# A New Hybrid Dynamic FMECA with Decision-Making Methodology: A Case Study in an Agri-Food Company

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## Abstract

**:**

## 1. Introduction

- (1)
- Identify all failure modes that have occurred or the potential failure of a system;
- (2)
- Identify the causes and effects of faults;
- (3)
- Rank the identified failure modes through Risk Priority Number (RPN);
- (4)
- Take corrective action.

- Occurrence (O) is the probability that a failure mode will occur. It is, therefore, strongly linked to the failure rate of the component;
- Severity (S) is related to the effect/impact of the fault model;
- Detectability (D) indicates the ability to diagnose the fault mode before its effects occur on the system.

- First is how the RPN index is calculated; many researchers have focused on determining a replicable method to identify different weights to be assigned to various criteria;
- Secondly, many scholars have focused on finding a method that would allow the proper evaluation of alternatives in the case of linguistic variables and, therefore, in cases of uncertainty;
- Finally, in recent years, the academic world has tried to solve another critical shortcoming of the traditional FMEA: the lack of some factors, first and foremost, the cost. Therefore, many methods involve the use of several factors.

- The absence of weights on O, S, and D factors;
- The lack of economic factors;
- The absence of a scientific basis in the RPN calculation formula and many duplicates in RPN results.

## 2. Methodology

- A case study carried out on a machine of an important Italian company in the agri-food sector is presented to evaluate the proposed mode’s robustness.
- The paper is organised as follows: In Section 2, a brief report on the state-of-the-art FMECA is proposed, with particular attention to the developments proposed in conjunction with MCDM. In Section 3, the problem is defined generically, and the methodology is proposed. Section 4 describes the case study. Finally, the last section focuses on conclusions and proposals for future work developments.

#### 2.1. Multidisciplinary Team Creation, Machine Breakdown into Functional Units and Identification of FMs and CFs

#### 2.2. Evaluation of the Factors O, S, D, and C

- Costs of non-production$${C}_{MP}=\left({C}_{hp}\ast {N}_{p}\ast {T}_{i}\right)+\left({Q}_{p}\ast {P}_{p}\ast {T}_{i}\right)+\left({C}_{hps}\ast {N}_{p}\ast {T}_{i}\right)$$
- Labour costs$${C}_{MDO}=\left({C}_{hm}\ast {N}_{m}\ast {T}_{i}\right)$$
- Costs of spare parts used$${C}_{R}={\displaystyle \sum}_{i=1}^{n}{C}_{i}{Q}_{i}$$$$C={C}_{MP}+{C}_{MDO}+{C}_{R}$$

#### 2.3. Criteria’s Weights’ Calculation through Entropy Method and Best Worst Method (BWM)

- The data of the matrix will be normalised to ensure a homogeneous and direct comparison between the criteria:$${Z}_{ij}=\frac{{x}_{ij}}{{{\displaystyle \sum}}_{i=1}^{n}{x}_{ij}}$$
- Entropy is calculated for each criterion:$${E}_{j}=\left(-\frac{1}{\mathrm{ln}\left(n\right)}\right)\ast {\displaystyle \sum}_{i=1}^{n}\left({Z}_{ij}\ast \mathrm{ln}{z}_{ij}\right)$$
- The values ${d}_{j}$ are calculated:$${d}_{j}=1-{E}_{j}$$
- Finally, weights ${W}_{j}$ are calculated:$${W}_{j}=\frac{{d}_{j}}{{{\displaystyle \sum}}_{j=1}^{m}{d}_{j}}$$

- The most important criterion and the least important criterion will be identified;
- Preferences of the most important criterion are expressed over the others by giving a number from one to nine, which obtains a line vector;
- Preferences of the least important criterion are expressed by giving a number from one to nine. A column vector is obtained;
- Finally, a problem of optimisation of the type is solved:$$\begin{array}{ccc}& \{\mathrm{min}{\xi}_{L}\P & \\ & & \begin{array}{l}\hspace{1em}subjectedto\\ \left|{w}_{B}-{a}_{Bj}{w}_{j}\right|\le {\xi}_{L}\\ \left|{w}_{j}-{a}_{jw}{w}_{w}\right|\le {\xi}_{L}\\ {\displaystyle \sum _{j=1}^{m}}{w}_{j}=1\end{array}\\ {w}_{j}\ge 0\}& & \end{array}$$

#### 2.4. Calculation of Final Weights

#### 2.5. Application of the EDAS Method to Rank Alternatives

- Calculate the average solution for each criterion ${\mathrm{AV}}_{\mathrm{j}}$$${\mathrm{AV}}_{\mathrm{j}}=\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{ij}}}{\mathrm{n}}$$
- Calculate the mean positive distance ${\mathrm{PDA}}_{\mathrm{ij}}$ for the benefit and disadvantage criteria:
- ▪
- Benefit$${\mathrm{PDA}}_{\mathrm{j}}=\frac{\left(\mathrm{max}\left\{0,{\text{}\mathrm{x}}_{\mathrm{ij}}-{\mathrm{AV}}_{\mathrm{j}}\right\}\right)}{{\mathrm{AV}}_{\mathrm{j}}}$$
- ▪
- Disadvantage$${\mathrm{PDA}}_{\mathrm{j}}=\frac{\left(\mathrm{max}\left\{0,{\text{}\mathrm{AV}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{ij}}\right\}\right)}{{\mathrm{AV}}_{\mathrm{j}}}$$

- Calculate the mean negative distance ${\mathrm{NDA}}_{\mathrm{ij}}$ for the benefit and disadvantage criteria:
- ▪
- Benefit$${\text{}\mathrm{NDA}}_{\mathrm{j}}=\frac{\left(\mathrm{max}\left\{0,{\text{}\mathrm{AV}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{ij}}\right\}\right)}{{\mathrm{AV}}_{\mathrm{j}}}$$
- ▪
- Disadvantage$${\mathrm{NDA}}_{\mathrm{j}}=\frac{\left(\mathrm{max}\left\{0,{\text{}\mathrm{x}}_{\mathrm{ij}}-{\mathrm{AV}}_{\mathrm{j}}\right\}\right)}{{\mathrm{AV}}_{\mathrm{j}}}$$

- Using the weights of the previously calculated criteria, the weighted sums are calculated, ${\mathrm{SP}}_{\mathrm{i}}$$${\mathrm{SP}}_{\mathrm{i}}={\displaystyle \sum}_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{w}}_{\mathrm{j}}\times {\mathrm{PDA}}_{\mathrm{j}}$$
- Using the weights of the previously calculated criteria, the weighted sums are calculated, ${\mathrm{SN}}_{\mathrm{i}}$$${\mathrm{SN}}_{\mathrm{i}}={\displaystyle \sum}_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{w}}_{\mathrm{j}}\times {\mathrm{NDA}}_{\mathrm{j}}$$
- The weighted sums are normalised$${\mathrm{NSP}}_{\mathrm{i}}=\frac{{\mathrm{SP}}_{\mathrm{i}}}{\mathrm{max}\left\{{\mathrm{SP}}_{\mathrm{i}}\right\}}$$$${\mathrm{NSN}}_{\mathrm{i}}=1-\frac{{\mathrm{SN}}_{\mathrm{i}}}{\mathrm{max}\left\{{\mathrm{SN}}_{\mathrm{i}}\right\}}$$
- The priority index, ${\mathrm{AS}}_{\mathrm{i}}$, is calculated$${\mathrm{AS}}_{\mathrm{i}}=\frac{1}{2}\left({\mathrm{NSP}}_{\mathrm{i}}+{\mathrm{NSN}}_{\mathrm{i}}\right)$$

#### 2.6. Criticality Analysis (CA)

#### 2.7. Definition and Impact Assessment of Corrective Actions

## 3. Case Study

#### 3.1. Multidisciplinary Team Creation, Machine Breakdown into Functional Units, Identification of FMs and CFs

#### 3.2. Evaluation of the Factors O, S, D, and C

#### 3.3. Criteria’s Weights Calculation through Entropy Method and Best Worst Method (BWM)

#### 3.4. Calculation of Final Weights

#### 3.5. Application of the EDAS Method to Rank Alternatives

#### 3.6. Criticality Analysis (CA)

- The tunnel chain is considerably longer than the sizing chain; if it breaks, it causes more damage at the economic level;
- The release guide, on the other hand, unlike the hooking guide, is subject to more significant stress and, therefore, more prone to failure.

- The causes of failure have been entered without a box;
- The failure modes have been entered in the circles;
- Effects have been placed in rectangles;
- Maintenance actions have been placed in hexes.

- FM10-E10-STOP PRODUCTION-Guide Maintenance-FM10;
- FM9-E10-STOP PRODUCTION-Guide Regulation-FM9;
- FM1-STOP PRODUCTION-Tunnel chain maintenance-FM1;
- FM26-STOP PRODUCTION-Transfer chain maintenance-FM26.

- Due to the causes CF11/CF86/CF91 (Blackout), CF2 (Incorrect feed speed), CF3 (Incorrect product life forecast), and CF20 (Inadequate tolerances) being purely random events, the model that best interprets the behaviour is the exponential one;$$F\left(t\right)=1-ex{p}^{-\lambda \ast t}$$$$\mathrm{f}\left(\mathrm{t}\right)=\lambda \ast ex{p}^{-\lambda \ast t}$$$$\mathrm{h}\left(\mathrm{t}\right)=\frac{f\left(t\right)}{1-F\left(t\right)}=\lambda $$
- For the causes CF18/CF21 (Wrong adjustment), CF19 (Excessive vibrations), CF38 (Over-stressing), CF1 (Insufficient lubrication), and CF4 (Over-stressing), being causes of failure of mechanical components, the model that best represents their behavior is Weibull’s model:$$\mathrm{F}\left(\mathrm{t}\right)=1-ex{p}^{-{\left(\frac{t}{\alpha}\right)}^{\beta}}$$$$\mathrm{f}\left(\mathrm{t}\right)=\frac{\beta}{{\alpha}^{\beta}}\ast {t}^{\beta -1}\ast ex{p}^{-{\left(\frac{t}{\alpha}\right)}^{\beta}}$$$$\mathrm{h}\left(\mathrm{t}\right)=\frac{f\left(t\right)}{1-F\left(t\right)}=\frac{\beta}{{\alpha}^{\beta}}\ast {t}^{\beta -1}$$

#### 3.7. Definition and Impact Assessment of Corrective Actions

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Ebeling, C.E. An Introduction to Reliability and Maintainability Engineering; Waveland Press Inc.: Long Grove, IL, USA, 2019. [Google Scholar]
- Kim, K.; Zuo, M. General model for the risk priority number in failure mode and effects analysis. Reliab. Eng. Syst. Saf.
**2018**, 169, 321–329. [Google Scholar] [CrossRef] - Cristea, G.; Constantinescu, D.M. A comparative critical study between FMEA and FTA risk analysis methods. In Proceedings of the IOP Conference Series: Materials Science and Engineering, Xiamen, China, 20–22 October 2017; p. 252. [Google Scholar] [CrossRef]
- Chang, K.-H. Evaluate the orderings of risk for failure problems using a more general RPN methodology. Microelectron. Reliab.
**2009**, 49, 1586–1596. [Google Scholar] [CrossRef] - Huang, J.; You, J.-X.; Liu, H.-C.; Song, M.-S. Failure mode and effect analysis improvement: A systematic literature review and future research agenda. Reliab. Eng. Syst. Saf.
**2020**, 199, 106885. [Google Scholar] [CrossRef] - Stamatis, D. Failure Mode and Effect Analysis: FMEA from Theory to Execution; ASQ Quality Press: New York, NY, USA, 2003. [Google Scholar]
- Ciani, L.; Guidi, G.; Patrizi, G. A Critical Comparison of Alternative Risk Priority Numbers in Failure Modes, Effects, and Criticality Analysis. IEEE Access
**2019**, 7, 92398–92409. [Google Scholar] [CrossRef] - Bowles, J.B.; Peláez, C.E. Fuzzy logic prioritisation of failures in a system failure mode, effects and criticality analysis. Reliab. Eng. Syst. Saf.
**1995**, 50, 203–213. [Google Scholar] [CrossRef] - Chin, K.-S.; Wang, Y.-M.; Poon, G.K.; Yang, J.-B. Failure mode and effects analysis by data envelopment analysis. Decis. Support Syst.
**2009**, 48, 246–256. [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] - Chin, K.-S.; Wang, Y.-M.; Poon, G.K.; 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] - 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] - Pillay, A.; Wang, J. Modified failure mode and effects analysis using approximate reasoning. Reliab. Eng. Syst. Saf.
**2003**, 79, 69–85. [Google Scholar] [CrossRef] - Seyed-Hosseini, S.; Safaei, N.; Asgharpour, M. Reprioritization of failures in a system failure mode and effects analysis by decision making trial and evaluation laboratory technique. Reliab. Eng. Syst. Saf.
**2006**, 91, 872–881. [Google Scholar] [CrossRef] - Liu, H.-C.; Chen, X.-Q.; Duan, C.-Y.; Wang, Y.-M. Failure mode and effect analysis using multi-criteria decision-making methods: A systematic literature review. Comput. Ind. Eng.
**2019**, 135, 881–897. [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] - Braglia, M. MAFMA: Multi-attribute failure mode analysis. Int. J. Qual. Reliab. Manag.
**2000**, 17, 1017–1033. [Google Scholar] [CrossRef] [Green Version] - Wang, Y.-M.; Chin, K.-S.; Poon, G.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] - Xu, K.; Tang, L.; Xie, M.; Ho, S.; Zhu, M. Fuzzy assessment of FMEA for engine systems. Reliab. Eng. Syst. Saf.
**2002**, 75, 17–29. [Google Scholar] [CrossRef] - Braglia, M.; Frosolini, M.; Montanari, R. Fuzzy TOPSIS Approach for Failure Mode, Effects and Criticality Analysis. Qual. Reliab. Eng. Int.
**2003**, 19, 425–443. [Google Scholar] [CrossRef] - Ekmekçioǧlu, M.; Kutlu, A.C. A fuzzy hybrid approach for fuzzy process FMEA: An application to a spindle manufacturing process. Int. J. Comput. Intell. Syst.
**2012**, 5, 611–626. [Google Scholar] [CrossRef] [Green Version] - Selim, H.; Yunusoglu, M.G.; Yılmaz Balaman, Ş. A dynamic maintenance planning framework based on fuzzy TOPSIS and FMEA: Application in an International Food Company. Qual. Reliab. Eng. Int.
**2016**, 32, 795–804. [Google Scholar] [CrossRef] - Qin, J.; Xi, Y.; Pedrycz, W. Failure mode and effects analysis (FMEA) for risk assessment based on interval type-2 fuzzy evidential reasoning method. Appl. Soft Comput.
**2020**, 89, 106134. [Google Scholar] [CrossRef] - Kolios, A.J.; Umofia, A.; Shafiee, M. Failure mode and effects analysis using a fuzzy-TOPSIS method: A case study of subsea control module. Int. J. Multicriteria Decis. Mak.
**2017**, 7, 29–53. [Google Scholar] [CrossRef] - Lolli, F.; Ishizaka, A.; Gamberini, R.; Rimini, B.; Messori, M. FlowSort-GDSS—A novel group multi-criteria decision support system for sorting problems with application to FMEA. Expert Syst. Appl.
**2015**, 42, 6342–6349. [Google Scholar] [CrossRef] [Green Version] - 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] - 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. J.
**2008**, 72, 636–646. [Google Scholar] [CrossRef] - Lo, H.; Liou, J. A novel multiple-criteria decision-making-based FMEA model for risk assessment. Appl. Soft Comput.
**2018**, 73, 684–696. [Google Scholar] [CrossRef] - Yazdi, M.; Nedjati, A.; Zarei, E.; Abbassi, R. A reliable risk analysis approach using an extension of best-worst method based on democratic-autocratic decision-making style. J. Clean. Prod.
**2020**, 256, 120418. [Google Scholar] [CrossRef] - Ouyang, L.; Zhu, Y.; Zheng, W.; Yan, L. An information fusion FMEA method to assess the risk of healthcare waste. J. Manag. Sci. Eng.
**2021**, 6, 111–124. [Google Scholar] [CrossRef] - Wang, P.; Meng, P.; Zhai, J.-Y.; Zhu, Z.-Q. A hybrid method using experiment design and grey relational analysis for multiple criteria. Knowl. -Based Syst.
**2013**, 53, 100–107. [Google Scholar] [CrossRef] - Trinkūnienė, E.; Podvezko, V.; Zavadskas, E. Evaluation of quality assurance in contractor contracts by multi-attribute decision-making. Econ. Res. -Ekon. Istraživanja
**2017**, 30, 1152–1180. [Google Scholar] [CrossRef] [Green Version] - Vala, S.; Chemweno, P.; Pintelon, L.; Muchiri, P. A risk-based maintenance approach for critical care medical devices: A case study application for a large hospital in a developing country. Int. J. Syst. Assur. Eng. Manag.
**2018**, 9, 1217–1233. [Google Scholar] [CrossRef] - Lipol, L.S.; Haq, J. Risk analysis method: FMEA/FMECA in the organisations. Int. J. Basic Appl. Sci.
**2011**, 11, 74–82. [Google Scholar] - Kochan, C.G.; Nowicki, D.R.; Sauser, B.; Randall, W.S. Impact of cloud-based information sharing on hospital supply chain performance: A system dynamics framework. Int. J. Prod. Econ.
**2018**, 195, 168–185. [Google Scholar] [CrossRef]

**Figure 1.**Flowchart of the Entropy Best Evaluation Distance Dynamic FMECA (EN-B-ED Dynamic FMECA) methodology.

**Figure 12.**The FM9 failure rate with maintenance every four months. AS-IS state: guide adjustment rate every two quarters. TO-BE state: guide adjustment rate every four months.

Functional Area | Components | Failure Mode | Failure Cause | Effect | Occurrence | Severity | Detectability | Cost |
---|---|---|---|---|---|---|---|---|

${U}_{i}$ | ${C}_{j}$ | $FM$ | CFL | ${E}_{m}$ | $X$ | $X$ | $X$ | $X$ |

S | Severity |

O | Occurrence |

D | Detectability |

C | Cost |

I | Index referring to the alternatives |

J | Index referring to the criteria |

${x}_{ij}$ | Element of initial Decision matrix |

${z}_{ij}$ | Element of Entropy normalisation-matrix |

N | Alternative’s number |

M | Criteria’s number |

${C}_{MP}$ | Cost of non-production |

${C}_{hp}$ | Cost of production manpower |

${C}_{hips}$ | The extraordinary cost of production manpower |

${C}_{MDO}$ | Cost of maintenance manpower |

${C}_{R}$ | Cost of spare parts |

${E}_{j}$ | Entropy of j-th criteria |

${d}_{j}$ | Degrees of variation |

${W}_{j\left(E\right)}$ | Weight of the j-th criteria by entropy method |

${W}_{j\left(BWM\right)}$ | Weight of the j-th criteria by Best Worst Method |

$A{V}_{j}$ | Average value of Decision Matrix |

PDA | Positive distance to average |

NDA | Negative distance to average |

SP | Weighted sum of PDA for each alternative |

SN | Weighted sum of NDA for each alternative |

NSP | Normalised SP |

NSN | Normalise SN |

AS | Appraisal score |

Time (Quarter) | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 |
---|---|---|---|---|---|---|---|---|---|

Failure rate FM9: STATUS TO-BE every four months | 0 | 0.1 | 0.8 | 0.1 | 0.8 | 0.1 | 0.8 | 0.1 | 0.8 |

Failure rate FM9: STATUS AS-IS every two quarters | 0 | 0.1 | 0.8 | 2.7 | 6.4 | 0.1 | 0.8 | 2.7 | 6.4 |

Time (Quarter) | STATE TO-BE Every Four Months | STATE AS-IS Every 2 Quarters |
---|---|---|

0 | 1.7 | 1.67 |

1 | 2.47 | 2.47 |

2 | 2.48 | 8.08 |

3 | 2.49 | 2.49 |

4 | 2.50 | 8.10 |

5 | 2.53 | 2.53 |

6 | 2.55 | 8.15 |

7 | 2.58 | 2.58 |

8 | 0.26 | 0.82 |

9 | 2.65 | 2.65 |

10 | 0.26 | 0.82 |

11 | 2.60 | 2.60 |

12 | 2.63 | 8.23 |

13 | 2.49 | 2.49 |

14 | 0.25 | 0.81 |

15 | 2.52 | 2.52 |

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**MDPI and ACS Style**

Di Nardo, M.; Murino, T.; Osteria, G.; Santillo, L.C.
A New Hybrid Dynamic FMECA with Decision-Making Methodology: A Case Study in an Agri-Food Company. *Appl. Syst. Innov.* **2022**, *5*, 45.
https://doi.org/10.3390/asi5030045

**AMA Style**

Di Nardo M, Murino T, Osteria G, Santillo LC.
A New Hybrid Dynamic FMECA with Decision-Making Methodology: A Case Study in an Agri-Food Company. *Applied System Innovation*. 2022; 5(3):45.
https://doi.org/10.3390/asi5030045

**Chicago/Turabian Style**

Di Nardo, Mario, Teresa Murino, Gianluca Osteria, and Liberatina Carmela Santillo.
2022. "A New Hybrid Dynamic FMECA with Decision-Making Methodology: A Case Study in an Agri-Food Company" *Applied System Innovation* 5, no. 3: 45.
https://doi.org/10.3390/asi5030045