﻿ 用于供应商风险评价的FMEA改进
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (1): 130-135.  DOI: 10.11908/j.issn.0253-374x.2019.01.017 0

### 引用本文

YOU Jianxin, LIU Wei, YANG Miying. An Improved FMEA for Supplier Risk Assessment[J]. Journal of Tongji University (Natural Science), 2019, 47(1): 130-135. DOI: 10.11908/j.issn.0253-374x.2019.01.017

### 文章历史

1. 同济大学 经济与管理学院，上海 200092;
2. 埃克塞特大学 工程、数学与物理科学学院，埃克塞特 EX4 4QF

An Improved FMEA for Supplier Risk Assessment
YOU Jianxin 1,2, LIU Wei 1, YANG Miying 2
1. School of Economics and Management, Tongji University, Shanghai 200092, China;
2. College of Engineering, Mathematics and Physical Science, University of Exeter, Exeter EX4 4QF, UK
Abstract: This paper proposes an improved failure mode and effects analysis(FMEA) method based on hesitant fuzzy sets and grey relational theory for supplier risk assessment. First, the potential risks of suppliers were identified and then experts evaluated these risks using hesitation fuzzy linguistic terms on the basis of their preferences. Next, the sematic-based computation method and the rough set idea were used to translate the assessment information into interval-valued numbers. Finally, it considered the relative importance of O, S, D when using grey relational theory to determine the risk priority. The case study shows that the method could help companies identify the main risks of cooperating suppliers, as well as provide support for managers to formulate risk management and control strategies.
Key words: supplier risk    risk assessment    failure mode and effects analysis    hesitant fuzzy set    gray relational theory

1 相关研究综述 1.1 供应商风险评价方法研究现状

1.2 FMEA研究述评

FMEA是常用的风险评估方法之一, 被广泛应用于航天、汽车、机械、医疗等各个领域[4].传统的FMEA通过对故障或风险模式的发生度(occurrence, O)、严重度(severity, S)和检测度(detection, D)进行评分, 并以三者乘积计算风险优先数(risk priority number, RPN), 从而进行风险评估.使用传统FMEA解决实际问题主要存在以下三个缺陷：①实际风险分析中, 失效模式的风险因子难以用数字精确评价.②传统方法没有考虑风险因子的发生度O、严重度S和检测度D之间的相对重要性.③不同的风险因子组合有时会计算出相同的RPN值, 但实际暗藏的风险可能大不相同.

2 改进FMEA模型的构建 2.1 供应商潜在风险识别

 图 1 供货期间供应商潜在风险 Fig.1 Suppliers' potential risks during delivery
2.2 建立犹豫模糊语义术语集

2.3 用二元语义处理犹豫模糊语义术语集

 ${\Delta ^{ - 1}}{H_L}\left( {{\vartheta _i}} \right) = \left\{ {f, \cdots ,u} \right\}$ (1)
2.4 基于粗糙思想的犹豫模糊语义评价信息转化[15]

 $\underline {{\rm{Apr}}} \left( {{C_i}} \right) = U\left\{ {Y \in U\left| {R\left( Y \right) \le {C_i}} \right.} \right\}$ (2)

Ci的上近似域定义为

 $\overline {{\rm{Apr}}} \left( {{C_i}} \right) = U\left\{ {Y \in U\left| {R\left( Y \right) \ge {C_i}} \right.} \right\}$ (3)

Lim(Ci)和Lim(Ci)分别为Ci的下限和上限, 分别定义为

 $\underline {{\rm{Lim}}} \left( {{C_i}} \right) = \frac{1}{{{M_L}}}\sum {R\left( Y \right)} \left| {Y \in \underline {{\rm{Apr}}} \left( {{C_i}} \right)} \right.$ (4)
 $\overline {{\rm{Lim}}} \left( {{C_i}} \right) = \frac{1}{{{M_U}}}\sum {R\left( Y \right)} \left| {Y \in \overline {{\rm{Apr}}} \left( {{C_i}} \right)} \right.$ (5)

 ${R_{{\rm{num}}}}\left( {{C_i}} \right) = \left[ {\underline {{\rm{Lim}}} \left( {{C_i}} \right),\overline {{\rm{Lim}}} \left( {{C_i}} \right)} \right]$ (6)

n个犹豫模糊集构成的群决策问题结果为

 ${\Delta ^{ - 1}}{H_L}\left( \vartheta \right) = \left[ {\frac{1}{n}\sum\limits_{i = 1}^n {\underline {{N_i}} } ,\frac{1}{n}\sum\limits_{i = 1}^n {\overline {{N_i}} } } \right]$ (7)
2.5 构建群评价矩阵

Xj表示供应商的第j种风险, 由于每种风险均有OSD三个变量, 因此反映第j种风险的数据列可表示为Xj={xj(1), xj(2), xj(3)}.xj(t)(t=1, 2, 3)表示FMEA专家小组对三个变量的群评价结果, 其代表的数值为通过2.4所示过程得到的区间数[$\underline {{N_j}}$(t), $\overline {{N_j}}$(t)].按照上述方法, 可以得到反映供应商n种风险的群评价矩阵为

 $\left\{ {{x_j}\left( t \right)} \right\} = \left( {\begin{array}{*{20}{c}} {{X_1}}\\ {{X_2}}\\ \cdots \\ {{X_n}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {\left[ {\underline {{N_1}} \left( 1 \right),\overline {{N_1}} \left( 1 \right)} \right]}&{\left[ {\underline {{N_1}} \left( 2 \right),\overline {{N_1}} \left( 2 \right)} \right]}&{\left[ {\underline {{N_1}} \left( 3 \right),\overline {{N_1}} \left( 3 \right)} \right]}\\ {\left[ {\underline {{N_2}} \left( 1 \right),\overline {{N_2}} \left( 1 \right)} \right]}&{\left[ {\underline {{N_2}} \left( 2 \right),\overline {{N_2}} \left( 2 \right)} \right]}&{\left[ {\underline {{N_2}} \left( 3 \right),\overline {{N_2}} \left( 3 \right)} \right]}\\ \cdots&\cdots&\cdots \\ {\left[ {\underline {{N_n}} \left( 1 \right),\overline {{N_n}} \left( 1 \right)} \right]}&{\left[ {\underline {{N_n}} \left( 2 \right),\overline {{N_n}} \left( 2 \right)} \right]}&{\left[ {\underline {{N_n}} \left( 3 \right),\overline {{N_n}} \left( 3 \right)} \right]} \end{array}} \right)$
2.6 建立参考矩阵

 $\left\{ {{x_0}\left( t \right)} \right\} = \left( {\begin{array}{*{20}{c}} {{X_0}}\\ {{X_0}}\\ \cdots \\ {{X_0}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {\left[ {g,g} \right]}&{\left[ {g,g} \right]}&{\left[ {g,g} \right]}\\ {\left[ {g,g} \right]}&{\left[ {g,g} \right]}&{\left[ {g,g} \right]}\\ \cdots&\cdots&\cdots \\ {\left[ {g,g} \right]}&{\left[ {g,g} \right]}&{\left[ {g,g} \right]} \end{array}} \right)$
2.7 建立距离矩阵

 $D\left( {A,B} \right) = \sqrt {\frac{1}{2}\left[ {{{\left( {\overline B - \overline A } \right)}^2} + {{\left( {\underline B - \underline A } \right)}^2}} \right]}$ (8)

 $\left\{ {{D_j}\left( t \right)} \right\} = \left( {\begin{array}{*{20}{c}} {{D_1}\left( 1 \right)}&{{D_1}\left( 2 \right)}&{{D_1}\left( 3 \right)}\\ {{D_2}\left( 1 \right)}&{{D_2}\left( 2 \right)}&{{D_2}\left( 3 \right)}\\ \cdots&\cdots&\cdots \\ {{D_n}\left( 1 \right)}&{{D_n}\left( 2 \right)}&{{D_n}\left( 3 \right)} \end{array}} \right)$
2.8 计算灰色关联系数

 $\xi \left( {{X_0}\left( t \right),{X_j}\left( t \right)} \right) = \frac{{\mathop {\min }\limits_j \mathop {\min }\limits_t {D_j}\left( t \right) + \rho \mathop {\max }\limits_j \mathop {\max }\limits_t {D_j}\left( t \right)}}{{{D_j}\left( t \right) + \rho \mathop {\max }\limits_j \mathop {\max }\limits_t {D_j}\left( t \right)}}$ (9)

2.9 计算灰色关联度

 $\gamma \left( {{X_0},{X_j}} \right) = \sum\limits_{t = 1}^3 {{\lambda _t}\left\{ {\xi \left( {{D_j}\left( t \right)} \right)} \right\}}$ (10)

2.10 排序

3 改进FMEA模型的应用 3.1 应用模型进行风险排序

 $\begin{array}{l} \left\{ {{x_j}\left( t \right)} \right\} = \\ \;\;\;\left( {\begin{array}{*{20}{c}} {\left[ {0.96,2.04} \right]}&{\left[ {3.67,4.33} \right]}&{\left[ {3.30,4.10} \right]}\\ {\left[ {0.19,1.00} \right]}&{\left[ {3.30,4.10} \right]}&{\left[ {2.54,3.46} \right]}\\ {\left[ {3.67,4.33} \right]}&{\left[ {3.30,4.10} \right]}&{\left[ {3.90,4.70} \right]}\\ {\left[ {5.40,5.87} \right]}&{\left[ {3.90,4.70} \right]}&{\left[ {4.13,4.60} \right]}\\ {\left[ {0.19,1.00} \right]}&{\left[ {3.30,4.10} \right]}&{\left[ {4.13,4.60} \right]}\\ {\left[ {0.19,1.00} \right]}&{\left[ {3.30,4.10} \right]}&{\left[ {2.54,3.46} \right]}\\ {\left[ {4.13,4.60} \right]}&{\left[ {2.54,3.46} \right]}&{\left[ {0.96,2.04} \right]} \end{array}} \right) \end{array}$

 $\left\{ {{x_0}\left( t \right)} \right\} = \left( {\begin{array}{*{20}{c}} {{X_0}}\\ {{X_0}}\\ \cdots \\ {{X_0}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {\left[ {6,6} \right]}&{\left[ {6,6} \right]}&{\left[ {6,6} \right]}\\ {\left[ {6,6} \right]}&{\left[ {6,6} \right]}&{\left[ {6,6} \right]}\\ \cdots&\cdots&\cdots \\ {\left[ {6,6} \right]}&{\left[ {6,6} \right]}&{\left[ {6,6} \right]} \end{array}} \right)$

 $\left\{ {{D_j}\left( t \right)} \right\} = \left( {\begin{array}{*{20}{c}} {6.41}&{2.87}&{3.30}\\ {7.67}&{3.30}&{4.29}\\ {2.87}&{3.30}&{2.47}\\ {0.61}&{2.47}&{2.33}\\ {7.67}&{3.30}&{2.33}\\ {7.67}&{3.30}&{4.29}\\ {2.33}&{4.29}&{6.41} \end{array}} \right)$

ρ=0.5, 根据式(9)计算潜在风险各变量与参考基准之间的关联系数, 得到如下灰色关联矩阵：

 $\left\{ {\xi \left( {{X_0}\left( t \right),{X_j}\left( t \right)} \right)} \right\} = \left( {\begin{array}{*{20}{c}} {0.43}&{0.66}&{0.62}\\ {0.39}&{0.62}&{0.55}\\ {0.66}&{0.62}&{0.71}\\ {1.00}&{0.71}&{0.72}\\ {0.39}&{0.62}&{0.72}\\ {0.39}&{0.62}&{0.55}\\ {0.72}&{0.55}&{0.43} \end{array}} \right)$

3.2 排序结果分析

3.3 风险管控策略的建议

4 结语

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