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

摘要/Abstract

摘要：

在备品备件库存决策问题中，对设备失效概率进行预测是解决问题的关键。当设备故障分布类型在参数模型框架下难以确定时，采用基于Dirichlet分布的非参数贝叶斯方法，对设备失效概率进行建模，并利用蒙特卡罗方法进行模拟仿真。由于未假定故障分布的参数模型，该方法具有很强的灵活性；对样本数据进行随机抽样后进行仿真和对比分析，预测结果波动很小，表明了该方法具有很强的稳健性。基于Dirichlet分布的模型可以解决在参数模型框架下故障分布类型难以确定时，对设备失效概率进行预测的问题。

关键词: 备件, Dirichlet分布, 蒙特卡罗方法, 概率预测

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

中图分类号:

O213.2

蒋铁军, 王俊柯. 基于Dirichlet分布的设备失效概率预测模型[J]. 系统工程与电子技术, 2023, 45(4): 1239-1246.

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

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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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