基于相似产品先验的产品Bayes可靠性验证

doi:10.12305/j.issn.1001-506X.2026.06.18

Abstract

Abstract:

To address the prolonged duration associated with reliability demonstration tests for long-life and high-reliability products, this paper focuses on products whose lifetimes follow exponential distributions and proposes a Bayes reliability demonstration test （RDT） design method incorporating prior information obtained from similar products. Firstly, the Bayesian method is introduced into the RDT design. Concretely, the experimental data achieved from similar products is viewed as prior information. The similarity between any two products is quantified by goodness-of-fit test statistics, and prior distribution is calculated through an inheritance factor. Secondly, the Bayes average risk criterion is utilized to describe the risks for both the manufacturer and the consumer. Finally, an optimal RDT plan is obtained through a numerical iteration method. Compared with the RDT plan in the GJB899A-2009 standard, the experimental results exhibit that the devised method can significantly reduce the test time.

Key words: reliability demonstration test, Bayes methods, similar products, inheritance factor

CLC Number:

TB 114

Yu WANG, Haobo QIU, Xiaoer HE, Mingjing WANG, Chen JIANG, Liang GAO. Bayes reliability demonstration of products based on priors from similar products[J]. Systems Engineering and Electronics, 2026, 48(6): 1972-1979.

Figures/Tables 10

Fig.1

Table 1

Fig.2

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Fig.3

References 31

1	XU J Y, HU Q P, YU D, et al. Reliability demonstration test for load-sharing systems with exponential and Weibull components[J]. Plos One, 2017, 12 (12): e0189863. doi: 10.1371/journal.pone.0189863
2	ZHENG H L, YANG J, ZHAO Y. Reliability demonstration test plan for degraded products subject to Gamma process with unit heterogeneity[J]. Reliability Engineering and System Safety, 2023, 240, 109617. doi: 10.1016/j.ress.2023.109617
3	LI Z, NG H K T, YU D, et al. Optimal acceptance sampling testing plan with pivotal quantity for log-location-scale distributions[J]. IEEE Trans. on Reliability, 2023, 72 (4): 1453- 1465. doi: 10.1109/TR.2022.3229262
4	FERNáNDEZ A J, CORREA-ALVAREZ C D, PERICCHI L R. Balancing producer and consumer risks in optimal attribute testing: a unified Bayesian/frequentist design[J]. European Journal of Operational Research, 2020, 286 (2): 576- 587. doi: 10.1016/j.ejor.2020.03.001
5	GUO H R, LIAO H T. Methods of reliability demonstration testing and their relationships[J]. IEEE Trans. on Reliability, 2011, 61 (1): 231- 237. doi: 10.1109/tr.2011.2167782
6	ELSAYED E A. Overview of reliability testing[J]. IEEE Trans. on Reliability, 2012, 61 (2): 282- 291. doi: 10.1109/TR.2012.2194190
7	CHEN S Y, LU L, ZHANG Q, et al. Optimal binomial reliability demonstration tests design under acceptance decision uncertainty[J]. Quality Engineering, 2020, 32 (3): 492- 508. doi: 10.1080/08982112.2020.1757703
8	HAMADA M S, WILSON A G, WEAVER B P, et al. Bayesian binomial assurance tests for system reliability using component data[J]. Journal of Quality Technology, 2014, 46 (1): 24- 32. doi: 10.1080/00224065.2014.11917952
9	WANG B, JIANG P, GUO B. A Bayesian design method for monopropellant engine system reliability qualification test plan[J]. Reliability Engineering & System Safety, 2024, 248, 110173. doi: 10.1016/j.ress.2024.110173
10	WANG B, LU L, CHEN S Y, et al. Optimal test design for reliability demonstration under multi-stage acceptance uncertainties[J]. Quality Engineering, 2024, 36 (1): 91- 104. doi: 10.1080/08982112.2023.2249188
11	GRUNDLER A, DAZER M. Reliability demonstration test planning for systems using prior knowledge[J]. IEEE Access, 2023, 12, 3339- 3355. doi: 10.1109/access.2023.3347035
12	CHEN S Y, LU L, LI M Y. Multi-state reliability demonstration tests[J]. Quality Engineering, 2017, 29 (3): 431- 445. doi: 10.1080/08982112.2017.1314493
13	杨政, 吴高龙, 郝顺义. 贝叶斯方法在代码转换器可靠性验证试验中的应用[J]. 系统工程与电子技术, 2007, 29 (8): 1402- 1404.
	YANG Z, WU G L, HAO S Y. Application of Bayesian method in reliability demonstration testing of code conversion equipment[J]. Systems Engineering and Electronics, 2007, 29 (8): 1402- 1404.
14	KLEYNER A, ELMORE D, BOUKAI B. A Bayesian approach to determine test sample size requirements for reliability demonstration retesting after product design change[J]. Quality Engineering, 2015, 27 (3): 289- 295. doi: 10.1080/08982112.2014.990035
15	GUIDA M, PULCINI G. Automotive reliability inference based on past data and technical knowledge[J]. Reliability Engineering & System Safety, 2002, 76 (2): 129- 137. doi: 10.1016/S0951-8320(01)00132-6
16	KLEYNER A, BHAGATH S, GASPARINI M, et al. Bayesian techniques to reduce the sample size in automotive electronics attribute testing[J]. Microelectronics and Reliability, 1997, 37 (6): 879- 883. doi: 10.1016/S0026-2714(96)00253-3
17	明志茂, 陶俊勇, 陈循, 等. 基于混合Beta分布的成败型产品Bayes可靠性鉴定试验方案研究[J]. 兵工学报, 2008, 29 (2): 204- 207. doi: 10.3321/j.issn:1000-1093.2008.02.016
	MING Z M, TAO J Y, CHEN X, et al. A Bayes plan of reliability qualification test based on the mixed beta distribution for success/failure product[J]. Acta Armamentarii, 2008, 29 (2): 204- 207. doi: 10.3321/j.issn:1000-1093.2008.02.016
18	FERNÁNDEZ A J, PEREZ-GONZÁLEZ C J, CARRIÓN-GARCÍA A, et al. Overdispersion effects on reliability test planning[J]. IEEE Trans. on Reliability, 2022, 72 (3): 1053- 1063. doi: 10.1109/tr.2022.3195055
19	ZHANG D, JIANG P, XING Y Y. A system reliability demonstration test design method based on subsystem test data[J]. Quality and Reliability Engineering International, 2025, 41 (1): 98- 112. doi: 10.1002/qre.3664
20	FERNÁNDEZ A J. Optimum lot inspection based on lognormal reliability tests[J]. International Journal of Production Research, 2023, 61 (5): 1424- 1435. doi: 10.1080/00207543.2022.2036852
21	KIM H, WILSON A G. Comparing risks for binomial reliability assurance test planning[J]. Applied Stochastic Models in Business and Industry, 2024, 41 (3): e2912. doi: 10.1002/asmb.2912
22	WILSON K J, FARROW M. Assurance for sample size determination in reliability demonstration testing[J]. Technometrics, 2021, 63 (4): 523- 535. doi: 10.1080/00401706.2020.1867646
23	LI M, ZHANG W, HU Q, et al. Design and risk evaluation of reliability demonstration test for hierarchical systems with multilevel information aggregation[J]. IEEE Trans. on Reliability, 2016, 66 (1): 135- 147. doi: 10.1109/tr.2016.2619689
24	FERNÁNDEZ A J. Planning reliability demonstration tests with limited expected risks[J]. Computers & Industrial Engineering, 2022, 165, 107918. doi: 10.1016/j.cie.2021.107918
25	赵勇, 刘建新, 牛青坡. 基于混合Beta先验分布的成败型产品的可靠性评估[J]. 航空兵器, 2014, 21 (6): 59- 61.
	ZHAO Y, LIU J X, NIU Q P. Reliability evaluation based on mixed Beta priori distribution in binomial case[J]. Aero Weaponry, 2014, 21 (6): 59- 61.
26	ZHANG Y, CHEN H, JIANG P, et al. Bayesian assessment for reliability of binomial components based on information fusion of similar products[J]. Journal of Donghua University （English Edition）, 2015, 32 (6): 940- 945.
27	杨军, 申丽娟, 黄金, 等. 利用相似产品信息的电子产品可靠性Bayes综合评估[J]. 航空学报, 2008, 29 (6): 1550- 1553.
	YANG J, SHEN L J, HUANG J, et al. Bayes comprehensive assessment of reliability for electronic products by using test information of similar products[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29 (6): 1550- 1553.
28	张立波, 王宏力, 陈聪, 等. 基于相似电子产品信息的可靠性评估方法[J]. 航天控制, 2012, 30 (3): 84- 87. doi: 10.3969/j.issn.1006-3242.2012.03.017
	ZHANG L B, WANG H L, CHEN C, et al. The method of reliability assessment for electronic products based on multiple similar samples[J]. Aerospace Control, 2012, 30 (3): 84- 87. doi: 10.3969/j.issn.1006-3242.2012.03.017
29	RUFO M J, MARTÍN J, PÉREZ C J. Bayesian analysis of finite mixture models of distributions from exponential families[J]. Computational Statistics, 2006, 21 (3/4): 621- 637. doi: 10.1007/s00180-006-0018-8
30	JIANG P, ZHAO Q, XIAO H, et al. A reliability demonstration test plan derivation method based on subsystem test data[J]. Computers & Industrial Engineering, 2022, 170, 108325. doi: 10.1016/j.cie.2022.108325
31	SONG Z L, ZHAO Q, JIANG P, et al. A numerical method for system residual life prediction based on simpson formula[J]. Communications in Statistics-Simulation and Computation, 2021, 50 (12): 4171- 4186. doi: 10.1080/03610918.2019.1642479

产品编号	失效间隔时间/h
A	13, 17, 23, 10, 39, 61, 16, 97, 144, 54, 100, 157, 22, 162, 46
B	83, 141, 35, 224, 88

α₀	β₀	T/h	C	α	β
0.1	0.1	761	10	0.090	0.099
0.1	0.1	820	11	0.075	0.099
0.1	0.1	879	12	0.063	0.099
0.1	0.1	937	13	0.043	0.099

α₀	β₀	T/h	C	α	β
0.2	0.2	329	4	0.176	0.199
0.2	0.2	388	5	0.140	0.198
0.2	0.2	445	6	0.111	0.199
0.2	0.2	503	7	0.090	0.198

α₀	β₀	T/h	C	α	β
0.3	0.3	119	1	0.286	0.297
0.3	0.3	176	2	0.209	0.299
0.3	0.3	232	3	0.157	0.299
0.3	0.3	288	4	0.120	0.297

T/h	C	$ {\alpha }_{0} $	$ {\beta }_{0} $	$ {\alpha }^{\prime} $	$ {\beta }^{\prime} $	$ \alpha $	$ \beta $
945	13	0.1	0.1	0.098	0.102	0.055	0.093
624	9	0.1	0.2	0.102	0.201	0.062	0.186
394	5	0.2	0.2	0.207	0.200	0.147	0.187
185	2	0.3	0.3	0.282	0.285	0.230	0.268

Bayes reliability demonstration of products based on priors from similar products

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 10

References 31

Related Articles 4

Recommended Articles

Metrics

Comments

双方风险	899A	本文方法	改进效果/%
$ {\alpha }_{0}=0.1,{\beta }_{0}=0.1 $	（945,13）	（761,10）	19.470
$ {\alpha }_{0}=0.1,{\beta }_{0}=0.2 $	（624,9）	（503,7）	19.391
$ {\alpha }_{0}=0.2,{\beta }_{0}=0.2 $	（394,5）	（329,4）	16.497
$ {\alpha }_{0}=0.3,{\beta }_{0}=0.3 $	（185,2）	（119,1）	35.675

[1]	Shengpeng ZHANG, Shuo HUANG, Ruyuan XU, Xiaobing MA. Storage life evaluation method for missile-borne products integrating information from design and testing [J]. Systems Engineering and Electronics, 2026, 48(3): 872-882.
[2]	Xiaoxiao LI, Chen ZHAI, Lili CHANG, Fangfang SHAO. Solution method for preventive maintenance strategy of multi-state components [J]. Systems Engineering and Electronics, 2026, 48(3): 962-969.
[3]	Jian CHU, Xing PAN, Lunhu HU, Jinpeng WEI, Zhenxiang LIU. Human-factor risk assessment of aviation support based on uncertain random Bow-tie model [J]. Systems Engineering and Electronics, 2025, 47(9): 3022-3030.
[4]	MA De-zhong,ZHOU Zhen,YU Xiao-yang,FAN Shang-chun,XING Wei-wei,GUO Zhan-she. Reliability analysis of multistate Bayesian networks based on fuzzy probability [J]. Journal of Systems Engineering and Electronics, 2012, 34(12): 2607-2611.