less than 0.10, the satisfaction of the judgments may be derived.
