基于非线性和测试覆盖率的软件可靠性增长模型

doi:10.3969/j.issn.1001-506X.2020.02.29

摘要/Abstract

摘要：

软件可靠性增长模型一般假设故障是独立的,且检测到的故障能够被排除。但在工程中,一些检测到的故障可能无法排除,在排除过程中也可能会引入新的故障。考虑上述因素,本文假设故障的引入过程与时间呈现非线性关系,通过测试覆盖率函数来表示软件故障检测率,建立了基于非齐次泊松过程(non-homogeneous Poisson process, NHPP)的软件可靠性增长模型。为规避参数估计过程中模型函数导数连续性和存在性的限制,应用一个自适应变化的实值遗传算法进行计算。最后通过一个真实软件失效数据集对模型参数进行计算,利用不同的评价准则将所提模型和现有模型进行比较,说明所提模型的优越性和准确性。

关键词: 测试覆盖率, 不完美调试, 非线性, 可靠性增长模型

Abstract:

Generally, it is assumed in the software reliability growth model that the fault is independent. When a fault is detected, it can be eliminated. But in engineering, some detected faults can not be eliminated and new faults may be introduced during the elimination process. In this paper, a model based on a non-homogeneous Poisson process (NHPP) is proposed. It is assumed that the fault introduction process has a nonlinear relationship with time. The software failure detection rate is based on the testing coverage. To avoid the restriction on continuity and existence of model function derivative, an adaptive change real-valued genetic algorithm is applied to calculation in this paper. Finally, the model parameters are calculated through a set of real software failure data. The performance of the proposed model is compared with several existing NHPP SRGMs based on several criteria. The superiority and accuracy of the proposed model are discussed.

Key words: test coverage, imperfect debugging, nonlinear, reliability growth model

中图分类号:

TB114.3

徐如远, 袁宏杰, 王乾元. 基于非线性和测试覆盖率的软件可靠性增长模型[J]. 系统工程与电子技术, 2020, 42(2): 473-479.

Ruyuan XU, Hongjie YUAN, Qianyuan WANG. Software reliability growth model based on nonlinearity and test coverage[J]. Systems Engineering and Electronics, 2020, 42(2): 473-479.

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模型名称	均值函数
G-O模型	m(t)=a(1-e^-bt)
Yamada不完美调试模型-1	$ m(t)=\frac{a b}{\alpha+b}\left(\mathrm{e}^{\alpha t}-\mathrm{e}^{-b t}\right)$
Zhang-Teng Pham模型	$ m(t)=\frac{\alpha}{p-\beta}\left\{1-\left(\frac{(1+\alpha) \mathrm{e}^{-b t}}{1+\alpha \mathrm{e}^{-b t}}\right) \frac{c}{b}(p-\beta)\right\}$
Teng-Pham模型	$ m(t)=\frac{a}{p-q}\left\{1-\left(\frac{\beta}{\beta+(p-q) \ln \left(\frac{c+\mathrm{e}^{b t}}{c+1}\right)}\right)^{\alpha}\right\}$
R-M-D模型	$ m(t)=a \alpha\left(1-\mathrm{e}^{-b t}\right)-\frac{a b}{b-\beta}\left(\mathrm{e}^{-\beta}-\mathrm{e}^{-b t}\right)$
V形浴盆故障检测率模型	$ m(t)=N\left(1-\left(\frac{\beta}{\beta+a t^{b}-1}\right)^{\alpha}\right)$
Chang模型	$ m(t)=N\left(1-\left(\frac{\beta}{\beta+(a t)^{b}}\right)^{\alpha}\right)$
本文模型	$ m(t)=\mathrm{e}^{-p t^{r}} \int_{0}^{t} \operatorname{prt}^{r-1} a\left(1+\alpha t^{d}\right) \mathrm{e}^{p t^{r}} d \tau$

模型名称	模型参数	MSE	SSE	AIC	PRR	PP
G-O模型	$ \hat{a}=46.14, \hat{b}=0.118$	3.63	43.56	62.83	0.528	2.574
Yamada不完美调试模型-1	$ \hat{a}=22.42, \hat{b}=0.312, \hat{\alpha}=0.05$	2.91	32.06	64.87	0.505	4.37
Zhang-Teng Pham模型	$ \begin{aligned} &\hat{a}=25.24, \hat{b}=7.94 e-6, \hat{c}=0.22\\ &\hat{\alpha}=2.7 \mathrm{e}-6, \hat{\beta}=0.3616, \hat{p}=0.91 \end{aligned}$	5.45	43.6	70.83	0.528	2.57
Teng-Pham模型	$ \hat{a}=78.53, \hat{b}=0.3843, \hat{c}=3.19 \mathrm{e}-8 $ $\hat{\alpha}=0.06, \hat{\beta}=0.291, \hat{p}=0.85, \hat{q}=0.67 $	5.25	36.75	72.7	0.513	3.57
R-M-D模型	$ \hat{a}=473.9, \hat{b}=0.389, \hat{\alpha}=1.038, \hat{\beta}=0.004$	3.287	32.87	66.8	0.512	4.28
V形浴盆故障检测率模型	$ \hat{a}=91.14, \hat{b}=0.5612, \hat{\alpha}=0.04$ $ \hat{\beta}=21.95, \hat{N}=74.0356$	3.772	33.95	201	0.44	2.1
Chang模型	$ \hat{a}=0.3318, \hat{b}=1.11, \hat{N}=584$ $\hat{\alpha}=0.035, \hat{\beta}=0.96 $	4.054	36.49	355.24	0.49	2.99
本文模型	$ \hat{a}=12.93, \hat{\alpha}=0.127, \hat{r}=2.186$ $ \hat{d}=1.047, \hat{p}=0.281$	1.78	16.04	62.77	0.22	0.55

θ	-20%	-10%	10%	20%
S_{β_c}	-0.156	-0.072	-0.050	-0.065
S_{β_m}	-0.046	-0.103	-0.025	-0.056
S_{n_c}	-0.242	-0.252	-0.124	-0.205
S_{n_m}	-0.221	-0.158	-0.096	-0.127
S_{p_c⁰}	-0.205	-0.211	-0.087	-0.183
S_{p_m⁰}	-0.190	0.084	-0.118	-0.096
S_b	0.090	-0.112	-0.239	-0.158
S_T₀	-0.059	0.006	-0.046	-0.087

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