基于不确定理论的退化数据分析方法

doi:10.3969/j.issn.1001-506X.2020.12.31

Abstract

Abstract:

As a traditional mathematical tool in reliability field, the probability theory is not applicable to solve the problem that modern reliability engineering encounters with. Taking the application of the uncertainty theory in degraded data analysis as the entry point, the fundamental axioms, operational rules and statistical methods of the uncertainty theory are expounded, and the reliability modeling guideline based on the brief reliability theory is provided. The methods of degraded data analysis and reliability modeling considering uncertain failure threshold is proposed. The degradation equation is established by adopting the time-varying uncertain normal distribution, and the uncertainty distribution of the failure threshold is constructed according to the expert's knowledge, so as to obtain the margin equation of the product. Finally, the reliability model is deduced based on the measurement equation. The problems of parameter estimation and model verification are solved by using the maximum likelihood estimation method and hypothesis test method of uncertain statistics, respectively. The case study shows that the reliability assessment results will obviously deviate if the uncertainty of failure threshold is not considered. The research indicates that the uncertainty theory is suitable to deal with the uncertainty problems in degradation data analysis and has a broad application prospect.

Key words: uncertainty theory, brief reliability, uncertain normal distribution, failure threshold, degradation data

CLC Number:

TB114.3

Haowei WANG, Rui KANG. Method of analyzing degradation data based on the uncertainty theory[J]. Systems Engineering and Electronics, 2020, 42(12): 2924-2930.

Figures/Tables 10

Table 1

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Table 2

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Table 4

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序号	测量时刻t_{i, j}/h
序号	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00	2.25	2.50	2.75	3.00	3.25	3.50	3.75	4.00
1	0.47	0.93	2.11	2.72	3.51	4.34	4.91	5.48	5.99	6.72	7.13	8.00	8.92	9.49	9.87	10.94
2	0.71	1.22	1.90	2.30	2.87	3.75	4.42	4.99	5.51	6.07	6.64	7.16	7.78	8.42	8.91	9.28
3	0.71	1.17	1.73	1.99	2.53	2.97	3.30	3.94	4.16	4.45	4.89	5.27	5.69	6.02	6.45	6.88
4	0.27	0.61	1.11	1.77	2.06	2.58	2.99	3.38	4.05	4.63	5.24	5.62	6.04	6.32	7.10	7.59
5	0.36	1.39	1.95	2.86	3.46	3.81	4.53	5.35	5.92	6.71	7.70	8.61	9.15	9.95	10.49	11.01
6	0.46	1.07	1.42	1.77	2.11	2.40	2.78	3.02	3.29	3.75	4.16	4.76	5.16	5.46	5.81	6.24
7	0.51	0.93	1.57	1.96	2.59	3.29	3.61	4.11	4.60	4.91	5.34	5.84	6.40	6.84	7.20	7.88
8	0.41	1.49	2.38	3.00	3.84	4.50	5.25	6.26	7.05	7.80	8.32	8.93	9.55	10.45	11.28	12.21
9	0.44	1.00	1.57	1.96	2.51	2.84	3.47	4.01	4.51	4.80	5.20	5.66	6.20	6.54	6.96	7.42
10	0.51	0.83	1.29	1.52	1.91	2.27	2.78	3.42	3.78	4.11	4.38	4.63	5.38	5.84	6.16	6.62

接受域边界	t_{i, j}/h
接受域边界	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00	2.25	2.50	2.75	3.00	3.25	3.50	3.75	4.00
Φ_{t_{i, j}}^-1(0.05)	0.22	0.44	0.66	0.88	1.10	1.32	1.54	1.77	1.99	2.21	2.43	2.65	2.87	3.09	3.31	3.53
Φ_{t_{i, j}}^-1(0.95)	0.93	1.86	2.80	3.73	4.66	5.59	6.53	7.46	8.39	9.32	10.26	11.19	12.12	13.05	13.99	14.92

测量序号	各测量时刻退化数据在各分布类型下的p值
测量序号	正态分布	对数正态分布	威布尔分布
1	0.255	0.516	0.225
2	0.970	0.897	0.952
3	0.990	0.990	0.979
4	0.178	0.347	0.153
5	0.370	0.571	0.329
6	0.649	0.788	0.593
7	0.347	0.455	0.328
8	0.485	0.658	0.466
9	0.583	0.817	0.546
10	0.267	0.461	0.262
11	0.281	0.453	0.269
12	0.169	0.301	0.157
13	0.106	0.196	0.094
14	0.100	0.180	0.097
15	0.164	0.286	0.161
16	0.159	0.307	0.152

序号	对数均值	对数标准差
1	-0.761	0.275
2	0.033	0.248
3	0.508	0.221
4	0.758	0.217
5	0.981	0.228
6	1.160	0.231
7	1.311	0.224
8	1.455	0.228
9	1.561	0.227
10	1.659	0.230
11	1.749	0.228
12	1.837	0.230
13	1.925	0.220
14	1.993	0.228
15	2.057	0.224
16	2.127	0.225

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Method of analyzing degradation data based on the uncertainty theory

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