Statistical Analysis of Flight Crew Safety Behavior Using Fuzzy Set

In this study, correlation analysis, t-test, ANOVA, structural equation modeling were conducted using survey constructed with a 5-point Likert scale. The survey aimed to investigate the perception of flight crew members regarding safety behavior and variables directly influencing safety behavior.

In this study, a confirmatory factor analysis was conducted on the structural equation of flight crew’s safety behavior, involving eight latent variables: Managerial Safety Performance, Organizational Support Perception, Personnel and Equipment, Colleague’s Safety Performance, Cooperation and Involvement, Operational Quality Assurance, Fairness and Voluntary Reporting, and Safety Behavior. The results shown as Fig. 1 revealed that the paths leading to the measurement variables were all statistically significant at a significance level of 0.001. Therefore, the goodness of fit for the structural equation model (SEM) was deemed excellent.

Refers to Fig. 2, to examine the causal relationships among the key variables, we constructed a structural equation model with eight latent variables and observed variables as targets for path analysis, as presented below.

Each path’s significance probability less than 0.05 (^*p<0.05, ^**p<0.01, ^***p<0.001) indicates a significant impact, while otherwise, it is considered insignificant. As a result, Collaboration & Involvement, Flight Quality Assurance, and Just Culture & Reporting were analyzed as not significantly influencing Safety Behavior.

In this study, a questionnaire with the content shown in Table 4 was utilized to investigate the subjective perception of safety behavior among flight crew members.

The value measured through the two steps, as shown in the Table 4, were expressed as fuzzy numbers. The membership function µ_A(X) of the LR fuzzy number A=(a,l_a,r_a)_LR with center ‘a’ and left and right spreads l_a and r_a is defined as follows :

Here, L_A (R_A) are monotonically increasing (decreasing) functions, satisfying L_A(0)=R_A(0)=1 and L_A(1)=R_A(1)=1. Additionally, symmetric fuzzy numbers, where the left and right widths are equal, are expressed as A=(a,a_s)_LR. When the membership functions are L_A(x)=R_A(x)=1–x, it is referred to as a triangular fuzzy number and denoted as A=(a,l_a,r_a)_T. The a-level set of the LR fuzzy number A is A(α)=x:µ_A(x)≥a=[l_a(α),r_a(α)], where the interval endpoints are l_a(α)=a–l_aL_A^-1(α) and r_a(α)=a–r_aR_A^-1(α) (Dubios and Prade, 1979; Kaufmann and Gupta, 1991).

Using flight crew members’ responses from a subjective questionnaire similar to Table 4, safety behavior and other variables were measured using fuzzy numbers. The variables essential for flight crew members’ safety behavior in Table 5 were represented as symmetrical triangular fuzzy numbers A=(a,s_a)_T through the following method (Serge et al., 2013; Gerami and Fayek, 2019; Lee and Choi, 2019).

How to get triangular fuzzy number for S_b

Step 1. Divide the universal set () into closed intervals [l_i,r_i](i=1,…,p).

Step 2. Record the values (a) belonging to the selected closed interval [l_k,r_k].

Step 3. Determination of spread (S_a) of fuzzy number such that S_a=Min|a–l_k|,|a–r_k|.

The existing research on flight crew members’ safety behavior has primarily employed a 5-point scale questionnaire. In order to analyze the correlation between the results of the conventional 5-point scale questionnaire and the subjectively perceived understanding of flight crew members surveyed with a single item, correlation analysis was conducted.

Table 6 shows the correlation coefficients between the 5-point scale survey and variables measured using fuzzy numbers.

According to Table 6, there is a statistically significant correlation between the perception of flight crew members measured using a 5-point scale and the perception obtained through a single-item inquiry about subjective thoughts. The potential differences in safety behavior based on the employing airline and flight hours, as analyzed earlier in Section 2.1, were also compared though subjective inquiries.

Table 7 illustrates that the perception of safety behavior among flight crew members from a major airline is higher than that of those from a low-cost airline. The Mann-Whitney test indicates a lack of concordance in the medians of the two groups (13,14). This result diverges from the outcomes obtained using the 5-point scale (refers to Table 2).

To investigate differences in flight crew members’ perceptions based on flight hours, the Kruskal–Wallis test was conducted. In Table 8, S_b(0) and x² represent the 0-level set and the statistics of the Kruskal–Wallistest, respectively (13,14). Table 8 indicates that there is no statistically significant difference in perception based on flight hours. This finding does not align with the results obtained using the survey instrument (refers to Table 3).

Regression analysis, widely applied in statistics, is a method for estimating a statistical model for the response variable (y_i) and the explanatory variables based on a finite number

The statistical model is represented as

In classical statistical models, explanatory variables with correlations among the mare typically excluded. Therefore, there are instances where variables essential for the actual environment or the researcher’s design are not included in the regression model.

In Section 2.2, there were originally seven variables identified as influencing safety behavior. However, the path analysis revealed that only four variables, namely Management Commitment to Safety, Perceived Organizational Support, Staff and Equipment, and Colleague Commitment to Safety were found to influence safety behavior. Additionally, the stepwise variable selection method for selecting variables influencing the response variable chose Management Commitment to Safety, Perceived Organizational Support, Staff and Equipment, Colleague Commitment to Safety and Flight Quality Assurance as explanatory variables.

Both path analysis and S Flight Quality Assurance VSM limits the variables influencing safety behavior, identifiedby experts, in the regression model. This approach also partially reflects the results of Structural Equation Modeling. To overcome such limitations, a fuzzy regression model is necessary (Jung et al., 2015, Li at el., 2023).

In 1982, Tanaka applied fuzzy sets proposed by Zadehto regression models, leading to wide spread applications of fuzzy regression models in various fields. In this study, a statistical model for safety behavioris estimated using the explanatory variables

incorporating expert opinions, prior research, and SEM results. To estimate fuzzy regression model

a thre-step procedure is employed, where E=(0,l_e,r_e)_T represents the fuzzy error.

Step 1 : Calculate Center of 0-level Set.

The center C_A of the 0-level set of the fuzzy number A=(0,l_a,r_a) is defined as $C_A=\alpha +\frac{1}{3}\left(r_a-l_a\right)$. Compute the centers for the response variables C_Sb(j) and explanatory variables C_ci(j), C_Jc(j).

Step 2 : Estimate the Regression Model of Center.

Estimate the regression model of the center for the response variable C_Sb(j) and the center set of explanatory variables

using the Lasso method (Gholamreza and Mohammad, 2019). The Lasso method minimizes the objective function,

to estimate the regression coefficients, where

and 0<α<1. In this study, we obtain estimates $\overline{a_j}\left({\alpha }_i\right)$ for specific values of α_i. Subsequently, the mean for the set α_i (i=1,⋯,p) is computed using the Lasso estimation, given by ${\widehat{a}}_l=\frac{1}{p}{\displaystyle {\sum }_{i=1}^p\overline{a_j}\left({\alpha }_i\right)}$.

Step 3 : Estimate Fuzzy Error E.

Estimate the left spread and right spread of the fuzzy error using the least absolute deviation method. Utilize the left endpoint (le_p (j)) and right endpoint (re_N (j)) of variables with positive and negative estimated regression coefficients from Step 2, respectively, to determine the left endpoint (le_Sb (j)) of the response variable.

In the other words, the estimate ${\widehat{l}}_e$ is obtained by minimizing the expression

Here, $l{e}_{S_b}\left(j\right)=S_b\left(j\right)-l_{S_b}\left(j\right)$ and $r{e}_{S_b}\left(j\right)=S_b\left(j\right)+r_{S_b}\left(j\right)$. A similar approach is employed to estimate ${\widehat{r}}_e$.

Utilizing the three-step method described above, we estimate the regression model for safety behavior as follows :

In this study, the Lasso regression method was employed in Step 2. The Lasso method, utilizing the L₁-norm, estimates regression coefficients for less informative variables to be close to zero, thus diminishing the influence of explanatory variables. In this research, the Lasso method was employed to identify variables with minimal impact on safety behavior. In Step 3, the L₁-norm |•| was used to estimate the spread of fuzzy errors. This approach is considered efficient as it is less sensitive to outliers compared to using the L₂-norm (•)² (Choi and Buckley, 2008; Choi and Yoon, 2010; Lee et al., 2021).

The data provided in Table 5 and the results estimated using the Lasso regression method are presented in Table 9.

The fuzzy error presented in Step 3 can be estimated as ${\widehat{l}}_e$ = 0.4 using le_p (j) and. Therefore, the fuzzy regression model for safety behavior can be estimated as:

Commentary: Among the variables influencing the safety behavior of domestic flight crews in South Korea, most of them were found to have a positive and significant impact. However, fairness and voluntary reporting showed a negative impact.

This indicates that flight crews perceive the airline’s reward and penalty system as unfair, leading to a reluctance to make normal voluntary reports.

Table 7 shows differences in flight crews’ subjective perceptions of safety behavior based on the airline they work for. The fuzzy regression models for safety behavior estimated using Steps 1 to 3 for flight crews working in a major airline ($S_b^1$) and a low-cost airline ($S_b^2$) are as follows :

Commentary: Flight crews working for low-cost airlines showed a relatively significant perception that the reward and penalty system is unfair compared to flight crews in major airlines.

Table 3 illustrates differences in safety behavior perceptions based on flight experience. The fuzzy regression model for safety behavior estimated using the methods presented in this paper, with a focus on flight hours, is as follows.

The perception ($S_b^m$) of flight crews with flight hours between 3,000 and 10,000 hours, was positively influenced by all explanatory variables. This indicates a difference between flight crews with less than 3,000 hours ($S_b^l$) and those with 10,000 hours or more ($S_b^h$).

Commentary: Flight crews with lower experience levels face difficulties in voluntary cooperation and participation in the cockpit compared to their more experienced counterparts, stemming from their lack of flight experience.

Moreover, highly experienced flight crew members demonstrate a relatively lower perception of a fair-culture. This indicates that, in comparison to their efforts for safe flight, the compensation is not adequately administered.