Development of a framework for resilience measurement: Suggestion of fuzzy Resilience Grade (RG) and fuzzy Resilience Early Warning Grade (REWG)

Abstract

BACKGROUND: Resilience engineering (RE) can be an alternative technique to the traditional risk assessment and management techniques, to predict and manage safety conditions of modern socio-technical organizations. While traditional risk management approaches are retrospective and highlight error calculation and computation of malfunction possibilities, resilience engineering seeks ways to improve capacity at all levels of organizations in order to build strong yet flexible processes.

OBJECTIVES: Considering the resilience potential measurement as a concern in complex working systems, the aim of this study was to quantify the resilience by the help of fuzzy sets and Multi-Criteria Decision-Making (MCDM) techniques. In this paper, we adopted the fuzzy analytic hierarchy process (FAHP) method to measure resilience in a gas refinery plant.

METHODS: A resilience assessment framework containing six indicators, each with its own sub-indicators, was constructed. Then, the fuzzy weights of the indicators and the sub-indicators were derived from pair-wise comparisons conducted by experts. The fuzzy evaluating vectors of the indicators and the sub-indicators computed according to the initial assessment data. Finally, the Comprehensive Resilience Index (CoRI), Resilience Grade (RG), and Resilience Early Warning Grade (REWG) were established.

RESULTS: To demonstrate the applicability of the proposed method, an illustrative example in a gas refinery complex (an instance of socio-technical systems) was provided. CoRI of the refinery ranked as “III”. In addition, for the six main indicators, RG and REWG ranked as “III” and “NEWZ”, respectively, except for C3, in which RG ranked as “II”, and REWG ranked as “OEWZ”.

CONCLUSIONS: The results revealed the engineering practicability and usefulness of the proposed method in resilience evaluation of socio-technical systems.

Keywords

Resilience engineering safety fuzzy AHP Resilience Grade Resilience Early Warning Grade

1 Introduction

As the complexity of a process increases, the ability to anticipate, monitor, and measure safety decreases. Previous attempts have only looked at cause-effect relationships to analyze the safety of systems; as a consequence, it is hard to track the connections in socio-technical systems. Chemical process industries, as an instance of the safety critical systems, have to consider this issue and seek methods dealing with the problem. In conventional safety and reliability engineering approaches, human operators were considered as a cause of operational uncertainty and a source responsible for most failures in socio-technical systems [1, 2]. In contrast, contemporary approaches to safety issues, accentuate that safety critical organizations must be capable of proactively evaluating and managing the safety of their actions. This proactivity should be authorized in the organizational safety management. Moreover, traditional safety engineering perspective generally describes accidents as due to some breakdowns (i.e., human-related, technical, or organizational) or something that is not predictable in the usual organization performance. Even though safety engineering has built up influential models, a comprehensive set of techniques, and instruments and systems to investigate and develop organization safety, most of these methods have been established based on a forced linearization of intricate systems. Therefore, these methods and techniques lack adequacy of comprehensive perspective to handle the complexity of events occurring in contemporary systems [3, 4].

The resilience engineering (RE) emerged as an alternative to traditional approaches to the management of safety functions in socio-technical systems. In the resilience engineering approach, failure and success are both normal outcomes of how organizations deal with unexpected events in intricate scenarios. Organizations must deal with deviations in their functions, necessitate adjustment and adaptation of people’s activities to respond adequately to the variability, and make decisions according to the finite resources and the time available in order to achieve the system goals. A resilient system can be considered as a system in which people successfully deal with complexity under demands; and resilience engineering is a novel pattern for safety management that essentially concentrates on the improvement of methods so as to guarantee that the organization maintains or recuperates to a safe steady condition. The aim of resilience engineering is to provide tools for these developments [3]. In other words, resilience can be seen as a type of forward and proactive protection.

Several studies have been conducted to quantify and measure the resilience potential in safety-critical systems. Trijp J. et al. [5] developed a quantitativemodel and established the “dynamic operational resilience” concept to evaluate the organizational resilience of Dutch emergency response safety. They conducted a large-scale study among safety stakeholders and applied a multiple-criteria analysis (MCA) method to weight four resilience factors: “quality”, “adaptive capacity”, “management of keystone vulnerabilities”, and “situation awareness”. One limitation of their study was that the indicators they were used could not perfectly reflect the RE potential of an organization. Aleksic et al. [6] developed a fuzzy mathematical model to assess the organizational resilience in the process industries. They used the extent Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) to rank the RFs in the SMEs. The contribution of this work was the application of an MCDM method to rank different enterprises. Shirali et al. [7] utilized the principal component analysis (PCA) method combined with natural taxonomy (NT) to analyze and score the resilience indicators in a process industry. The indicators they used to rank different units included the “top management commitment, “just culture”, “awareness and opacity”, “preparedness”, “learning culture”, and “flexibility”.

Azadeh et al. [8] used the data envelopment analysis (DEA) method to evaluate the performance of RE factors in a petrochemical plant. They applied ten indicators for RE assessment and introduced a new concept, that is integrated resilience engineering (IRE), for the evaluation of RE. They were included four new indicators namely “Teamwork”, “Redundancy”, “Fault tolerant” and “Flexibility” to the previously developed framework to assess the RE performance. In another study, Azadeh et al. [9] applied fuzzy cognitive maps (FCM) to assess resilience engineering factors in safety-critical systems such as petrochemical plants. In this study they used the FCM method to determine the weight of the RE indicators and to rank them.

Huber et al. [10] applied the concepts of resilience engineering to grasp the organization by the examination of cognitive tasks and activities. They developed a computerized scheme to monitor human activities and to formulate indicators that can reveal system resilience. Wachs et al. [11] conducted a survey to identify and re-interpret the Non-Technical Skills (NTS) of the electricians from the RE perspective in an electricity distributor. Grecco et al. [12] developed a method that utilizes the resilience indicators to proactively evaluate and manage the safety in radiopharmaceuticals. This study was only presented the RE indicators without developing any method for ranking the process under consideration by the RE indicators. Lima et al. [13] used the RE concepts to explain how workers of the airport dealt with the complains and constraint of the work, and how it interfere in abnormal or danger situations. Again, this study did not present any method to quantify the RE in the airport.

Although some of the published papers have considered the uncertainty in the data in the field of resilience and have applied fuzzy sets to deal with this problem, there has not been a comprehensive method that could create a categorized system to analyze and rank the safety critical environments based on resilience indicators, while considering these deficiencies. Moreover, as there are many factors that can affect the RE, then resilience evaluation in socio-technical systems should be investigated from a holistic standpoint and must be regarded as a multiple-criteria decision-making (MCDM)problem.

In sum, the motivation behind this work was the lack of a comprehensive structure that can measure the resiliency potential of a complex system and, at the same time, could handle the uncertainty in the measurement process. To overcome this problem, we proposed a framework in this study that incorporates the resilience engineering indicators in Fuzzy sets and MCDM techniques; three indicators, namely Comprehensive Resilience Index (CoRI), Resilience Grade (RG), and Resilience Early Warning Grade (REWG) were also proposed to evaluate the resiliency of a safety-critical system. This paper aims to present an effective framework to establish a resilience assessment and early warning ranking scheme for socio-technical systems. With regard to the resilience assessment and early warning ranking results, appropriate safety measures aligned with the risks and hazards in the safety critical environments can be performed in order to put off and decrease the undesirable effects of the unidentified consequences of interactions between components of thesystem.

2 Materials and methods

The current study is an analytical cross-sectional survey that utilized the Fuzzy sets and AHP method to evaluate the RE performance. In order to present the applicability and usefulness of the proposed method for the assessment of resilience socio-technicalsystems, a gas refinery complex selected as the case study. The selected gas refinery company established 50 years ago with about 1000 personnel.

The adopted analytical hierarchy process (AHP) technique in this study, is one of the most widely used multi criteria decision making (MCDM) methods [14]. The conventional AHP takes into account the distinct judgments of decision makers. Decision-making with the AHP is accomplished in two sequential phases: [1] construction of hierarchy, which includes breaking the decision dilemma into a hierarchy of consistent decision elements (i.e., goal, criteria, and alternatives) and [2] evaluation of hierarchy, which includes extracting weights of the criteria and combining these weights and preferences to establish alternative priorities [15].

Even though the conventional AHP takes account of experts’ opinions and performs a multiple-criteria assessment, it is not capable of revealing human’s fuzzy opinions [16]. The fuzzy set theory, puts together the comparison process more flexibly and potently in order to clarify experts’ preferences [17].

In sum, the steps of the proposed method summarized as followings:

Arrangement of a decision group

Establishment of the evaluation framework

Determination of the RE indicators weights

Evaluation of the RE indicators by the DMG

Calculation of the fuzzy evaluating vector

Rating of resilience in socio-technical systems

2.1 Arrangement of a decision group

Initially, a decision making group (DMG)including five process engineers, three safety specialists, and two operators organized to compare the importance of resilience indicators against each other and outline a benchmark structure for resilience rating of the process.

2.2 Establishment of the evaluation framework

The second step was to conduct a survey about the indicators that could effectively reflect the resiliency of the system. After a comprehensive review of the indicators (Table 1) and considering the opinions of the DMG, we concluded that the theme presented by Grecco et al. [12] is one of the most suitable themes that can be applied to effectively assess resilience potential in oil and gas refinery complexes. This theme, which is based on the LIOH (LeadingIndicators of Organizational Health) scheme[18, 19] and consider the most applied indicators of the Table 1, incorporates six main groups of indicators including “management commitment”, “just culture”, “learning culture”, “awareness”, “flexibility” and “preparedness”. With respect to the DMG expertise, we developed some sub-indicators for each indicator as shown in Fig. 1.

Table 1
RE indicators proposed by different authors

Management Just culture Learning Awareness Preparedness Flexibility Teamwork Redundancy Fault

commitment culture tolerant

Carvalho et al. [21]

Dijkstra [22]

Akselsson et al. [23]

Costella et al. [24]

Gomes et al. [25]

Huber et al. [26]

Morel et al. [27]

Størseth et al. [28]

Herrera et al. [29]

Saurin and Carim

Junior [30]

Shirali et al. [31]

Ouedraogo et al. [32]

Azadeh et al. [9]

Azadeh and Salehi;

Azadeh et al. [33]

Salzano et al. [34]

Saurin et al. [35]

Fig.1

Hierarchical structure of resiliency indicators and sub-indicators (Grecco et al. 2012).

2.3 Determination of the RE indicators weights

With regard to the resilience evaluation framework (Fig. 1), the DMG were required to perform pair-wise comparisons between the first and second levels of indicators. To do this, they applied linguistic terms shown in Table 2 to compare each indicator of the first and second levels with the adjacent indicators at its own level. Then, the weights of each indicator determined as follows:

Table 2
Linguistic variables and corresponding TrFNs for resilience indicators pair-wise comparison

Linguistic Trapezoidal fuzzy Linguistic Trapezoidal fuzzy

variable number (TrFN) variable fuzzy number (TrFN)

EI 1 1 1 1 ENIWNI 0.33 0.4 0.67 1

EIWI 1 1.5 2.5 3 WNI 0.25 0.29 0.4 0.5

WI 2 2.5 3.5 4 WNIENI 0.2 0.22 0.29 0.33

WIEI 3 3.5 4.5 5 ESNI 0.17 0.18 0.22 0.25

ESI 4 4.5 5.5 6 ENIVSNI 0.14 0.15 0.18 0.2

EIVSI 5 5.5 6.5 7 VSNI 0.13 0.13 0.15 0.17

VSI 6 6.5 7.5 8 VSNIANI 0.11 0.12 0.13 0.14

VSIAI 7 7.5 8.5 9 ANI 0.11 0.11 0.12 0.13

AI 8 8.5 9 9

Linguistic	Trapezoidal fuzzy	Linguistic	Trapezoidal fuzzy
EI	1	1	1	1	ENIWNI	0.33	0.4	0.67	1
EIWI	1	1.5	2.5	3	WNI	0.25	0.29	0.4	0.5
WI	2	2.5	3.5	4	WNIENI	0.2	0.22	0.29	0.33
WIEI	3	3.5	4.5	5	ESNI	0.17	0.18	0.22	0.25
ESI	4	4.5	5.5	6	ENIVSNI	0.14	0.15	0.18	0.2
EIVSI	5	5.5	6.5	7	VSNI	0.13	0.13	0.15	0.17
VSI	6	6.5	7.5	8	VSNIANI	0.11	0.12	0.13	0.14
VSIAI	7	7.5	8.5	9	ANI	0.11	0.11	0.12	0.13
AI	8	8.5	9	9

EI: Equally Important, EIWI: Equally Important to Weakly Important, WI: Weakly Important, WIEI: Weakly Important to Essentially Important, ESI: Essentially Important, EIVSI: Essentially Important, to Very strongly Important, VSI: Very strongly Important, VSIAI: Very strongly Important, to Absolutely Important, AI: Absolutely Important. ENIWNI: Equally Non-Important to Weakly Non-Important, WNI: Weakly Non-Important WNIENI: Weakly Non-Important to Essentially Non-Important, ESNI: Essentially Non-Important, ENIVSNI: Essentially Non-Important to Very strongly Non-Important, VSNI: Very strongly Non-Important, VSNIANI: Very strongly Non-Important to Absolutely Non-Important, ANI: Absolutely Non-Important.

2.3.1 Establishment of the pair-wise comparison (PWC) matrix

A matrix $\tilde{X}$ was created according to the pair-wise comparisons.

${\tilde{x}}_{ij} = [\begin{matrix} {\tilde{x}}_{11} & {\tilde{x}}_{12} & \dots & {\tilde{x}}_{1 n} \\ {\tilde{x}}_{21} & {\tilde{x}}_{22} & \dots & {\tilde{x}}_{2 n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ {\tilde{x}}_{n 1} & {\tilde{x}}_{n 2} & \dots & {\tilde{x}}_{nn} \end{matrix}]$ (1)

2.3.2 Comparison matrix consistency check

After the comparison, matrices were established, and the consistency checks of the matrices performed by computing the consistency ratio (CR): $CR = \frac{CI}{RI}; CI = (λ_{\max} - n) / (n - 1)$ (2)

Where: λ_max is the largest Eigen value of the comparison matrix. “CI” indicates the consistency index, “RI” denotes the random index, and “n” is the number of criteria that would be judged against (i.e., matrix size).

2.3.3 Calculation of the weights

In this work, we adopt Geometric mean method to determine the resilience indicator weights [20]. Based on the previously constructed pair-wise comparison matrix ${\tilde{x}}_{ij}$ , the weights determined as follows: $\begin{matrix} α_{j} = {[\prod_{j = 1}^{n} l_{ij}]}^{1 / n}; β_{j} = {[\prod_{j = 1}^{n} m_{ij}]}^{1 / n}; \end{matrix}$

$γ_{j} = {[\prod_{j = 1}^{n} n_{ij}]}^{1 / n}; δ_{j} = {[\prod_{j = 1}^{n} s_{ij}]}^{1 / n} and$ (3)

$α = \sum_{j = 1}^{n} α_{j}; β = \sum_{j = 1}^{n} β_{j}; γ = \sum_{j = 1}^{n} γ_{j}; δ = \sum_{j = 1}^{n} δ_{j}$ (4)

That l, m, n, and s are the vectors of the trapezoidal fuzzy number (TrFN) $\tilde{A} = (1, m, n, s)$ .

The indicators weights acquired as: ${\tilde{w}}_{j} = (α_{j} δ^{- 1}, β_{j} γ^{- 1}, γ_{j} β^{- 1}, δ_{j} α^{- 1}) j \in {1, 2, \dots, n}$ (5)

Subsequently, the fuzzy weight vector ${\tilde{w}}_{j}$ was determined as: $\tilde{W} = [{\tilde{w}}_{1}, {\tilde{w}}_{2}, \dots, {\tilde{w}}_{n}]$ (6)

2.4 Evaluation of the RE indicators by the DMG

After the indicators weights was determined, the DMG were required to evaluate each indicators applying the linguistic terms that are shown in Table 3.

Table 3
Linguistic variables and corresponding TrFNs for Resiliency evaluation

Linguistic variables Trapezoidal fuzzy

numbers (TrFNs)

Very poor (0, 1, 2, 3)

Poor (1, 2, 3, 4)

Medium (3, 4, 5, 6)

Good (5, 6, 7, 8)

Very good (7, 8, 9, 10)

Linguistic variables	Trapezoidal fuzzy
Very poor	(0, 1, 2, 3)
Poor	(1, 2, 3, 4)
Medium	(3, 4, 5, 6)
Good	(5, 6, 7, 8)
Very good	(7, 8, 9, 10)

2.5 Calculation of the fuzzy evaluating vector

The rating of the overall resilience of the plant performed based on the fuzzy evaluating vector (FEV). The FEV of a specific indicator is determined based on the comparison tables, the trapezoidal fuzzy numbers in Table 2, and the fuzzy weight vector (Equation 5); it was calculated as follows:

Let we have k decision makers (D1, D2,...,Dk) and n attributes (f1, f2,...,fn). The evaluating value $\tilde{f_{j}}$ of the attribute f_j presented by the decision group can be achieved by Equation (6). $\tilde{f_{j}} = \frac{1}{K} ({\tilde{f}}_{j}^{1} + {\tilde{f}}_{j}^{2} + \dots + {\tilde{f}}_{j}^{k})$ (7)

Subsequently, the fuzzy evaluating matrix acquired as follows (Equation 7): $\tilde{f} = [{\tilde{f}}_{1} {\tilde{f}}_{2} \dots {\tilde{f}}_{n}]$ (8)

The fuzzy evaluating vector $(\tilde{Z)}$ createdbased on the fuzzy evaluating matrix ${\tilde{f}}_{j}$ and calculated weights ${\tilde{w}}_{j}$ (Equation 9).

$\begin{matrix} \tilde{Z} = {({\tilde{w}}_{1} \otimes {\tilde{f}}_{1}) \oplus ({\tilde{w}}_{2} \otimes {\tilde{f}}_{2}) \\ \oplus ({\tilde{w}}_{3} \otimes {\tilde{f}}_{3}) \oplus \dots \oplus ({\tilde{w}}_{n} \otimes {\tilde{f}}_{j}) \\ ⊘ {\tilde{w}}_{1} \oplus {\tilde{w}}_{2} \oplus {\tilde{w}}_{3} \oplus \dots \oplus {\tilde{w}}_{j}} \end{matrix}$ (9)

2.6 Rating the resilience of the system

With regard to the fuzzy evaluating vector of socio-technical settings (Equation 8), the resiliency level of the system has been determined. A resilience ranking system, including two parameters, namely “resilience grade” (RG) and “resilience early warning grade” (REWG), was established as shown in Table 4. As it can be seen in the Table 4, when the resilience rating (grade) is I or II (indicated as “Red” or “Orange” early warning, respectively), it means that the resiliency is poor, and appropriate proactive and practical measures should be taken.

In order to practically demonstrate the assessment results, the fuzzy evaluating vector of the system has been characterized as a new index called “comprehensive resilience index” (CoRI). In addition, the fuzzy evaluating vector of the resilience indicators (C1-C6) were defined as “Top-level management commitment index” (TMCI), “Organizational learning index” (OLI), “Organizational flexibility index” (OFI), “Awareness index”(AI), “Just culture index” (JCI), and “Emergency preparedness index” (EPI), respectively. In order to rank the resiliency, the fuzzy scales converted into the corresponding crisp values by Equation (10), and, finally, the aforementioned indexes were determined. $\begin{matrix} {defuzz}_{(xij)} \\ = \frac{- l_{ij} m_{ij} + n_{ij} s_{ij} + \frac{1}{3} {(s_{ij} - n_{ij})}^{2} - \frac{1}{3} {(m_{ij} - l_{ij})}^{2}}{- l_{ij} - m_{ij} + n_{ij} + s_{ij}} \end{matrix}$ (10)

Table 4

Resilience rating system

Resilience	Resilience Early	Description	Trapezoidal fuzzy
grade	warning grade		numbers (TrFNs)
I	II	Red early warning zone (REWZ)	(0, 1, 2, 3) ≤ Z < (1, 2, 3, 4)
II	I	Orange early warning zone (OEWZ)	(1, 2, 3, 4) ≤ Z < (3, 4, 5, 6)
III		No early warning zone (NEWZ)	(3, 4, 5, 6) ≤ Z < (5, 6, 7, 8)
IV			(5, 6, 7, 8) ≤ Z < (7, 8, 9, 10)

3 Results and discussion

As previously mentioned, in order to present the applicability and usefulness of the proposed method for the assessment of resilience socio-technical systems, a gas refinery complex was selected as the case study.

With regard to the proposed method, the results of the study are shown in Tables 5–7. Table 5 shows the pair-wise comparison of the main indicators. Each row of the Table 5 indicates the pair-wise comparison of indicators (e.g. C1/C2) in terms of the linguistic variables. According to the results of pair-wise comparison matrixes extracted from the DMG, the weights of the sub-indicators were determined by Equations 2 to 5. The fuzzified, defuzzified and normalized weights of resilience weights are shown in Table 6. Consistency checks of the pair-wise matrices indicated that all of matrices were consistent (i.e. CR <0.10). In order to make judgments against the weights of the factors and sub-factors, the fuzzy weight vectors are defuzzified by Equation (9). Resultant defuzzified and normalized weights are given in Table 6.

Table 5
Main indicators pair-wise comparison’s of DMs

DM1 DM2 DM3 DM4 DM5 DM6 DM7 DM8 DM9 DM10

C1/C2

ESI VSI EIVSI ESI EIVSI ESI EIVSI ESI ESI VSI

C1/C3

EIVSI VSI VSIAI VSIAI VSIAI VSIAI VSIAI EIVSI VSI VSIAI

C1/C4

EIVSI VSI VSI VSI EIVSI EIVSI VSI VSI EIVSI VSI

C1/C5

WI EI EI EI EIWI WI EI EIWI EI EIWI

C1/C6

WI WI WI EIWI EIWI EIWI WI WI EIWI EIWI

C2/C3

EIWI EIWI WI EIWI WI WIEI EIWI EIWI WI WIEI

C2/C4

WNIEN WNI ENIWN ENIWN WNIEN WNIENI ENIWNI ENIWN WNIENI WNIENI

C2/C5

WNIEN WNI WNIEN ENIWN WNI WNIENI WNIENI ENIWN WNI WNIENI

C2/C6

WNIEN WNIEN ESNI WNIEN WNIEN ENIVSN ENIVSN WNIEN ESNI ENIVSNI

C3/C4

ENIWN ENIWN WNIEN WNI WNIEN ENIWNI WNI ENIWN WNIENI ENIWNI

C3/C5

WI WI WI WIEI WI WIEI WI WI WI WIEI

C3/C6

WNIEN WNIEN WNIEN ESNI WNIEN ENIVSN ENIVSN ESNI ENIVSN ESNI

C4/C5

EIWI WI WIEI WI WIEI WI WI EIWI EIWI WIEI

C4/C6

WNI ENIWN WNIEN WNIEN WNI WNI ENIWNI WNIEN WNI WNI

C5/C6

ENIWN WNI WNI ENIWN ENIWN WNI ENIWNI ENIWN ENIWNI ENIWNI

DM1	DM2	DM3	DM4	DM5	DM6	DM7	DM8	DM9	DM10
C1/C2
ESI	VSI	EIVSI	ESI	EIVSI	ESI	EIVSI	ESI	ESI	VSI
C1/C3
EIVSI	VSI	VSIAI	VSIAI	VSIAI	VSIAI	VSIAI	EIVSI	VSI	VSIAI
C1/C4
EIVSI	VSI	VSI	VSI	EIVSI	EIVSI	VSI	VSI	EIVSI	VSI
C1/C5
WI	EI	EI	EI	EIWI	WI	EI	EIWI	EI	EIWI
C1/C6
WI	WI	WI	EIWI	EIWI	EIWI	WI	WI	EIWI	EIWI
C2/C3
EIWI	EIWI	WI	EIWI	WI	WIEI	EIWI	EIWI	WI	WIEI
C2/C4
WNIEN	WNI	ENIWN	ENIWN	WNIEN	WNIENI	ENIWNI	ENIWN	WNIENI	WNIENI
C2/C5
WNIEN	WNI	WNIEN	ENIWN	WNI	WNIENI	WNIENI	ENIWN	WNI	WNIENI
C2/C6
WNIEN	WNIEN	ESNI	WNIEN	WNIEN	ENIVSN	ENIVSN	WNIEN	ESNI	ENIVSNI
C3/C4
ENIWN	ENIWN	WNIEN	WNI	WNIEN	ENIWNI	WNI	ENIWN	WNIENI	ENIWNI
C3/C5
WI	WI	WI	WIEI	WI	WIEI	WI	WI	WI	WIEI
C3/C6
WNIEN	WNIEN	WNIEN	ESNI	WNIEN	ENIVSN	ENIVSN	ESNI	ENIVSN	ESNI
C4/C5
EIWI	WI	WIEI	WI	WIEI	WI	WI	EIWI	EIWI	WIEI
C4/C6
WNI	ENIWN	WNIEN	WNIEN	WNI	WNI	ENIWNI	WNIEN	WNI	WNI
C5/C6
ENIWN	WNI	WNI	ENIWN	ENIWN	WNI	ENIWNI	ENIWN	ENIWNI	ENIWNI

Table 6

Fuzzified, Defuzzified and Normalized weights of resilience indicators

		W				Defuzzified	Normalized	Rank
		αjδ-1	βjγ-1	γjβ-1	δjα-1	weights	weights
C1		0.343	0.629	0.940	1.646	0.855	0.384	1
C2		0.048	0.090	0.144	0.310	0.138	0.062	6
C3		0.052	0.094	0.146	0.299	0.139	0.063	5
C4		0.087	0.188	0.306	0.615	0.282	0.127	3
C5		0.083	0.125	0.223	0.332	0.185	0.083	4
C6		0.223	0.482	0.830	0.905	0.625	0.281	2
C1	C1.1	0.126	0.267	0.359	0.666	0.341	0.162	3
	C1.2	0.221	0.383	0.520	1.011	0.506	0.240	2
	C1.3	0.112	0.211	0.284	0.503	0.268	0.127	4
	C1.4	0.034	0.058	0.078	0.131	0.073	0.035	6
	C1.5	0.049	0.120	0.164	0.148	0.128	0.061	5
	C1.6	0.277	0.639	0.981	0.993	0.752	0.356	1
	C1.7	0.016	0.032	0.054	0.064	0.042	0.020	7
C2	C2.1	0.098	0.179	0.276	0.540	0.258	0.050	7
	C2.2	0.058	0.099	0.149	0.279	0.139	0.027	8
	C2.3	0.264	0.526	0.819	1.564	0.753	0.146	4
	C2.4	0.097	0.217	0.347	0.656	0.314	0.061	6
	C2.5	0.247	0.701	1.126	1.465	0.894	0.173	3
	C2.6	0.308	0.859	1.525	1.807	1.147	0.223	2
	C2.7	0.085	0.275	0.553	0.509	0.375	0.073	5
	C2.8	0.429	0.962	1.543	1.737	1.196	0.232	1
	C2.9	0.038	0.059	0.090	0.133	0.078	0.015	9
C3	C3.1	0.396	0.667	0.944	1.556	0.862	0.284	2
	C3.2	0.075	0.121	0.172	0.298	0.160	0.053	5
	C3.3	0.036	0.053	0.073	0.118	0.068	0.022	6
	C3.4	0.089	0.155	0.229	0.389	0.208	0.068	4
	C3.5	0.228	0.449	0.647	0.564	0.497	0.164	3
	C3.6	0.486	1.028	1.720	1.481	1.244	0.409	1
C4	C4.1	0.338	0.504	0.648	0.940	0.597	0.338	1
	C4.2	0.231	0.336	0.429	0.620	0.397	0.225	2
	C4.3	0.026	0.040	0.060	0.121	0.058	0.033	9
	C4.4	0.014	0.020	0.027	0.048	0.026	0.015	10
	C4.5	0.037	0.066	0.097	0.135	0.083	0.047	7
	C4.6	0.042	0.099	0.150	0.174	0.119	0.067	4
	C4.7	0.032	0.070	0.098	0.100	0.078	0.044	8
	C4.8	0.118	0.184	0.248	0.252	0.206	0.117	3
	C4.9	0.047	0.079	0.111	0.128	0.093	0.053	6
	C4.10	0.058	0.092	0.131	0.154	0.110	0.062	5
C5	C5.1	0.398	0.557	0.714	0.995	0.656	0.284	2
	C5.2	0.090	0.125	0.167	0.262	0.156	0.068	4
	C5.3	0.121	0.191	0.264	0.385	0.236	0.102	3
	C5.4	0.035	0.045	0.056	0.083	0.053	0.023	5
	C5.5	0.450	1.093	1.418	1.765	1.206	0.523	1
C6	C6.1	0.039	0.068	0.104	0.213	0.099	0.042	5
	C6.2	0.358	0.598	0.850	1.424	0.780	0.331	2
	C6.3	0.093	0.171	0.241	0.402	0.220	0.093	4
	C6.4	0.119	0.192	0.273	0.531	0.263	0.112	3
	C6.5	0.310	0.773	1.117	1.453	0.924	0.392	1
	C6.6	0.035	0.046	0.074	0.140	0.069	0.029	6

Table 7

Resilience indicators evaluation results

	Fuzzy Evaluating Vector (FEW)				Defuzzified FEV	FEW Range		RG	REWG
	L	m	N	S		Lower Limit	Upper Limit
C1	3.584	4.518	5.471	6.725	5.089	Medium	Good	III	NEWZ
C2	3.104	4.102	5.065	5.960	4.553	Medium	Good	III	NEWZ
C3	1.605	2.540	3.501	4.692	3.096	Poor	Medium	II	OEWZ
C4	3.549	4.519	5.504	6.457	5.007	Medium	Good	III	NEWZ
C5	3.922	5.228	6.239	7.183	5.627	Medium	Good	III	NEWZ
C6	4.304	5.245	6.244	7.307	5.78	Medium	Good	III	NEWZ

Refinery		3.655	4.652	5.655	6.644	5.151	Medium	Good	III	NEWZ
C1	C1.1	5.400	6.400	7.400	8.400	6.9	Good	Very Good	IV	NEWZ
	C1.2	4.600	5.600	6.600	7.600	6.1	Medium	Good	III	NEWZ
	C1.3	2.400	3.400	4.400	5.400	3.9	Poor	Medium	II	OEWZ
	C1.4	3.100	4.100	5.100	6.100	4.6	Medium	Good	III	NEWZ
	C1.5	3.600	4.600	5.600	6.600	5.1	Medium	Good	III	NEWZ
	C1.6	2.400	3.400	4.400	5.400	3.9	Poor	Medium	II	OEWZ
	C1.7	5.000	6.000	7.000	8.000	6.5	Good	Very Good	IV	NEWZ
C2	C2.1	1.8	2.8	3.8	4.8	3.3	Poor	Medium	II	OEWZ
	C2.2	1.6	2.6	3.6	4.6	3.1	Poor	Medium	II	OEWZ
	C2.3	2.3	3.3	4.3	5.3	3.8	Poor	Medium	II	OEWZ
	C2.4	3.4	4.4	5.4	6.4	4.9	Medium	Good	III	NEWZ
	C2.5	3.3	4.3	5.3	6.3	4.8	Medium	Good	III	NEWZ
	C2.6	2.9	3.9	4.9	5.9	4.4	Poor	Medium	II	OEWZ
	C2.7	2.2	3.2	4.2	5.2	3.7	Poor	Medium	II	OEWZ
	C2.8	4.6	5.6	6.6	7.6	6.1	Medium	Good	III	NEWZ
	C2.9	2.5	3.5	4.5	5.5	4	Poor	Medium	II	OEWZ
C3	C3.1	2.400	3.400	4.400	5.400	3.9	Poor	Medium	II	OEWZ
	C3.2	2.200	3.200	4.200	5.200	3.7	Poor	Medium	II	OEWZ
	C3.3	2.100	3.100	4.100	5.100	3.6	Poor	Medium	II	OEWZ
	C3.4	1.700	2.700	3.700	4.700	3.2	Poor	Medium	II	OEWZ
	C3.5	1.200	2.200	3.200	4.200	2.7	Poor	Medium	II	OEWZ
	C3.6	1.000	2.000	3.000	4.000	2.5	Poor	Medium	II	OEWZ
C4	C4.1	2.200	3.200	4.200	5.200	3.7	Poor	Medium	II	OEWZ
	C4.2	5.400	6.400	7.400	8.400	6.9	Good	Very Good	IV	NEWZ
	C4.3	2.400	3.400	4.400	5.400	3.9	Poor	Medium	II	OEWZ
	C4.4	3.600	4.600	5.600	6.600	5.1	Medium	Good	III	NEWZ
	C4.5	2.600	3.600	4.600	5.600	4.1	Poor	Medium	II	OEWZ
	C4.6	2.600	3.600	4.600	5.600	4.1	Poor	Medium	II	OEWZ
	C4.7	3.700	4.700	5.700	6.700	5.2	Medium	Good	III	NEWZ
	C4.8	4.400	5.400	6.400	7.400	5.9	Medium	Good	III	NEWZ
	C4.9	4.800	5.800	6.800	7.800	6.3	Medium	Good	III	NEWZ
	C4.10	3.000	4.000	5.000	6.000	4.5	Medium	Medium	III	NEWZ
C5	C5.1	2.200	3.200	4.200	5.200	3.7	Poor	Medium	II	OEWZ
	C5.2	4.400	5.400	6.400	7.400	5.9	Medium	Good	III	NEWZ
	C5.3	4.800	5.800	6.800	7.800	6.3	Medium	Good	III	NEWZ
	C5.4	2.800	3.800	4.800	5.800	4.3	Poor	Medium	II	OEWZ
	C5.5	5.200	6.200	7.200	8.200	6.7	Good	Very Good	IV	NEWZ
C6	C6.1	5.400	6.400	7.400	8.400	6.9	Good	Very Good	IV	NEWZ
	C6.2	4.200	5.200	6.200	7.200	5.7	Medium	Good	III	NEWZ
	C6.3	5.400	6.400	7.400	8.400	6.9	Good	Very Good	IV	NEWZ
	C6.4	4.800	5.800	6.800	7.800	6.3	Medium	Good	III	NEWZ
	C6.5	3.800	4.800	5.800	6.800	5.3	Medium	Good	III	NEWZ
	C6.6	4.000	5.000	6.000	7.000	5.5	Medium	Good	III	NEWZ

It is clearly evident from Table 6 that “C1”,” C6”, “C4”, “C5”, “C3”, and “C2” ranked first to sixth, respectively. For the first indicator, “Top-management commitment” (C1), the results show that the contribution of the C1.6 indicator “Training programs” to the resilience is large, and the arrangement queue of the weight importance of the sub-indicators within the “C1” is C1.6 > C1.2 > C1.1 > C1.3 > C1.5 > C1.4 > C1.7, respectively. In other words, one can say that “Training programs” plays the most important role in the “Top- management commitment” resilience evaluation. This means that one way to improve the RE performance is to focus on training programs for the personnel. As for other sub-indicators, one may be referred to Table 6 to obtain the importance of each sub-indicator within the six main indicators.

Based on the initial assessment results, the assessment value $\tilde{f_{j}}$ of each sub-indicator is determined by Equation (6). Consequently, the fuzzy evaluating matrix was acquired. Later, the fuzzy evaluating vectors in each of the hierarchies are determined by Equation (8). The assessment results of the fuzzy evaluating vectors are presented in Table 7.

According to Table 7, the resilience potential of the gas refinery can be analyzed. Fig. 2 demonstrates the membership function sketch of the gas refinery in contrast to the five evaluation grades (viz., VG, G, M, P, and VP). As shown in Fig. 2, the resilience grade of the gas refinery is positioned between medium and good grades (i.e., the defuzzified value of 5.151). As for the main indicators (C1-C6), their evaluation results are positioned between medium and good, except for C3, with its value located between poor and medium. Therefore, it can be concluded that the “Organizational flexibility” of the refinery plant is not very good (Fig. 3).

Fig.2

Membership grade of the Gas Refinery (comprehensive resilience index).

Fig.3

Membership grades of sub-indicators.

With respect to Figs. 2 and 3 that show the defuzzified values of the evaluation results, “top-level commitment index”, “Organizational learning index”,“Organizational flexibility index”, “Awareness index”, “Just culture index”, and “Emergency preparedness index” of sub-indicators equal to 5.089, 4.553, 3.096, 5.007, 5.627, and 5.78, respectively.

Based on the presented framework for the resiliency evaluation (Table 4) as well as Table 7,it is evident that, for the refinery complex, the “comprehensive resilience index” (CoRI) equals to 5.151, and consequently, the “resilience grade” (RG) and “resilience early warning grade” (REWG) ranked as “III” and “NEWZ”, respectively. As “RG” of the refinery plant is positioned outside of the warning zone of the early warning system, it does not require any further attention about the resiliency of the plant. However, with a brief look at the sub-indicators evaluation results, it can be seen that although the REWG of the refinery is located outside the warning zone, any negligence may cause the sub-indicators to shift the current position of the “comprehensive safety index” and incline it to the warning zone I or maybe II. For the six main indicators, RG and REWG ranked as “III” and “NEWZ”, respectively, except for C3 in which RG ranked as “II,” and the corresponding REWG ranked as “OEWZ”. This means that the current state of the “organizational flexibility” is located in the orange early warning zone (OEWZ) of the warning system, and, accordingly, appropriate measures must be taken to improve the condition of this indicator. RG and REWG of the sub-indicators are also shown in Table 7. As it can be seen in the Table 7, REWG and RG of the indicators C1.4, C1.6, C2.1, to C2.9 (except for C2.4, C2.5, and C2.8), C3.1 to C3.6, C4.1, C4.3, C4.5, C4.6, C5.1, and C5.4 ranked as “OEWZ” and “II”, respectively. This piece of finding shows that if those mentioned sub-indicators are not be corrected, the comprehensive resilience index of the system must be reallocated to the “OEWZ” or, even worse, to the “REWZ”.

The first step of this study was to develop a new framework for RE performance evaluation and to test it in a real word application (gas refinery plant). It may be suggested to further validate the proposed method, the output of the suggested model (i.e. Resilience Grade) be compared with the near misses prevalence and investigate their correlation, in future works.Also the subjectivity of the expert opinions about the weight of the RE indicators may be another limitation in the assessment of RE performance. In this regard, it is recommended that it will be helped from the power of objective weighting method such as Shannon’s entropy to promote the efficiency of themethod.

4 Conclusions

There are many methods to analyze and manage safety in working environments; nevertheless, because of the tight coupling and intricate connections between components, tracking the changes in the performance of the systems in socio-technical settings is next to impossible. To deal with this problem, new approaches can be advantageous. Resilience engineering is a new approach that, in contrast to the traditional safety analysis methods, looks at what a system does instead of what it has. Even though there have been several research attempts focusing on the quantification of resilience, none of them has offered a comprehensive framework that can measure and evaluate resiliency potential of safety-critical systems. This work, thus, proposed a hierarchical framework based on resilience indicators and utilized the fuzzy set theory to deal with the uncertainty associated with input data. The proposed structure introduces “CoRI” and “REWG” concepts to evaluate resiliency in safety-critical systems. The results of the case study also showed the applicability of the proposed framework and the feasibility of the method in the conditions of vagueness and ambiguity, which is a characteristic of socio-technical systems. The proposed model can be used by the managers to be warned in case of deterioration of resiliency and shifting from the safe boundaries of the system to unsafe regions.

Conflict of interest

The authors have no conflict of interest to report.

Footnotes

Acknowledgments

This study was part of a PhD thesis supported by Tehran University of Medical Sciences, School of Public Health, Department of Occupational Health Engineering. The National Iran Gas Company (NIGC) is acknowledged for their financial support of this research. In addition, the authors express their full thanks to the member of expert’s panel of the NIGC for their kind corporation valuable comments in this study.

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	Management	Just culture	Learning	Awareness	Preparedness	Flexibility	Teamwork	Redundancy	Fault
	commitment		culture						tolerant
Carvalho et al. [21]
Dijkstra [22]
Akselsson et al. [23]
Costella et al. [24]
Gomes et al. [25]
Huber et al. [26]
Morel et al. [27]
Størseth et al. [28]
Herrera et al. [29]
Saurin and Carim
Junior [30]
Shirali et al. [31]
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Azadeh et al. [9]
Azadeh and Salehi;
Azadeh et al. [33]
Salzano et al. [34]
Saurin et al. [35]

Development of a framework for resilience measurement: Suggestion of fuzzy Resilience Grade (RG) and fuzzy Resilience Early Warning Grade (REWG)

Abstract

Keywords

1 Introduction

2 Materials and methods

2.1 Arrangement of a decision group

2.2 Establishment of the evaluation framework

Table 3 Linguistic variables and corresponding TrFNs for Resiliency evaluation Linguistic variables Trapezoidal fuzzy numbers (TrFNs) Very poor (0, 1, 2, 3) Poor (1, 2, 3, 4) Medium (3, 4, 5, 6) Good (5, 6, 7, 8) Very good (7, 8, 9, 10)

Conflict of interest

Footnotes

Acknowledgments

References

Table 3
Linguistic variables and corresponding TrFNs for Resiliency evaluation

Linguistic variables Trapezoidal fuzzy

numbers (TrFNs)

Very poor (0, 1, 2, 3)

Poor (1, 2, 3, 4)

Medium (3, 4, 5, 6)

Good (5, 6, 7, 8)

Very good (7, 8, 9, 10)