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

Abstract

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

CLC Number:

TB114.3

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.

Figures/Tables 11

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References 27

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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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Software reliability growth model based on nonlinearity and test coverage

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周	累计故障数目
1	2
2	13
3	15
4	19
5	22
6	23
7	24
8	26
9	30
10	30
11	34
12	35
13	38
14	38