相关向量机软件可靠性建模中失效数据选择

doi:10.11959/j.issn.1000-0801.2015192

摘要/Abstract

摘要：

摘要：基于核函数的软件可靠性模型一般对软件失效时间数据与发生在其之前的m次失效时间数据的关系进行建模，着重研究了m取值不同时，其对核函数可靠性模型预测能力的影响。在5个不同类型失效数据集上，采用Mann-Kendall检验观测到m值增大时模型预测能力逐渐下降，说明现时失效时间数据能比较久之前观测的失效时间数据更好地用于预测未来，通过把m的取值划分成几个区间，运用配对T检验进行实验研究，结果表明当m∈｛6,7,8,9,10｝时，模型能够得到最好的预测性能。

Abstract:

The high complexity of software is the major contributing factor of software reliability problems, and traditional parametric models may exhibit different predictive capabilities among different software projects, it is hard to select a suitable model for every software projects. Compared to traditional models, kernel based models could achieve better prediction accuracy, and had arouse the interesting of many researchers. The RVM learning scheme was applied to model the failure time data so as to capture the inner correlation between software failure time data and the m nearest failure time data. In addition, the trend of predictive accuracy with the varying of m was detected by way of Mann-Kendall test method. Thereupon, the reasonable value range of m was achieved,thus m∈｛6,7,8,9,10｝ through paired T-test in 5 common used software failure data.

Key words: software reliability predicting model, relevance vector machine, kernel function, software failure data, Mann-Kendall test

杨小明,楼俊钢,沈张果,胡文军. 相关向量机软件可靠性建模中失效数据选择[J]. 电信科学, 2015, 31(9): 90-96.

Xiaoming Yang,Jungang Lou,Zhangguo Shen,Wenjun Hu. Selection of Failure Data in Software Reliability Modeling Based on RVM[J]. Telecommunications Science, 2015, 31(9): 90-96.

图/表 8

图1

表1

图2

表2

表3

数据集1～数据集5上m值不同时模型单步预测值"

m	r		数据集1			数据集2			数据集3			数据集4			数据集5
m	r	1	3.8	10	1	3.1	10	1	5.6	10	1	1.9	10	1	4.4	10
	6	3.78	0.92	2.12	2.58	2.02	4.45	8.34	4.34	10.31	2.45	0.82	1.32	8.94	4.60	10.26
	7	3.58	1.64	1.86	2.24	2.12	4.22	7.78	4.53	10.89	1.78	0.29	1.43	8.89	4.36	10.32
	8	3.30	1.11	4.03	2.67	2.04	4.11	8.93	3.96	9.24	2.37	1.21	2.51	8.67	4.11	11.18
	9	4.23	0.87	1.98	2.94	2.09	5.08	8.88	4.73	10.72	2.34	0.65	1.64	9.76	5.03	11.40
	10	4.49	1.39	2.25	3.12	2.12	4.24	9.11	5.01	10.64	1.93	0.82	1.89	10.25	5.24	12.14
	11	5.03	2.01	2.87	3.06	2.03	5.00	10.19	4.99	11.32	2.94	0.76	1.73	10.08	5.09	11.81
	12	4.93	1.83	2.99	2.98	2.21	5.17	12.21	5.03	12.43	3.03	0.79	1.83	10.22	5.19	12.05
	13	5.22	2.12	3.00	3.17	2.04	4.42	11.79	5.25	12.65	1.68	0.45	1.99	10.46	5.21	12.45
	14	5.34	2.02	3.08	2.79	1.75	4.11	12.02	5.32	12.18	2.87	0.84	2.04	9.86	4.54	11.90
	15	4.35	2.05	2.85	2.65	2.53	5.53	11.98	4.96	12.01	3.24	1.03	2.16	10.14	5.18	12.30
	16	3.83	2.09	2.68	3.14	3.23	5.35	12.15	5.11	12.67	3.47	0.96	2.54	11.48	6.37	14.02
	17	4.34	2.13	2.21	3.45	2.36	4.76	11.99	5.26	12.84	3.59	1.10	2.64	11.07	5.81	13.71
	18	3.13	2.22	1.83	4.02	2.07	5.09	11.26	4.72	13.11	4.23	1.12	2.74	10.81	6.09	13.55
	19	4.87	2.21	1.98	2.42	1.65	4.87	12.09	5.04	12.98	3.62	1.19	1.85	9.11	4.07	10.96
	20	4.73	1.96	2.23	3.65	2.23	5.23	11.37	4.87	12.56	3.86	1.01	3.18	10.75	5.88	13.93
	21	3.43	2.25	2.84	3.85	2.25	5.53	12.17	5.25	9.74	4.14	1.24	3.28	11.35	6.10	14.63
	22	5.67	2.32	3.12	3.79	2.35	6.25	12.43	6.02	12.86	4.35	1.03	3.46	12.16	6.14	15.62
	23	5.99	2.20	2.99	3.68	2.53	5.23	12.53	6.15	13.10	4.86	1.18	3.22	12.36	6.21	15.58
	24	6.21	2.40	3.34	2.34	2.06	5.46	12.36	6.35	12.02	4.53	1.14	3.31	10.75	4.40	14.06
	25	6.24	2.41	3.49	3.43	2.38	5.43	13.02	6.12	13.14	6.15	0.98	2.96	11.93	5.81	14.89
	26	3.53	2.27	3.24	3.66	2.57	4.89	12.26	5.53	13.21	4.84	1.25	3.29	11.76	6.23	15.05
	27	5.98	2.29	4.00	3.98	2.89	5.22	12.46	6.00	20.56	5.94	1.43	3.52	12.87	6.87	16.39
	28	5.69	2.42	4.15	2.24	2.03	5.57	12.64	6.43	12.99	5.62	0.87	3.19	10.74	4.27	13.89
	29	6.32	2.36	5.04	4.15	3.31	6.19	13.09	7.24	12.53	5.43	0.99	2.90	14.70	7.46	17.60
	30	5.31	2.17	8.21	4.37	2.26	7.23	12.59	7.34	14.17	5.48	1.11	2.53	13.97	6.63	16.50

表3

图3

表4

表5

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数据集	代码行数	失效数	软件系统类型
数据集1	21 700	136	实时命令控制系统
数据集2	10 000	118	飞行器控制软件
数据集3	35 000	279	硬件控制系统
数据集4	870000	535	实时控制系统
数据集5	200000	481	监控及实时控制系统

数据集	r	Z统计量	解释
	1	2.872 7	上升
数据集1	3.8	5.021 3	上升
	10	3.479 9	上升
	1	2.989 4	上升
数据集2	3.1	2.499 0	上升
	10	2.805 4	上升
	1	4.719 0	上升
数据集3	5.6	4.857 8	上升
	10	4.133 8	上升
	1	5.722 0	上升
数据集4	1.9	3.012 8	上升
	10	4.414 1	上升
	1	4.530 9	上升
数据集5	4.4	3.269 7	上升
	10	5.161 4	上升

配对	平均值	T统计量	Sig.（双边）	性能比较
pair 1 ｛A｝→｛B｝	-0.542 07	-7.460	0.048	｛A｝＞｛B｝
pair 2 ｛A｝→｛C｝	-0.906 20	-10.409	0.009	｛A｝＞｛C｝
pair 3 ｛A｝→｛D｝	-1.506 00	-14.866	0.002	｛A｝＞｛D｝
pair 4 ｛A｝→｛E｝	-2.083 00	-16.327	0.007	｛A｝＞｛E｝
pair 5 ｛B｝→｛C｝	-0.364 13	-5.609	0.004	｛B｝＞｛C｝
pair 6 ｛B｝→｛D｝	-0.963 93	-11.960	0.010	｛B｝＞｛D｝
pair 7 ｛B｝→｛E｝	-1.540 93	-12.951	0.010	｛B｝＞｛E｝
pair 8 ｛C｝→｛D｝	-0.599 80	-8.812	0.009	｛C｝＞｛D｝
pair 9 ｛C｝→｛E｝	-1.176 80	-9.999	0.005	｛C｝＞｛E｝
pair 10 ｛D｝→｛E｝	-0.577 00	-5.811	0.026	｛D｝＞｛E｝

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