基于Dirichlet分布的设备失效概率预测模型

doi:10.12305/j.issn.1001-506X.2023.04.34

Abstract

Abstract:

The prediction of equipment failure probability is the key to solve the problem of spare parts inventory decision. When it is difficult to determine the type of equipment fault distribution under the framework of parameter model, the non-parametric Bayesian method based on Dirichlet distribution is used to model the equipment failure probability, and Monte Carlo method is used to simulate. Since no parametric model of fault distribution is assumed, this method has strong flexibility. After random sampling of sample data, simulation and comparative analysis show that the fluctuation of prediction results is very small, which shows that the method has strong robustness.The model based on Dirichlet distribution can solve the problem of predicting equipment failure probability when the fault distribution type is difficult to determine under the framework of parameter model.

Key words: spare parts, Dirichlet distribution, Monte Carlo method, probability prediction

CLC Number:

O213.2

Tiejun JIANG, Junke WANG. Equipment failure probability prediction model based on Dirichlet distribution[J]. Systems Engineering and Electronics, 2023, 45(4): 1239-1246.

Figures/Tables 9

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Table 2

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Table 5

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References 32

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时间区间	工作时间
(0, 1]	—	—	—	—	—	—
(1, 2]	—	—	—	—	—	—
(2, 3]	2.1	2.4	2.6	—	—	—
(3, 4]	3.3	3.8	—	—	—	—
(4, 5]	4.3	4.6	4.9	—	—	—
(5, 6]	5.1	5.4	5.5	5.6	5.8	—
(6, 7]	6.3	6.5	6.6	6.9	—	—
(7, 8]	7.1	7.2	7.2	7.5	7.6	7.8
(7, 8]	7.9	—	—	—	—	—
(8, 9]	8.2	8.4	8.8	8.9	8.9	—
(9, 10]	9.2	9.2	9.5	9.8	—	—
(10, 11]	10.1	10.3	10.3	10.4	10.6	10.8
(10, 11]	10.8	10.9	—	—	—	—
(11, 12]	11.1	11.1	11.3	11.3	11.3	11.5
	11.5	11.5	11.6	11.6	11.7	11.8
	11.8	11.9	11.9	—	—	—
(12, 13]	12.3	12.4	12.7	12.7	—	—
(13, 14]	13.1	13.2	13.2	13.2	13.2	13.2
	13.5	13.5	13.6	13.6	13.7	13.7
	13.7	13.8	13.8	13.8	13.8	13.9
	13.9	13.9	—	—	—	—
(14, 15]	14.2	14.3	14.3	14.3	14.5	14.5
	14.5	14.5	14.6	14.6	14.7	14.7
	14.7	14.8	14.8	14.8	14.9	—
(15, 16]	15.4	15.7	15.7	15.8	—	—
(16, 17]	16.1	16.2	16.3	16.3	16.4	16.4
	16.5	16.5	16.5	16.6	16.6	16.7
	16.8	16.9	16.9	16.9	—	—
(17, 18]	17.2	17.2	17.3	17.3	17.4	17.4
	17.6	17.6	17.6	17.7	17.7	17.7
	17.8	17.8	17.8	17.9	17.9	17.9
(18, 19]	18.1	18.3	18.4	18.5	18.6	18.6
(18, 19]	18.7	18.8	18.9	18.9	—	—
(19, 20]	19.1	19.2	19.2	19.2	19.2	19.3
	19.3	19.3	19.4	19.4	19.5	19.5
	19.5	19.5	19.6	19.6	19.6	19.7
	19.7	19.8	19.8	19.8	19.9	20
	20	—	—	—	—	—

拟合优度检验	P值	拟合优度检验	P值
正态	< 0.005	最小极值	< 0.010
Box-Cox变换	< 0.005	最大极值	< 0.010
对数正态	< 0.005	Gamma	< 0.005
3参数对数正态	—	3参数Gamma	—
指数	< 0.003	Logistic	< 0.005
2参数指数	< 0.010	对数Logistic	< 0.005
Weibull	< 0.010	3参数对数Logistic	—
3参数Weibull	< 0.005	Johnson变换	0.339

时间	概率	时间	概率
1	0.002 777 778	11	0.047 222 222
2	0.002 777 778	12	0.086 111 111
3	0.019 444 444	13	0.025 000 000
4	0.013 888 889	14	0.113 888 889
5	0.019 444 444	15	0.097 222 222
6	0.030 555 556	16	0.025 000 000
7	0.025 000 000	17	0.091 666 667
8	0.041 666 667	18	0.102 777 778
9	0.030 555 556	19	0.058 333 333
10	0.025 000 000	20	0.141 666 667

更新次数	概率	累积概率
0	0.082 483 550	0.082 483 550
1	0.311 646 600	0.394 130 150
2	0.369 089 200	0.763 219 350
3	0.184 948 200	0.948 167 550
4	0.045 492 020	0.993 659 570
5	0.005 901 182	0.999 560 752≈1

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[15]	ZHANG Xinbo, WANG Naichao, XIAO Boping, MA Lin给出了综合考虑系统结构、库存备件量和故障件维修周转等因素影响下的系统可用度计算模型。将由并串混联系统和备件组成的广义系统按功能划分为工作系统与库存系统两个子系统, 通过引入备件平均到达率反映库存系统对工作系统的影响, 并据此分别建立备件充足与缺货时的工作系统状态转移关系。利用二项分布表征期望备件短缺数的概率分布函数以计算库存系统备件的缺货概率, 进而根据全概率公式计算得到系统可用度。示例表明:所提模型针对单部件串联系统所得结果比已有模型更为精确, 其次, 在库存备件量及维修周转时间的影响下, 多部件子系统串联时并不比单部件串联时的可用度高, 且可用度曲线随着库存量的增加并不是严格单调递增的凸曲线。. Availability modeling of parallel-series system under influence of spare parts and maintenance turnover [J]. Systems Engineering and Electronics, 2019, 41(1): 223-228.

Equipment failure probability prediction model based on Dirichlet distribution

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时间	失效次数	时间	失效次数
1	0	11	8
2	0	12	15
3	3	13	4
4	2	14	20
5	3	15	17
6	5	16	4
7	4	17	16
8	7	18	18
9	5	19	10
10	4	20	25