基于模糊网络层次分析和群决策的测试性指标分配方法

doi:10.12305/j.issn.1001-506X.2025.08.15

Abstract

Abstract:

Rational allocation of testability index is a critical task in the current equipment validation process. To address issues such as the limited calculation methods of classical approaches, such as failure rate-based distribution, a method for testability index allocation based on fuzzy analytic network process and group decision-making is proposed. Firstly, an evaluation system for the weights of testability index influencing factors is developed, using a triangular fuzzy number matrix for scoring. Analytic network process is employed for computation, and group decision-making is utilized to resolve weight conflicts. Secondly, an S-shaped function is introduced to improve the index allocation function, overcoming the limitations of linear distribution. Finally, the testability index allocation is validated through application in a specific airborne system. The results demonstrate that this method effectively integrates the advantages of objective calculations and subjective analyses, while also considering a broader range of factors, making it a more effective approach for testability index allocation.

Key words: testability index allocation, triangular fuzzy judgment matrix, analytic network process, group decision-making, S-shaped function optimization

CLC Number:

TP 206.1

Chao ZHANG, Yingtao FANG, Zhijie DONG, Shilie HE, Zhenwei ZHOU. Testability index allocation method based on fuzzy analytic network process and group decision-making[J]. Systems Engineering and Electronics, 2025, 47(8): 2570-2580.

Figures/Tables 11

Fig.1

Table 1

Fig.2

Table 2

Meaning and symbol of evaluation criteria for testability index influence factors weights"

评价准则	一级指标元素	元素内部相关性
系统顶层需求（$ S $）	任务要求（$ {S}_{1} $）	$ {S}_{1}\to {R}_{1}、{R}_{2} $
	性能要求（$ {S}_{2} $）	$ {S}_{2}\to {S}_{4}、{R}_{2}、{R}_{3}、{R}_{5}、{O}_{2}、{O}_{3}、{O}_{5} $
	战技指标要求（$ {S}_{3} $）	$ {S}_{3}\to {R}_{2}、{R}_{5} $
	结构功能要求（$ {S}_{4} $）	$ {S}_{4}\to {R}_{2}、{R}_{3}、{R}_{4} $
可靠性要求（$ R $）	保障性（$ {R}_{1} $）	$ {R}_{1}\to {O}_{2}、{O}_{3}、{O}_{5}、{R}_{2}、{R}_{6} $
	可靠性（$ {R}_{2} $）	$ {R}_{2}\to {S}_{1}、{S}_{2}、{S}_{4}、{R}_{1}、{R}_{3}、{R}_{4}、{R}_{5}、{R}_{6}、{O}_{2}、{O}_{3}、{O}_{5} $
	安全性（$ {R}_{3} $）	$ {R}_{3}\to {S}_{2}、{S}_{3}、{R}_{2}、{R}_{5}、{O}_{2}、{O}_{3}、{O}_{5} $
	测试性（$ {R}_{4} $）	$ {R}_{4}\to {S}_{1}、{S}_{2}、{S}_{3}、{R}_{1}、{R}_{2}、{R}_{3}、{R}_{4}、{R}_{5}、{R}_{6}、{O}_{1}、{O}_{2}、{O}_{3}、{O}_{4}、{O}_{5} $
	环境适应性（$ {R}_{5} $）	$ {R}_{5}\to {S}_{1}、{S}_{2}、{R}_{1}、{R}_{2}、{R}_{3}、{R}_{4}、{R}_{6}、{O}_{2}、{O}_{3}、{O}_{5} $
	维修性（$ {R}_{6} $）	$ {R}_{6}\to {S}_{1}、{S}_{2}、{S}_{3}、{S}_{4}、{R}_{1}、{R}_{2}、{R}_{3}、{R}_{4}、{R}_{5}、{R}_{6}、{O}_{2}、{O}_{3}、{O}_{5} $
客观约束条件（$ O $）	体积和重量（$ {O}_{1} $）	$ {O}_{1}\to {S}_{1}、{S}_{4}、{R}_{1}、{O}_{5} $
	可利用可达性（$ {O}_{2} $）	$ {O}_{2}\to {S}_{1}、{S}_{2}、{S}_{3}、{R}_{1}、{R}_{2}、{R}_{3}、{R}_{4}、{R}_{5}、{R}_{6}、{O}_{1}、{O}_{3}、{O}_{5} $
	故障率（$ {O}_{3} $）	$ {O}_{3}\to {S}_{1}、{R}_{1}、{R}_{2}、{R}_{3}、{R}_{4}、{R}_{5}、{R}_{6}、{O}_{5} $
	类似测试信息（$ {O}_{4} $）	$ {O}_{4}\to {R}_{4}、{O}_{5} $
	费用成本（$ {O}_{5} $）	$ {O}_{5}\to {R}_{1}、{R}_{2}、{R}_{3}、{R}_{4}、{R}_{5}、{R}_{6}、{O}_{1}、{O}_{2} $、$ {O}_{5} $

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

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$ {a}_{ij} $	含义
1	元素$ i $与元素$ j $同样重要
3	元素$ i $比元素$ j $略微重要
5	元素$ i $比元素$ j $明显重要
7	元素$ i $比元素$ j $非常重要
9	元素$ i $比元素$ j $特别重要
2,4,6,8	中间值

$ {R}_{1} $	$ {R}_{2} $	$ {R}_{6} $	$ {W}_{R1} $
$ {R}_{2} $	（1,1,1）	（1,2,3）	0.692
$ {R}_{6} $	（1/3,1/2,1/1）	（1,1,1）	0.308

元素	$ {{R}}_{1} $	$ {{R}}_{2} $	$ {{R}}_{3} $	$ {{R}}_{4} $	$ {{R}}_{5} $	$ {{R}}_{6} $	$ {{O}}_{1} $	$ {{O}}_{2} $	$ {{O}}_{3} $	$ {{O}}_{4} $	$ {{O}}_{5} $	$ {{\alpha }}_{{M}} $	$ {{\alpha }}_{{F}} $	$ {{\alpha }}_{{\lambda }} $	$ {{\alpha }}_{{T}} $	$ {{\alpha }}_{{C}} $	$ {{S}}_{1} $	$ {{S}}_{2} $	$ {{S}}_{3} $	$ {{S}}_{4} $
$ {{R}}_{1} $	0	0.195	0	0.119	0.143	0.110	1	0.087	0.115	0	0.125	0.092	0.107	0.133	0.133	0.096	0.250	0	0	0
$ {{R}}_{2} $	0.692	0	0.750	0.224	0.286	0.243	0	0.170	0.245	0	0.250	0.155	0.206	0.244	0.243	0.276	0.750	0.333	0.750	0.238
$ {{R}}_{3} $	0	0.407	0	0.199	0.286	0.280	0	0.312	0.264	0	0.250	0.309	0.306	0.266	0.277	0.298	0	0.528	0	0.625
$ {{R}}_{4} $	0	0.153	0	0.205	0.143	0.139	0	0.200	0.141	1	0.125	0.200	0.154	0.144	0.133	0.170	0	0	0	0.137
$ {{R}}_{5} $	0	0.104	0.250	0.113	0	0.114	0	0.095	0.111	0	0.125	0.160	0.107	0.069	0.070	0.072	0	0.140	0.250	0
$ {{R}}_{6} $	0.308	0.140	0	0.140	0.143	0.114	0	0.135	0.123	0	0.125	0.084	0.120	0.144	0.144	0.087	0	0	0	0
$ {{O}}_{1} $	0	0	0	0.107	0	0	0	0.196	0	0	0.196	0	0	0	0	0	0	0	0	0
$ {{O}}_{2} $	0.163	0.196	0.196	0.141	0.196	0.196	0	0	0	0	0.493	0.333	0.333	0.333	0.333	0.333	0	0.327	0	0
$ {{O}}_{3} $	0.540	0.493	0.493	0.185	0.493	0.493	0	0.493	0	0	0	0.333	0.333	0.333	0.333	0.333	0	0.413	0	0
$ {{O}}_{4} $	0	0	0	0.245	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
$ {{O}}_{5} $	0.297	0.311	0.311	0.323	0.311	0.311	1	0.311	1	1	0.311	0.333	0.333	0.333	0.333	0.333	0	0.260	0	0
$ {{\alpha }}_{{M}} $	0.098	0.162	0.189	0.190	0.187	0.171	0	0.180	0.188	0	0.194	0	0	0	0	0	0.184	0.187	0	0
$ {{\alpha }}_{{F}} $	0.441	0.379	0.357	0.316	0.306	0.259	0	0.286	0.344	0	0.249	0	0	0	0	0	0.408	0.330	0	0
$ {{\alpha }}_{{\lambda }} $	0.249	0.227	0.237	0.274	0.195	0.225	0	0.197	0.188	0	0.222	0	0	0	0	0	0.203	0.229	0	0
$ {{\alpha }}_{{T}} $	0.119	0.106	0.109	0.110	0.124	0.149	0	0.156	0.136	0	0.141	0	0	0	0	0	0.103	0.141	0	0
$ {{\alpha }}_{{C}} $	0.092	0.126	0.109	0.110	0.187	0.196	0	0.180	0.145	0	0.194	0	0	0	0	0	0.103	0.112	0	0
$ {{S}}_{1} $	0	0.311	0	0.333	0.250	0.138	0.750	0.594	1	0	0	0.250	0.333	0.333	0.333	0.250	0	0	0	0
$ {{S}}_{2} $	0	0.493	0.667	0.333	0.750	0.276	0	0.249	0	0	0	0.750	0.667	0.667	0.667	0.750	0	0	0	0
$ {{S}}_{3} $	0	0	0.333	0.333	0	0.391	0	0.157	0	0	0	0	0	0	0	0	0	0	0	0
$ {{S}}_{4} $	0	0.196	0	0	0	0.195	0.250	0	0	0	0	0	0	0	0	0	0	1	0	0

元素集	$ R $	$ O $	$ \alpha $	$ S $
$ R $	0.244	0.256	0.239	0.226
$ O $	0.146	0.138	0.137	0.141
$ \alpha $	0.098	0.075	0	0.239
$ S $	0.512	0.531	0.625	0.394

参数	值
${\alpha }_{\lambda } $	0.219
$ {\alpha }_{F} $	0.363
${\alpha }_{M} $	0.180
$ {\alpha }_{C} $	0.118
${\alpha }_{T} $	0.120

Testability index allocation method based on fuzzy analytic network process and group decision-making

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权重	专家1	专家2	专家3	专家4	专家5	组合权重	奇异点
权重	专家1	专家2	专家3	专家4	专家5	组合权重	第1次去除	第2次去除
$ {\alpha }_{\lambda } $	0.219	0.205	0.200	0.300	0.220	0.213 1	0.300	无
$ {\alpha }_{F} $	0.363	0.325	0.290	0.310	0.280	0.315 3	无	无
$ {\alpha }_{M} $	0.180	0.210	0.220	0.180	0.200	0.199 7	无	无
$ {\alpha }_{C} $	0.118	0.070	0.120	0.100	0.110	0.114 1	0.070	无
$ {\alpha }_{T} $	0.120	0.190	0.170	0.110	0.190	0.157 7	无	无

名称代号	数量	$ {\lambda }_{i} $	$ {K}_{i} $	$ {\gamma }_{{\mathrm{FD}}i} $	$ {\gamma }_{{\mathrm{FI}}i} $	影响因素
名称代号	数量	$ {\lambda }_{i} $	$ {K}_{i} $	$ {\gamma }_{{\mathrm{FD}}i} $	$ {\gamma }_{{\mathrm{FI}}i} $	$ {k}_{\lambda i} $	$ {k}_{Fi} $	$ {k}_{Mi} $	$ {k}_{Ci} $	$ {k}_{Ti} $
二次电源	1	0.000 09	5.930 2	0.990 3	0.994 4	6	9	5	3	3
X轴动调陀螺	1	0.000 07	5.070 1	0.979 2	0.986 9	5	4	5	7	6
YZ轴动调陀螺	1	0.000 14	5.922 5	0.990 3	0.994 4	9	4	5	7	6
X轴再平衡放大器组合	1	0.000 02	3.788 3	0.935 6	0.954 2	1	3	5	6	6
YZ轴再平衡放大器组合	1	0.000 04	4.214 5	0.955 6	0.969 8	3	3	5	6	6
X轴角速度计	1	0.000 07	3.684 3	0.929 5	0.949 4	4	3	4	4	4
Y轴角速度计	1	0.000 07	3.684 3	0.929 5	0.949 4	4	3	4	4	4
Z轴角速度计	1	0.000 07	3.684 3	0.929 5	0.949 4	4	3	4	4	4
滤波放大电路	1	0.000 04	4.787 9	0.973 2	0.982 8	3	7	7	2	2
模拟-数字转换电路	1	0.000 01	4.631 7	0.969 3	0.979 9	1	7	7	2	2
总计	10	0.000 62	—	0.963	0.975	—	—	—	—	—

单元编号	$ {\lambda }_{i}/{10}^{-6} $	故障率分配法		综合加权分配法		反正切函数分配法		本方法
单元编号	$ {\lambda }_{i}/{10}^{-6} $	$ {\gamma }_{\mathrm{FD}i}$	$ {\gamma }_{\mathrm{FI}i} $	$ {\gamma }_{\mathrm{FD}i} $	$ {\gamma }_{\mathrm{FI}i} $	$ {\gamma }_{\mathrm{FD}i} $	$ {\gamma }_{\mathrm{FI}i} $	$ {\gamma }_{\mathrm{FD}i} $	$ {\gamma }_{\mathrm{FI}i} $
$ {{\mathrm{LRM}}}_{1} $	30	0.278 8	0.259 5	0.900 0	0.763 6	0.880 7	0.755 4	0.922 9	0.856 9
$ {{\mathrm{LRM}}}_{2} $	30	0.278 8	0.259 5	0.900 0	0.763 6	0.880 7	0.755 4	0.947 5	0.893 7
$ {{\mathrm{LRM}}}_{3} $	100	0.929 3	0.865 0	0.940 0	0.871 8	0.963 8	0.929 7	0.937 6	0.878 5
$ {{\mathrm{LRM}}}_{4} $	150	1.394 0	1.297 6	0.980 0	0.980 0	0.975 9	0.952 7	0.972 7	0.936 1
$ {{\mathrm{LRM}}}_{5} $	50	0.464 7	0.432 5	0.940 0	0.871 8	0.927 9	0.855 9	0.924 6	0.859 4
综合	360	0.967 7	0.899 9	0.950 0	0.898 8	0.950 0	0.900 0	0.950 0	0.900 0

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