Risk prioritization based on the combination of FMEA and dual hesitant fuzzy sets method

Calache, Lucas Daniel Del Rosso; Zanon, Lucas Gabriel; Arantes, Rafael Ferro Munhoz; Osiro, Lauro; Carpinetti, Luiz Cesar Ribeiro

doi:10.1590/0103-6513.20200081

Lucas Daniel Del Rosso Calache ^* * lucascalache@usp.br

Universidade de São Paulo, São Carlos, SP, Brasil

https://orcid.org/0000-0002-0706-917X

Lucas Gabriel Zanon

Universidade de São Paulo, São Carlos, SP, Brasil

https://orcid.org/0000-0003-4004-0405

Rafael Ferro Munhoz Arantes

Universidade de São Paulo, São Carlos, SP, Brasil

https://orcid.org/0000-0003-4784-7455

Lauro Osiro

Universidade Federal do Triângulo Mineiro, Uberaba, MG, Brasil

https://orcid.org/0000-0002-9454-2403

Luiz Cesar Ribeiro Carpinetti

Universidade de São Paulo, São Carlos, SP, Brasil

https://orcid.org/0000-0002-8357-2607

* lucascalache@usp.br

Rating	Occurrence	Severity	Detection
1	Almost never	No severity	Certainty of detection
2	Extremely Low	Extremely Low	Extremely high
3	Very low	Very low	Very High
4	Low	Low	High
5	Moderately Low	Moderately Low	Average
6	Average	Average	Moderately Low
7	Moderately High	Moderately High	Low
8	High	High	Very low
9	Very High	Very High	Extremely Low
10	Extremely High	Extremely High	Almost impossible

Paper	Proposal	Pondering risk factors weights	Consider individual judgments	Deals with imprecision	Use linguistic terms for judgments	Hesitation in the linguistic terms parameterization	Hesitation in the judgment
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Our proposal	Combining FMEA with DHFS.	✔	✔	✔	✔	✔	✔

Linguistic Terms	Membership degree	Non-membership degree
Very Low Importance (VL)	0.10	0.85
Low Importance (L)	0.30	0.65
Medium Importance (M)	0.50	0.50
High Importance (H)	0.75	0.20
Very High Importance (VH)	0.90	0.05

Linguistic Terms	Severity and Occurrence		Detection
Linguistic Terms	Membership degree	Non-membership degree	Membership degree	Non-membership degree
(EL) Extremely low	0.00	0.90	1.00	0.00
(VL) Very Low	0.10	0.75	0.90	0.10
(L) Low	0.25	0.60	0.75	0.10
(ML) Medium Low	0.40	0.50	0.60	0.25
(M) Medium	0.50	0.45	0.50	0.45
(MH) Medium High	0.60	0.25	0.40	0.50
(H) High	0.75	0.10	0.25	0.60
(VH) Very High	0.90	0.10	0.10	0.75
(EH) Extremely High	1.00	0.00	0.00	0.90

	Potential Failure Effect	Potential Cause of Failure	Current process of control
$F M_{1}$ - Supplier's inability to meet quality requirements	-Production of non-conforming products;	-Lack of process control;	- Sampling inspection.
	-Commitment of the image with customers;	-Material used inappropriate;
	- Loss of product quality.	-Lack of training
$F M_{2}$ - Can not provide competitive pricing	- Higher production costs;	- High transportation cost	- Benchmarking
$F M_{2}$ - Can not provide competitive pricing	- Decrease in profit margin.	- High transportation cost	- Benchmarking
$F M_{3}$ - Low supplier financial health	- Increase in the cost of production;	- Inefficient management;	- Audit programs.
	- Late delivery;	- Low sales volume.
	- Fines for delay;
	- Do not deliver products;
	-Commitment of the image with the client.
$F M_{4}$ - Inability to cope with changes in volume demand	- Do not deliver products;	-Ineffective communication;	- Communication by e-mail and telephone;
	- Late delivery;	-Lack of capacity.
	- Fines for delay;
	-Commitment of the image with the client.
$F M_{5}$ - Lack of integration between customer and supplier	- Unbalance of production;	-Ineffective communication;	- No control process.
	- Late delivery;
	- Fines for delay;
	-Commitment of the image with the client;
	- Increased cost of raw material.
$F M_{6}$ - Failure to meet delivery requirements	- Delays in production;	-Cargo theft.	- Monitoring of arrival times in the logistics sector.
	- Late delivery;
	- Fines for delay;
	-Commitment of the image with the client.

$D M_{1}$	$S e v e r i t y$	Occurrence	$D e t e c t i o n$
$F M_{1}$	H, VH	L, ML	M
$F M_{2}$	VH, EH	M, MH	MH, H
$F M_{3}$	H, VH	M	H
$F M_{4}$	H	H, VH	MH
$F M_{5}$	M, MH	H	L, ML
$F M_{6}$	H, VH	L, ML	ML, M

$D M_{2}$	$S e v e r i t y$	Occurrence	$D e t e c t i o n$
$F M_{1}$	H, VH	ML, M	M, MH
$F M_{2}$	H	M	H, VH
$F M_{3}$	M, MH	ML, M	VH
$F M_{4}$	M	H	M, MH
$F M_{5}$	L, ML	VH	M
$F M_{6}$	H, VH	VL	ML, M, MH

$D M_{3}$	$S e v e r i t y$	Occurrence	$D e t e c t i o n$
$F M_{1}$	VH, EH	VL, L	L, ML, M
$F M_{2}$	L, ML, M	ML, M	MH, H
$F M_{3}$	L, ML	L, ML	MH, H
$F M_{4}$	MH, H	H, VH	H, VH, EH
$F M_{5}$	MH, H	H, VH	M; MH
$F M_{6}$	H	VL, L	M, MH

	Aggregated score			Translated score
	$S e v e r i t y$	Occurrence	$D e t e c t i o n$	$S e v e r i t y$	Occurrence	$D etection$
$F M_{1}$	0.872	-0.230	0.152	9.424	4.464	6.184
$F M_{2}$	0.799	0.099	-0.297	9.096	5.944	4.162
$F M_{3}$	0.420	-0.047	-0.430	7.391	5.289	3.564
$F M_{4}$	0.487	0.714	-0.209	7.692	8.712	4.559
$F M_{5}$	0.228	0.733	0.264	6.525	8.798	6.689
$F M_{6}$	0.714	-0.420	0.096	8.712	3.610	5.931

d_{1} \oplus d_{2} = \cup_{{\tilde{γ}}_{1} \in {\tilde{h}}_{1}, {\tilde{γ}}_{2} \in {\tilde{h}}_{2}, {\tilde{η}}_{1} \in {\tilde{g}}_{1}, {\tilde{η}}_{2} \in {\tilde{g}}_{2}} \{\{{\tilde{γ}}_{1} + {\tilde{γ}}_{2} - {\tilde{γ}}_{1} {\tilde{γ}}_{2}\}, \{{\tilde{η}}_{1} {\tilde{η}}_{2}\}\}

d_{1} \otimes d_{2} = \cup_{{\tilde{γ}}_{1} \in {\tilde{h}}_{1}, {\tilde{γ}}_{2} \in {\tilde{h}}_{2}, {\tilde{η}}_{1} \in {\tilde{g}}_{1}, {\tilde{η}}_{2} \in {\tilde{g}}_{2}} \{\{{\tilde{γ}}_{1} {\tilde{γ}}_{2}\}, \{{\tilde{η}}_{1} + {\tilde{η}}_{2} - {\tilde{η}}_{1} {\tilde{η}}_{2}\}\}

D H F W A ({\tilde{d}}_{1}, {\tilde{d}}_{2}, \dots, {\tilde{d}}_{n}) = \oplus_{j = 1}^{n} (ω_{j} {\tilde{d}}_{j}) = \cup_{{\tilde{γ}}_{j} \in {\tilde{h}}_{j}, {\tilde{η}}_{j} \in {\tilde{g}}_{j}} \{\{1 - \prod_{j = 1}^{n} {(1 - \tilde{γ})}^{ω_{j}}\}, \{\prod_{j = 1}^{n} {(\tilde{η})}^{ω_{j}}\}\}

\begin{matrix} \begin{matrix} D M_{1} \\ D M_{2} \end{matrix} \\ ⋮ \\ D M_{n} \end{matrix} (\begin{matrix} \begin{matrix} {\tilde{w}}_{11} & {\tilde{w}}_{12} & {\tilde{w}}_{13} \\ {\tilde{w}}_{21} & {\tilde{w}}_{22} & {\tilde{w}}_{23} \\ ⋮ & ⋮ & ⋮ \end{matrix} \\ \begin{matrix} {\tilde{w}}_{n 1} & {\tilde{w}}_{n 2} & {\tilde{w}}_{n 3} \end{matrix} \end{matrix})

{\tilde{A}}_{k} = \begin{matrix} \begin{matrix} F M_{1} \\ F M_{2} \end{matrix} \\ ⋮ \\ F M_{m} \end{matrix} (\begin{matrix} \begin{matrix} {\tilde{a}}_{11}^{k} & {\tilde{a}}_{12}^{k} & {\tilde{a}}_{13}^{k} \\ {\tilde{a}}_{21}^{k} & {\tilde{a}}_{22}^{k} & {\tilde{a}}_{23}^{k} \\ ⋮ & ⋮ & ⋮ \end{matrix} \\ \begin{matrix} {\tilde{a}}_{m 1}^{k} & {\tilde{a}}_{m 2}^{k} & {\tilde{a}}_{m 3}^{k} \end{matrix} \end{matrix})

\begin{array}{l} D H F W A ({\tilde{a}}_{11}^{1}, {\tilde{a}}_{11}^{2}, {\tilde{a}}_{11}^{3}) = \{\{1 - ({0.75}^{0.4} * {0.75}^{0.3} * {0.90}^{0.3})\}, \{{0.10}^{0.4} * {0.10}^{0.3} * {0.10}^{0.3}\}\}; \\ \{\{1 - ({0.90}^{0.4} * {0.75}^{0.3} * {0.90}^{0.3})\}, \{{0.10}^{0.4} * {0.10}^{0.3} * {0.10}^{0.3}\}\}; \\ \{\{1 - ({0.75}^{0.4} * {0.90}^{0.3} * {0.9}^{0.3})\}, \{{0.10}^{0.4} * {0.10}^{0.3} * {0.10}^{0.3}\}\}; \\ \{\{1 - ({0.75}^{0.4} * {0.75}^{0.3} * {0.9}^{0.3})\}, \{{0.10}^{0.4} * {0.10}^{0.3} * {0.0}^{0.3}\}\}; \\ \{\{1 - ({0.75}^{0.4} * {0.75}^{0.3} * {1.0}^{0.3})\}, \{{0.10}^{0.4} * {0.10}^{0.3} * {0.0}^{0.3}\}\}; \\ \{\{1 - ({0.90}^{0.4} * {0.75}^{0.3} * {1.0}^{0.3})\}, \{{0.10}^{0.4} * {0.10}^{0.3} * {0.0}^{0.3}\}\} \\ = \{0.810, 0.868, 0.856, 1.0, 1.0, 1.0\} \{0.1, 0.1, 0.1, 0.0, 0.0, 0.0\} \end{array}

[1] * lucascalache@usp.br

	$S e v e r i t y$	Occurrence	$D e t e c t i o n$
Aggregated score	0.792	0.532	0.489
Translated and weighted score	0.372	0.318	0.309

Failure Modes	RPN	Ranking
$F M_{1}$	6.509	3
$F M_{2}$	6.226	4
$F M_{3}$	5.294	6
$F M_{4}$	6,794	2
$F M_{5}$	7.217	1
$F M_{6}$	5.833	5

Brasil

Brasil

Risk prioritization based on the combination of FMEA and dual hesitant fuzzy sets method

Abstract

Paper aims

Originality

Research method

Main findings

Implications for theory and practice