多粒度概率语言环境下基于PROMETHEE的改进FMEA方法

鞠萍华; 陈资; 冉琰; 胡晓波

doi:10.13700/j.bh.1001-5965.2019.0142

多粒度概率语言环境下基于PROMETHEE的改进FMEA方法

doi: 10.13700/j.bh.1001-5965.2019.0142

重庆大学机械传动国家重点实验室, 重庆 400044

基金项目:

国家自然科学基金 51835001

国家自然科学基金 51705048

国家重大科技专项 2018ZX04032-001

国家重大科技专项 2016ZX04004-005

详细信息

作者简介:
鞠萍华  男, 博士, 副教授, 硕士生导师。主要研究方向:机械设备故障诊断、机电产品可靠性

陈资  男, 硕士研究生。主要研究方向:机电产品可靠性

冉琰  女, 博士, 讲师。主要研究方向:现代质量工程、数控机床可靠性技术等

通讯作者:
冉琰.E-mail:ranyan@cqu.edu.cn

中图分类号: X931;V46
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出版历程
- 收稿日期: 2019-04-01
- 录用日期: 2019-05-31
- 网络出版日期: 2019-11-20

Improved FMEA method based on PROMETHEE in multi-granular probabilistic linguistic environment

State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China

Funds:

National Natural Science Foundation of China 51835001

National Natural Science Foundation of China 51705048

National Science and Technology Major Program 2018ZX04032-001

National Science and Technology Major Program 2016ZX04004-005

More Information

Corresponding author: RAN Yan, E-mail: ranyan@cqu.edu.cn

摘要

摘要:
针对传统故障模式和影响分析（FMEA）方法中存在关于故障模式评估、风险因子权重和风险优先级排序等方面的固有缺陷，提出了一种多粒度概率语言环境下基于偏好顺序结构评估法（PROMETHEE）的改进FMEA方法。该方法运用多粒度概率语言术语集（PLTS）刻画了专家评估信息的多样性和不确定性，并基于二元语义转换函数为引入工具的语言计算模型统一各专家多粒度风险评估信息，运用最优最劣法（BWM）和熵权法相结合的综合赋权法确定风险因子权重，将PROMETHEE拓展到概率语言环境中用于确定故障模式风险优先序。最后，运用托盘交换架故障风险评估案例来验证该方法的适用性和有效性，并进一步通过敏感度与对比分析以显示该方法的优越性。
- 故障模式和影响分析(FMEA) /
- 概率语言术语集(PLTS) /
- 多粒度语言 /
- 偏好顺序结构评估法(PROMETHEE) /
- 最优最劣法(BWM)
Abstract:
With respect to some inherent drawbacks regarding failure mode evaluations, risk factor weights and risk priority ranking in traditional failure mode and effect analysis (FMEA)method, an improved FMEA method based on preference ranking organization method for enrichment evaluations (PROMETHEE) in multi-granular probabilistic linguistic environment was proposed. The multi-granular probabilistic linguistic term sets (PLTS) were used to characterize the diversity and uncertainty of experts' assessment information, and a new linguistic computational model was developed based on the 2-tuple linguistic transformation formulas to unify the multi-granular risk assessment information provided by FMEA team members. Best-worst method (BWM) and the entropy weighting method were adopted to determine subjective and objective combined weights of risk factors. The PROMETHEEE was extended to probabilistic linguistic environment to determine the risk ranking of failure modes. Finally, an empirical case concerning the failure risk evaluation of tray automatic exchange device was presented to demonstrate the practicality and effectiveness of the proposed method, and sensitivity analysis and comparison study were also performed to show its merits.

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图 1 改进FMEA方法框架流程图

Figure 1. Flowchart of improved FMEA method

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图 2 参数γ的敏感度分析

Figure 2. Sensitivity analysis on parameter γ

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图 3 不同方法故障模式间相对偏差量

Figure 3. Relative deviations between failure modes by different methods

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表 1 一致性指数

Table 1. Consistency index

a_BW	CI
1	0
2	0.44
3	1.00
4	1.63
5	2.30
6	3.00
7	3.73
8	4.47
9	5.23

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表 2 3位专家提供的概率语言评估信息

Table 2. Probabilistic linguistic evaluation information provided by three experts

E_q	RF_j	FM₁	FM₂	FM₃	FM₄	FM₅	FM₆
E₁	O	{s₂⁵(0.8)}	{s₃⁵(0.8), s₄⁵(0.2)}	{s₂⁵(0.8)}	{s₂⁵(0.8), s₃⁵(0.2)}	{s₁⁵(0.5), s₂⁵(0.5)}	{s₁⁵(0.4), s₂⁵(0.6)}
	S	{s₂⁵(0.5), s₃⁵(0.5)}	{s₂⁵(0.4), s₃⁵(0.4)}	{s₃⁵(0.4), s₄⁵(0.6)}	{s₃⁵(0.5), s₄⁵(0.5)}	{s₂⁵(0.4), s₃⁵(0.6)}	{s₃⁵(0.8)}
	D	{s₃⁵(0.5), s₄⁵(0.5)}	{s₀⁵(0.6), s₁⁵(0.4)}	{s₂⁵(1)}	{s₄⁵(0.8)}	{s₁⁵(0.2), s₂⁵(0.8))}	{s₄⁵(1)}
E₂	O	{s₃⁷(0.2), s₄⁷(0.8)}	{s₄⁷(0.5), s₅⁷(0.5)}	{s₃⁷(0.8), s₄⁷(0.2)}	{s₃⁷(0.8), s₄⁷(0.2)}	{s₂⁷(0.75), s₃⁷(0.25)}	{s₁⁷(0.4), s₂⁷(0.6)}
	S	{s₃⁷(0.25), s₄⁷(0.75)}	{s₃⁷(0.2), s₄⁷(0.6), s₅⁷(0.2)}	{s₄⁷(0.5), s₅⁷(0.5)}	{s₄⁷(0.4), s₅⁷(0.4)}	{s₃⁷(0.8), s₄⁷(0.2)}	{s₄⁷(0.5), s₅⁷(0.5)}
	D	{s₄⁷(0.25), s₅⁷(0.5), s₆⁷(0.25)}	{s₀⁷(0.25), s₁⁷(0.75)}	{s₂⁷(0.2), s₃⁷(0.8)}	{s₅⁷(0.8), s₆⁷(0.2)}	{s₁⁷(0.25), s₂⁷(0.5), s₃⁷(0.25)}	{s₅⁷(0.75), s₆⁷(0.25)}
E₃	O	{s₃⁷(0.8), s₄⁷(0.2)}	{s₄⁷(0.2), s₅⁷(0.2), s₆⁷(0.6)}	{s₃⁷(0.2), s₄⁷(0.8)}	{s₃⁷(0.8), s₄⁷(0.2)}	{s₁⁷(0.4), s₂⁷(0.6)}	{s₂⁷(0.4), s₃⁷(0.4)}
	S	{s₃⁷(0.25), s₄⁷(0.75)}	{s₃⁷(0.8), s₄⁷(0.2)}	{s₅⁷(0.6), s₆⁷(0.2)}	{s₄⁷(0.8)}	{s₃⁷(0.25), s₄⁷(0.5), s₅⁷(0.25)}	{s₄⁷(0.5), s₅⁷(0.5)}
	D	{s₄⁷(0.6), s₅⁷(0.2)}	{s₁⁷(0.6), s₂⁷(0.4)}	{s₂⁷(0.75), s₃⁷(0.25)}	{s₅⁷(0.8), s₆⁷(0.2)}	{s₃⁷(0.8)}	{s₅⁷(0.2), s₆⁷(0.8)}

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表 3 一致化处理后的专家3故障模式评估信息

Table 3. Unified E'₃ s evaluation information of each failure mode

RF_j	FM₁	FM₂	FM₃	FM₄	FM₅	FM₆
O	{s₃⁷(0.8)}	{s₄⁷(0.4), s₅⁷(0.4), s₆⁷(0.2)}	{s₃⁷(0.8)}	{s₃⁷(0.8), s₄⁷(0.1), s₅⁷(0.1)}	{s₁⁷(0.25), s₂⁷(0.25), s₃⁷(0.5)}	{s₁⁷(0.2), s₂⁷(0.2), s₃⁷(0.6)}
S	{s₃⁷(0.5), s₄⁷(0.25), s₅⁷(0.25)}	{s₃⁷(0.4), s₄⁷(0.2), s₅⁷(0.2)}	{s₄⁷(0.2), s₅⁷(0.2), s₆⁷(0.6)}	{s₄⁷(0.25), s₅⁷(0.25), s₆⁷(0.5)}	{s₃⁷(0.4), s₄⁷(0.3), s₅⁷(0.3)}	{s₄⁷(0.4), s₅⁷(0.4)}
D	{s₄⁷(0.25), s₅⁷(0.25), s₆⁷(0.5)}	{s₀⁷(0.6), s₁⁷(0.2), s₂⁷(0.2)}	{s₃⁷(1)}	{s₆⁷(0.8)}	{s₁⁷(0.1), s₂⁷(0.1), s₃⁵(0.8)}	{s₆⁷(1)}

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表 4 群体故障评估矩阵

Table 4. Group failure evaluation matrix

RF_j	FM₁	FM₂	FM₃	FM₄	FM₅	FM₆
O	{s₃⁷(0), s₄⁷(0.4), s₃⁷(0.6)}	{s₄⁷(0.16), s₅⁷(0.36), s₆⁷(0.48)}	{s₃⁷(0), s₄⁷(0.4), s₃⁷(0.6)}	{s₅⁷(0.02), s₄⁷(0.18), s₃⁷(0.8)}	{s₁⁷(0.21), s₃⁷(0.2), s₂⁷(0.59)}	{s₁⁷(0.2), s₂⁷(0.48), s₃⁷(0.32)}
S	{s₅⁷(0.05), s₃⁷(0.3), s₄⁷(0.65)}	{s₅⁷(0.13), s₄⁷(0.37), s₃⁷(0.5)}	{s₄⁷(0.24), s₆⁷(0.22), s₅⁷(0.54)}	{s₆⁷(0.1), s₅⁷(0.25), s₄⁷(0.65)}	{s₅⁷(0.16), s₄⁷(0.34), s₃⁷(0.5)}	{s₄⁷(0), s₄⁷(0.5), s₅⁷(0.5)}
D	{s₆⁷(0.2), s₅⁷(0.35), s₄⁷(0.45)}	{s₀⁷(0.22), s₂⁷(0.2), s₁⁷(0.58)}	{s₂⁷(0), s₂⁷(0.38), s₃⁷(0.62)}	{s₅⁷(0), s₆⁷(0.36), s₅⁷(0.64)}	{s₁⁷(0.12), s₂⁷(0.22), s₃⁷(0.66)}	{s₅⁷(0), s₅⁷(0.38), s₆⁷(0.62)}

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表 5 最佳标准的风险因子评级向量

Table 5. Preference rating vectors for the best risk factor

E_q	RF_B	O	S	D
E₁	S	2	1	8
E₂	S	9	1	3
E₃	O	1	3	8

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表 6 最差标准的风险因子评级向量

Table 6. Preference rating vectors for the worst risk factor

E_q	RF_W	O	S	D
E₁	D	2	8	1
E₂	O	1	7	4
E₃	D	7	3	1

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表 7 风险因子主观权重

Table 7. Subjective weights of risk factor

E_q	O	S	D	CR
E₁	0.246	0.663	0.091	0.157
E₂	0.078	0.622	0.300	0.191
E₃	0.652	0.261	0.087	0.112
w_j^S	0.341	0.486	0.173

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表 8 不同方法故障模式风险排序比较

Table 8. Risk ranking comparison of failure modes by different methods

故障模式	传统FMEA					PL-TOPSIS^[15]		HFL-PROMETHEE^[8]		PL-PROMETHEE
故障模式	O	S	D	RPN	排序	CI(FM_i)	排序	Φ(FM_i)	排序	Φ(FM_i)	排序
FM₁	5	6	7	210	3	-0.743	4	0.176	3	0.050	4
FM₂	8	4	6	192	4	-0.962	5	-0.440	5	-0.556	5
FM₃	6	8	4	192	4	-0.556	3	0.368	2	0.879	2
FM₄	5	6	9	270	1	0	1	2.017	1	1.272	1
FM₅	3	6	5	90	5	-1.368	6	-2.167	6	-2.146	6
FM₆	4	7	9	252	2	-0.353	2	0.045	4	0.500	3

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