# Identification and Prioritization of Risk Factors in an Electrical Generator Based on the Hybrid FMEA Framework

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## Abstract

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## 1. Introduction

- The same RPN value may be generated from different values of O, S, and D; however, their hidden risk rank could be wholly dissimilar.
- RPN calculation considers that the three risk elements have the same important weight, which is difficult to be installed in practice.
- Three factors are difficult to accurately evaluate by experts with a different background.
- Interdependencies are not considered between several failure approaches and effects.

- (1)
- The ability to clarify the independence on alternatives or criteria.
- (2)
- The ability to offer the interdependence between the criteria in the same cluster and offer feedback of alternatives or sub-criteria to the main criteria.

## 2. Proposed Method of Hybrid LFMEA Framework

**Step 1**: Classify main dimensions and failure modes of the system in the industrial plant to be analyzed through the methodology. Data is extracted from the Computerized Maintenance Management System (CMMS) database, vendor documents, a literature review, and the opinion of experts. A team of $n$ experts ${E}^{t}=\left\{{E}^{1},{E}^{2},\dots ,{E}^{\mathrm{n}}\right\}$ will structure and organize the data into $m$ main risk factor dimensions $MD=\left\{M{D}_{1},M{D}_{2},\dots ,M{D}_{m}\right\}$ and failure modes $FM=\left\{F{M}_{1},F{M}_{2},\dots ,F{M}_{k}\right\}$, where $k$ is the number of failure modes.

#### 2.1. Extended Linguistic FMEA

- $k\otimes \text{}{V}_{A}\text{}=\text{}{V}_{k\otimes A}$
- ${\left({V}_{A}\right)}^{k}\text{}=\text{}{V}_{{A}^{k}}$
- ${V}_{A}\oplus {V}_{B}=\text{}{V}_{B}\oplus {V}_{A}=\text{}{V}_{A+B}$
- ${V}_{A}\ast \text{}{V}_{A}=\text{}{V}_{A}\text{}\otimes {V}_{A}\text{}=\text{}{V}_{A\ast B}$

**Step 2**: Apply the improved linguistic FMEA risk evaluation method to obtain weights for experts and failure modes with the main clusters based on fuzzy priority and the linguistic operator.

- (i)
- Calculate the risk factor weights by the experts as $W=\left({w}_{O},{w}_{S},{w}_{D}\right)$ through an Analytic Network Process (ANP) where $\sum W=1$.
- (ii)
- Calculate linguistic evaluation matrix values ${V}_{tj}$ for main risk factor clusters of failure mode, which will consist of $n$ rows of expert and $m$ columns of main FM clusters.${V}_{tj}=\{({V}_{tj}^{O},{V}_{tj}^{S},{V}_{tj}^{D})\}$, where $t=\left\{1,\text{}2,\text{}3,\cdots ,\text{}n\text{}\right\},\text{}j=\left\{1,\text{}2,\text{}3,\cdots m\right\}$${V}_{tj}^{O},{V}_{tj}^{S},{V}_{tj}^{D}$ are risk language evaluation weights given by expert ${E}^{t}$ for $\text{}F{M}_{j}$ failure mode, where $E$ is the expert weight.
- (iii)
- Calculate the risk priority number ${V}_{tj}^{RPN}$ for every $j$ main risk factor and $t$ expert member with power of weights of the risk factor $W=\left({w}_{O},{w}_{S},{w}_{D}\right)$, where ${\mathsf{\phi}}_{x}$ is the risk constant calculated by experts.$${V}_{tj}^{RPN}={({\mathsf{\phi}}_{O}\text{}{V}_{tj}^{O})}^{{w}_{O}}\times {({\mathsf{\phi}}_{S}{V}_{tj}^{S})}^{{w}_{S}}\times {({\mathsf{\phi}}_{D}\text{}{V}_{tj}^{D})}^{{w}_{D}}$$
- (iv)
- Calculate a weight for every expert ${\overline{W}}_{Et}=\left(\overline{w}{\text{}}_{E1},\overline{w}{\text{}}_{E2},\dots ,\overline{w}{\text{}}_{En}\right)$ by using the fuzzy priority matrix F for the prioritization purpose, as in Equations (2)–(5).Rank of failure modes for every expert {$F{M}_{1}^{t},F{M}_{2}^{t},\dots ,F{M}_{m}^{t}\}$ is $F{M}_{1}^{t}>F{M}_{2}^{t}>\cdots >F{M}_{m}^{t}$ (Note: C > D, means C leads D).Construct the matrix F of the fuzzy priority matrix for the prioritization purpose with $FM$ failure mode fuzzy preference ${p}_{ij}$ for $F{M}_{j}$ failure mode. Describe the partial order of the ${p}_{ij}^{t}$ fuzzy priority number [49]:$${p}_{ij}^{t}=\{\begin{array}{c}1,\text{}F{M}_{i}^{t}\text{}is\text{}superior\text{}to\text{}F{M}_{j}^{t}\\ 0.5,\text{}F{M}_{i}^{t}\text{}is\text{}equal\text{}to\text{}F{M}_{j}^{t}\\ 1-{p}_{ij}^{t},\text{\hspace{1em}}\mathrm{when}\text{}i\text{}\ne \text{}j;\\ 0,\text{\hspace{1em}}i=j\text{}or\text{}other\end{array}$$$${p}_{ij}={{\displaystyle \sum}}_{t=1}^{n}{p}_{ij}^{t};\text{}i,\text{}j\text{}=\text{}1,\text{}2,\text{}\cdots ,m$$$$F=\left[\begin{array}{cccc}{p}_{11}& {p}_{12}& \cdots & {p}_{1m}\\ {p}_{21}& {p}_{22}& \cdots & {p}_{2m}\\ \vdots & \vdots & \ddots & \vdots \\ {p}_{m1}& {p}_{m2}& \cdots & {p}_{mm}\end{array}\right]$$For example, if the rank of failure modes for an expert $t$ is equal to ${R}^{t}\text{}=F{M}_{5}^{t}F{M}_{3}^{t}F{M}_{1}^{t}\cdots F{M}_{x}^{t},$ the ordering consistency index will be ${\mathsf{\gamma}}_{t}={p}_{51}+{p}_{53}+{p}_{51}+\cdots +{p}_{5x}+{p}_{31}+\cdots +{p}_{3x}+\cdots +{p}_{tx}$.Then, calculate the summation of every row in the fuzzy priority matrix F and rank them to get ${R}^{t}$. Assume the rank of the summation column is ${R}^{\mathrm{s}}={\sum}_{i=1}^{m}{p}_{2i}>{\sum}_{i=1}^{m}{p}_{5i}>{\sum}_{i=1}^{m}{p}_{mi}>\cdots >{\sum}_{i=1}^{m}{p}_{3i}$, and $\mathsf{\gamma}\left({R}^{\mathrm{s}}\right)$ will be calculated in the same equation used with a consistency index ${\mathsf{\gamma}}_{t}$ [49]:$${\mathsf{\gamma}}_{t}=\frac{\mathsf{\gamma}\left({R}^{t}\right)}{\text{}\mathsf{\gamma}\left({R}^{\mathrm{s}}\right)}\text{};\text{}{\gamma}_{t}\u03f5\left[0,1\right]$$$${\overline{W}}_{Et}={\mathsf{\gamma}}_{t}/{\displaystyle \sum}_{t=1}^{n}{\mathsf{\gamma}}_{t}$$Then, calculate the expert constant ${\beta}_{t}$:$${\beta}_{t\text{}}=\{\begin{array}{c}1,\text{}if\text{}{V}_{tj}^{RPN}\cong \text{}{V}_{xj}^{RPN}\\ \mathrm{max}\{\text{}{\mathsf{\gamma}}_{t}/{\sum}_{t=1}^{n}{\mathsf{\gamma}}_{t}\},\text{}other\end{array}$$
- (v)
- Determine the linguistic priority risk number $L{V}_{j}^{risk}$ for every failure mode $F{M}_{j}$ using expert weights.$$L{V}_{j}^{RPN}={\displaystyle \prod}_{t=1}^{n}{({\beta}_{t\text{}}{V}_{tj}^{RPN})}^{{\overline{W}}_{Et}}={\left({\beta}_{1}\text{}{V}_{1j}\right)}^{{\overline{W}}_{E1}}\times {\left({\beta}_{2}{V}_{2j}\right)}^{{\overline{W}}_{E2}}\times \cdots \times {\left({\beta}_{n}{V}_{nj}\right)}^{{\overline{W}}_{En}}$$

#### 2.2. DEMATEL Approach

**Step 3:**Identify the relationship weights between the main risk factor dimensions and failure modes using the DEMATEL approach through a pairwise comparison matrix and using the following steps [50,51]:

- Determine the direct relation matrix D by pairwise comparisons. Experts are questioned to give the influence values as the pair-wise comparison between each pair of the main risk factor or within each cluster of failure mode elements. These calculations will give a matrix D with the dimensions of m × m:$$\begin{array}{c}\begin{array}{cccc}\text{}F{M}_{1}& \text{}F{M}_{2}& \dots & F{M}_{m}\end{array}\\ D=\begin{array}{c}F{M}_{1}\\ F{M}_{2}\\ \vdots \\ {FM}_{m}\end{array}\left[\begin{array}{ccc}0& \text{}\begin{array}{cc}{a}_{12}& \dots \end{array}\text{}& {a}_{1m}\\ {a}_{21}& \begin{array}{cc}0& \text{}\dots \end{array}& {a}_{2m}\\ \begin{array}{c}\vdots \\ {a}_{m1}\end{array}& \begin{array}{c}\text{}\begin{array}{cc}\vdots & \text{}0\end{array}\\ \begin{array}{cc}{a}_{m2}& \dots \end{array}\end{array}& \begin{array}{c}\vdots \\ 0\end{array}\end{array}\right]\end{array}$$
- Calculate the normalized direct relation N as the following equation:$$N\text{}=\text{}s\text{}\times \text{}D$$The normalization factor is$$s=\mathrm{Min}\left[\frac{1}{{\mathrm{Max}}_{1\le i\le m}({\sum}_{j=1}^{m}{a}_{ij})},\frac{1}{{\mathrm{Max}}_{1\le j\le m}({\sum}_{i=1}^{m}{a}_{ij})}\right]$$
- Calculate the total-influence matrix T by the following equation formula:$$T=N{(I-N)}^{-1}=\left[\begin{array}{ccc}{t}_{11}& \text{}\begin{array}{cc}{t}_{12}& \dots \end{array}\text{}& {t}_{1m}\\ {t}_{21}& \begin{array}{cc}{t}_{22}& \dots \end{array}& {t}_{2m}\\ \begin{array}{c}\vdots \\ {t}_{m1}\end{array}& \begin{array}{c}\text{}\begin{array}{cc}\vdots & \text{}\ddots \end{array}\\ \begin{array}{cc}{t}_{m2}& \dots \end{array}\end{array}& \begin{array}{c}\vdots \\ {t}_{mm}\end{array}\end{array}\right]$$
- The cause and effect relationships are determined by the total relation matrix T, where ${r}_{i},{c}_{j}$ are the summation of row $i$ and column $j$, respectively, as follows:$$\begin{array}{c}T=\left[\begin{array}{ccc}{t}_{11}& \text{}\begin{array}{cc}{t}_{12}& \dots \end{array}\text{}& {t}_{1m}\\ {t}_{21}& \begin{array}{cc}{t}_{22}& \dots \end{array}& {t}_{2m}\\ \begin{array}{c}\vdots \\ {t}_{m1}\end{array}& \begin{array}{c}\text{}\begin{array}{cc}\vdots & \text{}\ddots \end{array}\\ \begin{array}{cc}{t}_{m2}& \dots \end{array}\end{array}& \begin{array}{c}\vdots \\ {t}_{mm}\end{array}\end{array}\right]\begin{array}{c}{r}_{1}={{\displaystyle \sum}}_{j=1}^{m}{t}_{1j}\\ {r}_{2}={{\displaystyle \sum}}_{j=1}^{m}{t}_{2j}\\ {\begin{array}{c}\vdots \\ r\end{array}}_{m}={{\displaystyle \sum}}_{j=1}^{m}{t}_{mj}\end{array}\text{}\\ \begin{array}{ccc}{c}_{1}=\text{}{{\displaystyle \sum}}_{i=1}^{m}{t}_{i1};& {c}_{2}=\text{}{{\displaystyle \sum}}_{i=1}^{m}{t}_{i2};\text{}\cdots \text{};& {c}_{m}=\text{}{{\displaystyle \sum}}_{i=1}^{m}{t}_{im}\end{array}\end{array}$$$${\left[{r}_{i}\right]}_{m\times 1}={\left[{{\displaystyle \sum}}_{j=1}^{m}{t}_{ij}\right]}_{m\times 1},\text{}{\left[{c}_{j}\right]}_{1\times m}={\left[{{\displaystyle \sum}}_{i=1}^{m}{t}_{ij}\right]}_{1\times m}$$
- Finally, draw the cause and effect graph after removing some negligible effects in matrix T through calculating a threshold value α [52].$$\alpha =\frac{{\sum}_{i=1}^{m}{\sum}_{j=1}^{m}\left[{t}_{ij}\right]}{m\times m}$$The cause and effect graph can be drawn by plotting the data set of $\left({r}_{i}+{c}_{j}\right)$ as the x-axis to (${r}_{i}-{c}_{j})$ as the y-axis.

#### 2.3. ANP Approach

**Step 4:**Apply the ANP process to evaluate the weights of all failure mode risks. The details of the ANP method are described in the following [30,53,54]:

- Arrange failure modes and clusters of the network structure based on the nature of the relationship between clusters and failure modes. The influence of clusters and FMs can be exemplified in the following supermatrix, which will provide the feedback and the interdependence of FMs in the higher level in ANP.$$\begin{array}{c}\begin{array}{ccc}\text{}M{D}_{1}& \cdots & M{D}_{m}\\ \text{}F{M}_{1}& \cdots & F{M}_{k}\end{array}\\ A=\begin{array}{cc}M{D}_{1}& F{M}_{1}\\ \vdots & \vdots \\ M{D}_{m}& F{M}_{k}\end{array}\left[\begin{array}{ccc}{w}_{11}& \cdots & {w}_{1m}\\ \vdots & \ddots & \vdots \\ {w}_{m1}& \cdots & {w}_{mm}\end{array}\right]\end{array}$$
- The weights of the supermatrix are calculated through the expression$$\mathrm{Aw}={\mathsf{\lambda}}_{\mathrm{max}\text{}}\text{}\mathrm{w}$$The inconsistency ratio (CR) for the pairwise comparison matrix must be smaller than 0.1 [55]:$$\mathrm{CR}=\frac{{\mathsf{\lambda}}_{\mathrm{max}}-n}{\mathrm{RI}\left(n-1\right)}$$
- Calculate the weighted supermatrix ${\mathrm{W}}_{r}$ by dividing each column by its summation.
- Calculate the limit supermatrix ${\mathrm{W}}_{L}$ by powering the weighted supermatrix ${\mathrm{W}}_{r}$ to (2k + 1) to get the equalized weights, as follows:$${\mathrm{W}}_{L}={W}_{r}^{2k+1}$$

#### 2.4. Hybrid Risk Priority Weight

**Step 5:**Calculate the final risk weights of all failure modes and main clusters by using the proposed hybrid formal which contains all weights of the LFMEA, DEMATEL, and ANP supermatrix, as follows:

## 3. Case Study

#### Implementation of the Proposed Framework

## 4. Result and Discussion

#### 4.1. Linguistic FMEA Weights

#### 4.2. Interrelationships among Clusters and FMs

#### 4.3. The Interdependency and Impact Feedback

#### 4.4. Final Prioritization with Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bowles, J.B.; Peláez, C.E. Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis. Reliab. Eng. Syst. Saf.
**1995**, 50, 203–213. [Google Scholar] [CrossRef] - Certa, A.; Hopps, F.; Inghilleri, R.; La Fata, C.M. A Dempster-Shafer Theory-based approach to the Failure Mode, Effects and Criticality Analysis (FMECA) under epistemic uncertainty: Application to the propulsion system of a fishing vessel. Reliab. Eng. Syst. Saf.
**2017**, 159, 69–79. [Google Scholar] [CrossRef] - Rausand, M. Reliability of Safety-Critical Systems: Theory and Applications; John Wiley & Sons: Hoboken, NJ, USA, 2014. [Google Scholar]
- Tay, K.M.; Lim, C.P. Enhancing the failure mode and effect analysis methodology with fuzzy inference techniques. J. Intell. Fuzzy Syst.
**2010**, 21, 135–146. [Google Scholar] - McDermott, R.; Mikulak, R.J.; Beauregard, M. The Basics of FMEA; Steiner Books Productivity Press: New York, NY, USA, 1996. [Google Scholar]
- Doostparast, M.; Kolahan, F.; Doostparast, M. A reliability-based approach to optimize preventive maintenance scheduling for coherent systems. Reliab. Eng. Syst. Saf.
**2014**, 126, 98–106. [Google Scholar] [CrossRef] - Arunraj, N.S.; Maiti, J. Risk-based maintenance—Techniques and applications. J. Hazard. Mater.
**2007**, 142, 653–661. [Google Scholar] [CrossRef] - Moore, W.J.; Starr, A.G. An intelligent maintenance system for continuous cost-based prioritisation of maintenance activities. Comput. Ind.
**2006**, 57, 595–606. [Google Scholar] [CrossRef][Green Version] - Shafiee, M.; Dinmohammadi, F.; Shafiee, M.; Dinmohammadi, F. An FMEA-Based Risk Assessment Approach for Wind Turbine Systems: A Comparative Study of Onshore and Offshore. Energies
**2014**, 7, 619–642. [Google Scholar] [CrossRef][Green Version] - Tazi, N.; Châtelet, E.; Bouzidi, Y. Using a Hybrid Cost-FMEA Analysis for Wind Turbine Reliability Analysis. Energies
**2017**, 10, 276. [Google Scholar] [CrossRef] - Chin, K.-S.; Wang, Y.-M.; Ka Kwai Poon, G.; Yang, J.-B. Failure mode and effects analysis using a group-based evidential reasoning approach. Comput. Oper. Res.
**2009**, 36, 1768–1779. [Google Scholar] [CrossRef] - Liu, H.-C.; Liu, L.; Bian, Q.-H.; Lin, Q.-L.; Dong, N.; Xu, P.-C. Failure mode and effects analysis using fuzzy evidential reasoning approach and grey theory. Expert Syst. Appl.
**2011**, 38, 4403–4415. [Google Scholar] [CrossRef] - Faiella, G.; Parand, A.; Franklin, B.D.; Chana, P.; Cesarelli, M.; Stanton, N.A.; Sevdalis, N. Expanding healthcare failure mode and effect analysis: A composite proactive risk analysis approach. Reliab. Eng. Syst. Saf.
**2018**, 169, 117–126. [Google Scholar] [CrossRef] - Yssaad, B.; Abene, A. Rational Reliability Centered Maintenance Optimization for power distribution systems. Int. J. Electr. Power Energy Syst.
**2015**, 73, 350–360. [Google Scholar] [CrossRef] - Matteson, S. Methods for multi-criteria sustainability and reliability assessments of power systems. Energy
**2014**, 71, 130–136. [Google Scholar] [CrossRef] - Scipioni, A.; Saccarola, G.; Centazzo, A.; Arena, F. FMEA methodology design, implementation and integration with HACCP system in a food company. Food Control
**2002**, 13, 495–501. [Google Scholar] [CrossRef] - Wang, Z.; Gao, J.-M.; Wang, R.-X.; Chen, K.; Gao, Z.-Y.; Zheng, W. Failure Mode and Effects Analysis by Using the House of Reliability-Based Rough VIKOR Approach. IEEE Trans. Reliab.
**2018**, 67, 230–248. [Google Scholar] [CrossRef] - Barends, D.M.; Oldenhof, M.T.; Vredenbregt, M.J.; Nauta, M.J. Risk analysis of analytical validations by probabilistic modification of FMEA. J. Pharm. Biomed. Anal.
**2012**, 64–65, 82–86. [Google Scholar] [CrossRef] [PubMed] - Carmignani, G. An integrated structural framework to cost-based FMECA: The priority-cost FMECA. Reliab. Eng. Syst. Saf.
**2009**, 94, 861–871. [Google Scholar] [CrossRef] - Kutlu, A.C.; Ekmekçioğlu, M. Fuzzy failure modes and effects analysis by using fuzzy TOPSIS-based fuzzy AHP. Expert Syst. Appl.
**2012**, 39, 61–67. [Google Scholar] [CrossRef] - Liu, H.-C.; Liu, L.; Liu, N. Risk evaluation approaches in failure mode and effects analysis: A literature review. Expert Syst. Appl.
**2013**, 40, 828–838. [Google Scholar] [CrossRef] - Liu, H.-C.; Liu, L.; Liu, N.; Mao, L.-X. Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment. Expert Syst. Appl.
**2012**, 39, 12926–12934. [Google Scholar] [CrossRef] - Nepal, B.P.; Yadav, O.P.; Monplaisir, L.; Murat, A. A framework for capturing and analyzing the failures due to system/component interactions. Q. Reliab. Eng. Int.
**2008**, 24, 265–289. [Google Scholar] [CrossRef] - Xiao, N.; Huang, H.-Z.; Li, Y.; He, L.; Jin, T. Multiple failure modes analysis and weighted risk priority number evaluation in FMEA. Eng. Failure Anal.
**2011**, 18, 1162–1170. [Google Scholar] [CrossRef] - Fattahi, R.; Khalilzadeh, M. Risk evaluation using a novel hybrid method based on FMEA, extended MULTIMOORA, and AHP methods under fuzzy environment. Saf. Sci.
**2018**, 102, 290–300. [Google Scholar] [CrossRef] - Vahdani, B.; Salimi, M.; Charkhchian, M. A new FMEA method by integrating fuzzy belief structure and TOPSIS to improve risk evaluation process. Int. J. Adv. Manuf. Technol.
**2015**, 77, 357–368. [Google Scholar] [CrossRef] - Mohsen, O.; Fereshteh, N. An extended VIKOR method based on entropy measure for the failure modes risk assessment—A case study of the geothermal power plant (GPP). Saf. Sci.
**2017**, 92, 160–172. [Google Scholar] [CrossRef] - Nazeri, A.; Naderikia, R. A new fuzzy approach to identify the critical risk factors in maintenance management. Int. J. Adv. Manuf. Technol.
**2017**, 92, 3749–3783. [Google Scholar] [CrossRef] - Shieh, J.-I.; Wu, H.-H.; Huang, K.-K. A DEMATEL method in identifying key success factors of hospital service quality. Knowl. Based Syst.
**2010**, 23, 277–282. [Google Scholar] [CrossRef] - Saaty, T.L. Decision Making with Dependence and Feedback: The Analytic Network Process; RWS Publications: Pittsburgh, PA, USA, 1996; Volume 4922. [Google Scholar]
- Boran, S.; Goztepe, K. Development of a fuzzy decision support system for commodity acquisition using fuzzy analytic network process. Expert Syst. Appl.
**2010**, 37, 1939–1945. [Google Scholar] [CrossRef] - Liang, C.; Li, Q. Enterprise information system project selection with regard to BOCR. Int. J. Proj. Manag.
**2008**, 26, 810–820. [Google Scholar] [CrossRef] - Kumar, G.; Maiti, J. Modeling risk based maintenance using fuzzy analytic network process. Expert Syst. Appl.
**2012**, 39, 9946–9954. [Google Scholar] [CrossRef] - Ergu, D.; Kou, G.; Shi, Y.; Shi, Y. Analytic network process in risk assessment and decision analysis. Comput. Oper. Res.
**2014**, 42, 58–74. [Google Scholar] [CrossRef] - Fargnoli, M.; Haber, N. A practical ANP-QFD methodology for dealing with requirements’ inner dependency in PSS development. Comput. Ind. Eng.
**2018**. [Google Scholar] [CrossRef] - Fargnoli, M.; Lombardi, M.; Haber, N.; Guadagno, F. Hazard function deployment: A QFD-based tool for the assessment of working tasks—A practical study in the construction industry. Int. J. Occup. Saf. Ergon.
**2018**, 1–22. [Google Scholar] [CrossRef] [PubMed] - Fazli, S.; Kiani Mavi, R.; Vosooghidizaji, M. Crude oil supply chain risk management with DEMATEL–ANP. Oper. Res.
**2015**, 15, 453–480. [Google Scholar] [CrossRef] - Dedasht, G.; Mohamad Zin, R.; Ferwati, M.S.; Mohammed Abdullahi, M.A.; Keyvanfar, A.; McCaffer, R. DEMATEL-ANP risk assessment in oil and gas construction projects. Sustainability
**2017**, 9, 1420. [Google Scholar] [CrossRef] - Chen, W.-C.; Chang, H.-P.; Lin, K.-M.; Kan, N.-H.; Chen, W.-C.; Chang, H.-P.; Lin, K.-M.; Kan, N.-H. An Efficient Model for NPD Performance Evaluation Using DEMATEL and Fuzzy ANP—Applied to the TFT-LCD Touch Panel Industry in Taiwan. Energies
**2015**, 8, 11973–12003. [Google Scholar] [CrossRef][Green Version] - Chou, Y.-C.; Yang, C.-H.; Lu, C.-H.; Dang, V.; Yang, P.-A. Building Criteria for Evaluating Green Project Management: An Integrated Approach of DEMATEL and ANP. Sustainability
**2017**, 9, 740. [Google Scholar] [CrossRef] - Wang, Y.-M.; Chin, K.-S.; Poon, G.K.K.; Yang, J.-B. Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean. Expert Syst. Appl.
**2009**, 36, 1195–1207. [Google Scholar] [CrossRef] - Li, Z.S.; Wu, G. AText Mining based Reliability Analysis Method in Design Failure Mode and Effect Analysis. In Proceedings of the 2018 IEEE International Conference on Prognostics and Health Management (ICPHM), Seattle, WA, USA, 11–13 June 2018; pp. 1–8. [Google Scholar]
- Safari, H.; Faraji, Z.; Majidian, S. Identifying and evaluating enterprise architecture risks using FMEA and fuzzy VIKOR. J. Intell. Manuf.
**2016**, 27, 475–486. [Google Scholar] [CrossRef] - Tian, Z.-P.; Wang, J.-Q.; Zhang, H.-Y. An integrated approach for failure mode and effects analysis based on fuzzy best-worst, relative entropy, and VIKOR methods. Appl. Soft Comput.
**2018**, 72, 636–646. [Google Scholar] [CrossRef] - Jiang, W.; Xie, C.; Zhuang, M.; Tang, Y. Failure mode and effects analysis based on a novel fuzzy evidential method. Appl. Soft Comput.
**2017**, 57, 672–683. [Google Scholar] [CrossRef] - Kim, K.O.; Zuo, M.J. General model for the risk priority number in failure mode and effects analysis. Reliab. Eng. Syst. Saf.
**2018**, 169, 321–329. [Google Scholar] [CrossRef] - Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci.
**1975**, 8, 199–249. [Google Scholar] [CrossRef] - Xu, Z. A method for multiple attribute decision making with incomplete weight information in linguistic setting. Knowl. Based Syst.
**2007**, 20, 719–725. [Google Scholar] [CrossRef] - Zhou, Y.; Xia, J.; Zhong, Y.; Pang, J. An improved FMEA method based on the linguistic weighted geometric operator and fuzzy priority. Q. Eng.
**2016**, 28, 491–498. [Google Scholar] [CrossRef] - Huang, C.-Y.; Shyu, J.Z.; Tzeng, G.-H. Reconfiguring the innovation policy portfolios for Taiwan’s SIP Mall industry. Technovation
**2007**, 27, 744–765. [Google Scholar] [CrossRef] - Li, C.-W.; Tzeng, G.-H. Identification of interrelationship of key customers’ needs based on structural model for services/capabilities provided by a Semiconductor-Intellectual-Property Mall. Appl. Math. Comput.
**2009**, 215, 2001–2010. [Google Scholar] [CrossRef] - Liou, J.J.H.; Tzeng, G.-H.; Chang, H.-C. Airline safety measurement using a hybrid model. J. Air Transport Manag.
**2007**, 13, 243–249. [Google Scholar] [CrossRef] - Saaty, T.L. Fundamentals of the analytic network process—Dependence and feedback in decision-making with a single network. J. Syst. Sci. Syst. Eng.
**2004**, 13, 129–157. [Google Scholar] [CrossRef] - Saaty, T.L. Decision making with the analytic hierarchy process. Int. J. Serv. Sci.
**2008**, 1, 83–97. [Google Scholar] [CrossRef] - Saaty, T.L. How to make a decision: The analytic hierarchy process. Eur. J. Oper. Res.
**1990**, 48, 9–26. [Google Scholar] [CrossRef] - Huang, J.; Li, Z.; Liu, H.-C. New approach for failure mode and effect analysis using linguistic distribution assessments and TODIM method. Reliab. Eng. Syst. Saf.
**2017**, 167, 302–309. [Google Scholar] [CrossRef]

Main FM. Symbol | Main Clusters $\mathit{M}\mathit{D}$ | $\mathit{F}{\mathit{M}}_{\mathit{i}}$ | Risk of FM Description |
---|---|---|---|

$\mathit{M}{\mathit{D}}_{\mathbf{1}}$ | Operation (OP) | OP1 | = wrong operator action |

OP2 | = overload/unbalanced voltage | ||

OP3 | = wrong startup | ||

OP4 | = wrong shutdown | ||

$\mathit{M}{\mathit{D}}_{\mathbf{2}}$ | Instrumentation and control system (IN) | IN1 | = instrumentation failure |

IN2 | = failure of calibration | ||

IN3 | = failure of the control system | ||

IN4 | = failure of data communication | ||

$\mathit{M}{\mathit{D}}_{\mathbf{3}}$ | Electrical (EL) | EL1 | = rotor failure |

EL2 | = stator failure | ||

EL3 | = winding & insulation failure | ||

EL4 | = output power failure | ||

$\mathit{M}{\mathit{D}}_{\mathbf{4}}$ | Mechanical (ME) | ME1 | = cooling system failure |

ME2 | = bearing failure | ||

ME3 | = shaft failure | ||

ME4 | = gearbox failure | ||

$\mathit{M}{\mathit{D}}_{\mathbf{5}}$ | Other external risks (OT) | OT1 | = material degradation |

OT2 | = failure of the purging system | ||

OT3 | = lubricant contamination | ||

OT4 | = gas leakage |

$({\mathit{V}}_{\mathit{t}\mathit{j}}^{\mathit{O}},{\mathit{V}}_{\mathit{t}\mathit{j}}^{\mathit{S}},{\mathit{V}}_{\mathit{t}\mathit{j}}^{\mathit{D}})$ | OP | IN | EL | ME | OT |
---|---|---|---|---|---|

E1 | $\left({V}_{2},{V}_{1/3},{V}_{1/4}\right)$ | $\left({V}_{3},{V}_{1/4},{V}_{1/5}\right)$ | $\left({V}_{1/4},{V}_{2},{V}_{1/2}\right)$ | $\left({V}_{2},{V}_{3},{V}_{1/5}\right)$ | $\left({V}_{2},{V}_{1/5},{V}_{1}\right)$ |

E2 | $\left({V}_{3},{V}_{1/4},{V}_{1/5}\right)$ | $\left({V}_{2},{V}_{1/4},{V}_{1/4}\right)$ | $\left({V}_{1/3},{V}_{1},{V}_{1}\right)$ | $\left({V}_{1},{V}_{2},{V}_{1/4}\right)$ | $\left({V}_{1},{V}_{1/4},{V}_{1/4}\right)$ |

E3 | $\left({V}_{4},{V}_{1/5},{V}_{1/4}\right)$ | $\left({V}_{1},{V}_{1/5},{V}_{1/5}\right)$ | $\left({V}_{1/5},{V}_{1},{V}_{1/2}\right)$ | $\left({V}_{2},{V}_{1},{V}_{1/5}\right)$ | $\left({V}_{1/2},{V}_{1/3},{V}_{1/2}\right)$ |

E4 | $\left({V}_{1},{V}_{1/3},{V}_{1/3}\right)$ | $\left({V}_{1},{V}_{1/5},{V}_{1/4}\right)$ | $\left({V}_{1/4},{V}_{1/2},{V}_{1}\right)$ | $\left({V}_{2},{V}_{1},{V}_{1/4}\right)$ | $\left({V}_{1/2},{V}_{1/5},{V}_{1}\right)$ |

E5 | $\left({V}_{5},{V}_{1/5},{V}_{1/2}\right)$ | $\left({V}_{4},{V}_{1/5},{V}_{1/3}\right)$ | $\left({V}_{4},{V}_{1/3},{V}_{2}\right)$ | $\left({V}_{3},{V}_{3},{V}_{1/4}\right)$ | $\left({V}_{1/2},{V}_{1/2},{V}_{1/3}\right)$ |

${\mathit{V}}_{\mathit{t}\mathit{i}}^{\mathit{R}\mathit{P}\mathit{N}}$ | OP | IN | EL | ME | OT | FM Priority |
---|---|---|---|---|---|---|

E1 | 0.554 | 0.528 | 0.737 | 1.386 | 0.615 | ME > EL > OT > OP > IN |

E2 | 0.528 | 0.488 | 0.702 | 0.978 | 0.391 | ME > EL > OP > IN > OT |

E3 | 0.553 | 0.336 | 0.505 | 0.854 | 0.418 | ME > OP > EL > OT > IN |

E4 | 0.475 | 0.354 | 0.471 | 0.900 | 0.393 | ME > OP > EL > OT > IN |

E5 | 0.701 | 0.592 | 1.135 | 1.665 | 0.454 | ME > EL > OP > IN > OT |

Main FM Clusters | FMs | O | S | D | $\mathit{L}{\mathit{V}}_{\mathit{j}}^{\mathit{R}\mathit{P}\mathit{N}}$ Risk Priority Number | Ranking within Cluster |
---|---|---|---|---|---|---|

OP | OP1 | 2 | 0.5 | 0.2 | 1.179 | 1 |

OP2 | 0.2 | 4 | 0.333 | 1.118 | 3 | |

OP3 | 4 | 0.25 | 0.2 | 0.869 | 4 | |

OP4 | 0.5 | 0.5 | 0.333 | 0.681 | 2 | |

IN | IN1 | 2 | 0.333 | 1 | 1.155 | 2 |

IN2 | 0.2 | 0.333 | 0.25 | 0.873 | 3 | |

IN3 | 1 | 1 | 0.5 | 1.273 | 1 | |

IN4 | 3 | 0.25 | 0.2 | 0.695 | 4 | |

EL | EL1 | 0.2 | 2 | 0.25 | 0.873 | 1 |

EL2 | 0.2 | 1 | 0.2 | 0.610 | 3 | |

EL3 | 0.333 | 1 | 0.333 | 0.812 | 2 | |

EL4 | 1 | 0.25 | 0.2 | 0.556 | 4 | |

ME | ME1 | 0.333 | 0.333 | 0.333 | 0.500 | 4 |

ME2 | 0.5 | 1 | 1 | 1.200 | 3 | |

ME3 | 0.2 | 4 | 1 | 1.646 | 1 | |

ME4 | 0.2 | 4 | 0.5 | 1.397 | 2 | |

OT | OT1 | 0.25 | 1 | 1 | 0.960 | 3 |

OT2 | 0.333 | 5 | 0.2 | 1.462 | 1 | |

OT3 | 0.2 | 0.5 | 2 | 0.776 | 4 | |

OT4 | 0.25 | 5 | 3 | 2.533 | 2 |

OP | IN | EL | ME | OT | c Sum | r Sum | $({\mathit{r}}_{\mathit{i}}+{\mathit{c}}_{\mathit{j}})$ | $({\mathit{r}}_{\mathit{i}}-{\mathit{c}}_{\mathit{j}})$ | Status | |
---|---|---|---|---|---|---|---|---|---|---|

OP | 0.274 | 0.147 | 0.226 | 0.389 | 0.292 | 2.519 | 1.328 | 3.847 | −1.192 | effect |

IN | 0.506 | 0.090 | 0.417 | 0.380 | 0.261 | 0.671 | 1.655 | 2.325 | 0.984 | cause |

EL | 0.417 | 0.075 | 0.167 | 0.313 | 0.215 | 1.898 | 1.186 | 3.084 | −0.712 | effect |

ME | 0.691 | 0.244 | 0.569 | 0.360 | 0.448 | 1.934 | 2.312 | 4.245 | 0.378 | cause |

OT | 0.631 | 0.115 | 0.520 | 0.492 | 0.241 | 1.458 | 1.999 | 3.457 | 0.542 | cause |

OP | OP1 | OP2 | OP3 | OP4 | c Sum | r Sum | $({\mathit{r}}_{\mathit{i}}+{\mathit{c}}_{\mathit{j}})$ | $({\mathit{r}}_{\mathit{i}}-{\mathit{c}}_{\mathit{j}})$ | Status |
---|---|---|---|---|---|---|---|---|---|

OP1 | 0 | 0.199 | 0.49 | 0.596 | 0 | 1.285 | 1.285 | 1.285 | cause |

OP2 | 0 | 0.063 | 0.16 | 0.348 | 0.544 | 0.571 | 1.115 | 0.027 | cause |

OP3 | 0 | 0.075 | 0.082 | 0.414 | 0.958 | 0.571 | 1.529 | −0.387 | effect |

OP4 | 0 | 0.207 | 0.226 | 0.139 | 1.497 | 0.572 | 2.069 | −0.925 | effect |

IN | IN1 | IN2 | IN3 | IN4 | c Sum | r Sum | $({\mathit{r}}_{\mathit{i}}+{\mathit{c}}_{\mathit{j}})$ | $({\mathit{r}}_{\mathit{i}}-{\mathit{c}}_{\mathit{j}})$ | Status |
---|---|---|---|---|---|---|---|---|---|

IN1 | 0.034 | 0 | 0.376 | 0 | 0.940 | 0.410 | 1.350 | −0.530 | effect |

IN2 | 0.41 | 0 | 0.513 | 0 | 0.000 | 0.923 | 0.923 | 0.923 | cause |

IN3 | 0.094 | 0 | 0.035 | 0 | 1.343 | 0.129 | 1.472 | −1.214 | effect |

IN4 | 0.402 | 0 | 0.419 | 0 | 0.000 | 0.821 | 0.821 | 0.821 | cause |

EL | EL1 | EL2 | EL3 | EL4 | c Sum | r Sum | $({\mathit{r}}_{\mathit{i}}+{\mathit{c}}_{\mathit{j}})$ | $({\mathit{r}}_{\mathit{i}}-{\mathit{c}}_{\mathit{j}})$ | Status |
---|---|---|---|---|---|---|---|---|---|

EL1 | 0.215 | 0.446 | 0.406 | 0.742 | 1.034 | 1.809 | 2.843 | 0.775 | cause |

EL2 | 0.443 | 0.212 | 0.397 | 0.660 | 1.034 | 1.712 | 2.746 | 0.678 | cause |

EL3 | 0.342 | 0.342 | 0.197 | 0.598 | 1.120 | 1.479 | 2.599 | 0.359 | cause |

EL4 | 0.034 | 0.034 | 0.120 | 0.060 | 2.060 | 0.248 | 2.308 | −1.812 | effect |

ME | ME1 | ME2 | ME3 | ME4 | c Sum | r Sum | $({\mathit{r}}_{\mathit{i}}+{\mathit{c}}_{\mathit{j}})$ | $({\mathit{r}}_{\mathit{i}}-{\mathit{c}}_{\mathit{j}})$ | Status |
---|---|---|---|---|---|---|---|---|---|

ME1 | 0.056 | 0.696 | 0.56 | 0.518 | 0.255 | 1.830 | 2.085 | 1.575 | cause |

ME2 | 0.033 | 0.249 | 0.331 | 0.356 | 2.190 | 0.969 | 3.159 | −1.221 | effect |

ME3 | 0.13 | 0.725 | 0.296 | 0.56 | 1.545 | 1.711 | 3.256 | 0.166 | cause |

ME4 | 0.036 | 0.52 | 0.358 | 0.219 | 1.653 | 1.133 | 2.786 | −0.520 | effect |

OT | OT1 | OT2 | OT3 | OT4 | c Sum | r Sum | $({\mathit{r}}_{\mathit{i}}+{\mathit{c}}_{\mathit{j}})$ | $({\mathit{r}}_{\mathit{i}}-{\mathit{c}}_{\mathit{j}})$ | Status |
---|---|---|---|---|---|---|---|---|---|

OT1 | 0.485 | 0.642 | 0.910 | 0.330 | 2.007 | 2.367 | 4.374 | 0.360 | cause |

OT2 | 0.330 | 0.143 | 0.536 | 0.073 | 1.744 | 1.082 | 2.826 | −0.662 | effect |

OT3 | 0.495 | 0.214 | 0.304 | 0.110 | 2.436 | 1.123 | 3.559 | −1.313 | effect |

OT4 | 0.697 | 0.745 | 0.686 | 0.155 | 0.668 | 2.283 | 2.951 | 1.615 | cause |

Goal | OP | IN | EL | ME | OT | OP1 | OP2 | OP3 | OP4 | IN1 | IN2 | IN3 | IN4 | EL1 | EL2 | EL3 | EL4 | ME1 | ME2 | ME3 | ME4 | OT1 | OT2 | OT3 | OT4 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Goal | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OP | 0.045 | 0 | 0 | 0 | 0 | 0 | 0.221 | 0.312 | 0.168 | 0.201 | 0.227 | 0.260 | 0.299 | 0.169 | 0.235 | 0.249 | 0.221 | 0.190 | 0.217 | 0.219 | 0.247 | 0.212 | 0.171 | 0.273 | 0.186 | 0.210 |

IN | 0.073 | 0 | 0 | 0 | 0 | 0 | 0.221 | 0.060 | 0.102 | 0.060 | 0.133 | 0.333 | 0.172 | 0.109 | 0.058 | 0.106 | 0.108 | 0.063 | 0.092 | 0.091 | 0.069 | 0.076 | 0.158 | 0.091 | 0.099 | 0.210 |

EL | 0.123 | 0 | 0 | 0 | 0 | 0 | 0.158 | 0.312 | 0.130 | 0.175 | 0.224 | 0.110 | 0.299 | 0.273 | 0.336 | 0.293 | 0.240 | 0.436 | 0.205 | 0.219 | 0.247 | 0.206 | 0.186 | 0.273 | 0.162 | 0.173 |

ME | 0.506 | 0 | 0 | 0 | 0 | 0 | 0.124 | 0.187 | 0.300 | 0.313 | 0.091 | 0.110 | 0.102 | 0.058 | 0.129 | 0.189 | 0.192 | 0.144 | 0.217 | 0.299 | 0.326 | 0.243 | 0.240 | 0.091 | 0.246 | 0.173 |

OT | 0.253 | 0 | 0 | 0 | 0 | 0 | 0.275 | 0.129 | 0.300 | 0.251 | 0.325 | 0.187 | 0.127 | 0.392 | 0.243 | 0.164 | 0.240 | 0.166 | 0.270 | 0.172 | 0.111 | 0.264 | 0.245 | 0.273 | 0.306 | 0.234 |

OP1 | 0 | 0.517 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OP2 | 0 | 0.168 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OP3 | 0 | 0.077 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OP4 | 0 | 0.238 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

IN1 | 0 | 0 | 0.158 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

IN2 | 0 | 0 | 0.108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

IN3 | 0 | 0 | 0.649 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

IN4 | 0 | 0 | 0.085 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

EL1 | 0 | 0 | 0 | 0.561 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

EL2 | 0 | 0 | 0 | 0.168 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

EL3 | 0 | 0 | 0 | 0.227 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

EL4 | 0 | 0 | 0 | 0.044 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

ME1 | 0 | 0 | 0 | 0 | 0.039 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

ME2 | 0 | 0 | 0 | 0 | 0.126 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

ME3 | 0 | 0 | 0 | 0 | 0.565 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

ME4 | 0 | 0 | 0 | 0 | 0.270 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OT1 | 0 | 0 | 0 | 0 | 0 | 0.085 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OT2 | 0 | 0 | 0 | 0 | 0 | 0.522 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OT3 | 0 | 0 | 0 | 0 | 0 | 0.051 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OT4 | 0 | 0 | 0 | 0 | 0 | 0.051 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Goal | OP | IN | EL | ME | OT | OP1 | OP2 | OP3 | OP4 | IN1 | IN2 | IN3 | IN4 | EL1 | EL2 | EL3 | EL4 | ME1 | ME2 | ME3 | ME4 | OT1 | OT2 | OT3 | OT4 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Goal | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OP | 0 | 0.237 | 0.237 | 0.237 | 0.237 | 0.237 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

IN | 0 | 0.119 | 0.119 | 0.119 | 0.119 | 0.119 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

EL | 0 | 0.242 | 0.242 | 0.242 | 0.242 | 0.242 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

ME | 0 | 0.179 | 0.179 | 0.179 | 0.179 | 0.179 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OT | 0 | 0.223 | 0.223 | 0.223 | 0.223 | 0.223 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

OP1 | 0.123 | 0 | 0 | 0 | 0 | 0 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 | 0.123 |

OP2 | 0.040 | 0 | 0 | 0 | 0 | 0 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 | 0.040 |

OP3 | 0.018 | 0 | 0 | 0 | 0 | 0 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 | 0.018 |

OP4 | 0.056 | 0 | 0 | 0 | 0 | 0 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 | 0.056 |

IN1 | 0.019 | 0 | 0 | 0 | 0 | 0 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 |

IN2 | 0.013 | 0 | 0 | 0 | 0 | 0 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 | 0.013 |

IN3 | 0.077 | 0 | 0 | 0 | 0 | 0 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 |

IN4 | 0.010 | 0 | 0 | 0 | 0 | 0 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 | 0.010 |

EL1 | 0.136 | 0 | 0 | 0 | 0 | 0 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 | 0.136 |

EL2 | 0.041 | 0 | 0 | 0 | 0 | 0 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 | 0.041 |

EL3 | 0.055 | 0 | 0 | 0 | 0 | 0 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 |

EL4 | 0.011 | 0 | 0 | 0 | 0 | 0 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 |

ME1 | 0.007 | 0 | 0 | 0 | 0 | 0 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 |

ME2 | 0.023 | 0 | 0 | 0 | 0 | 0 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 | 0.023 |

ME3 | 0.101 | 0 | 0 | 0 | 0 | 0 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 | 0.101 |

ME4 | 0.048 | 0 | 0 | 0 | 0 | 0 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 | 0.048 |

OT1 | 0.019 | 0 | 0 | 0 | 0 | 0 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 | 0.019 |

OT2 | 0.116 | 0 | 0 | 0 | 0 | 0 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 |

OT3 | 0.011 | 0 | 0 | 0 | 0 | 0 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 |

OT4 | 0.076 | 0 | 0 | 0 | 0 | 0 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 | 0.076 |

Clusters and FMs | LRPN Weights | DEMATEL Weights | ANP Weights | $\mathit{H}\mathit{R}\mathit{P}{\mathit{V}}_{\mathit{j}}^{\mathit{f}\mathit{i}\mathit{n}\mathit{a}\mathit{l}}$ | Final Rank | |
---|---|---|---|---|---|---|

Within Clusters | Without Clusters | |||||

OP | 0.558 | 3.847 | 0.237 | 0.509 | 2 | 4 |

IN | 0.448 | 2.325 | 0.119 | 0.124 | 5 | 12 |

EL | 0.674 | 3.084 | 0.242 | 0.503 | 3 | 5 |

ME | 1.114 | 4.245 | 0.179 | 0.846 | 1 | 1 |

OT | 0.446 | 3.457 | 0.223 | 0.344 | 4 | 7 |

OP1 | 1.179 | 1.286 | 0.123 | 0.186 | 1 | 10 |

OP2 | 1.118 | 1.116 | 0.040 | 0.050 | 3 | 18 |

OP3 | 0.869 | 1.530 | 0.018 | 0.024 | 4 | 21 |

OP4 | 0.681 | 2.068 | 0.056 | 0.079 | 2 | 16 |

IN1 | 1.155 | 1.351 | 0.019 | 0.030 | 2 | 20 |

IN2 | 0.873 | 0.923 | 0.013 | 0.010 | 3 | 23 |

IN3 | 1.273 | 1.470 | 0.077 | 0.144 | 1 | 11 |

IN4 | 0.695 | 0.821 | 0.010 | 0.006 | 4 | 25 |

EL1 | 0.873 | 2.843 | 0.136 | 0.338 | 1 | 8 |

EL2 | 0.610 | 2.747 | 0.041 | 0.069 | 3 | 17 |

EL3 | 0.812 | 2.598 | 0.055 | 0.116 | 2 | 13 |

EL4 | 0.556 | 2.308 | 0.011 | 0.014 | 4 | 22 |

ME1 | 0.500 | 2.085 | 0.007 | 0.007 | 4 | 24 |

ME2 | 1.200 | 3.159 | 0.023 | 0.087 | 3 | 14 |

ME3 | 1.646 | 3.255 | 0.101 | 0.541 | 1 | 3 |

ME4 | 1.397 | 2.785 | 0.048 | 0.187 | 2 | 9 |

OT1 | 0.960 | 4.373 | 0.019 | 0.080 | 3 | 15 |

OT2 | 1.462 | 2.825 | 0.116 | 0.479 | 2 | 6 |

OT3 | 0.776 | 3.558 | 0.011 | 0.030 | 4 | 19 |

OT4 | 2.533 | 2.951 | 0.076 | 0.568 | 1 | 2 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alrifaey, M.; Sai Hong, T.; Supeni, E.E.; As’arry, A.; Ang, C.K.
Identification and Prioritization of Risk Factors in an Electrical Generator Based on the Hybrid FMEA Framework. *Energies* **2019**, *12*, 649.
https://doi.org/10.3390/en12040649

**AMA Style**

Alrifaey M, Sai Hong T, Supeni EE, As’arry A, Ang CK.
Identification and Prioritization of Risk Factors in an Electrical Generator Based on the Hybrid FMEA Framework. *Energies*. 2019; 12(4):649.
https://doi.org/10.3390/en12040649

**Chicago/Turabian Style**

Alrifaey, Moath, Tang Sai Hong, Eris Elianddy Supeni, Azizan As’arry, and Chun Kit Ang.
2019. "Identification and Prioritization of Risk Factors in an Electrical Generator Based on the Hybrid FMEA Framework" *Energies* 12, no. 4: 649.
https://doi.org/10.3390/en12040649