Mathematical modeling of software reliability testing with imperfect debugging

doi:10.1016/j.camwa.2010.03.011

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	Mathematical modeling of software reliability testing with imperfect debugging
	Cai, Kai-Yuan 1; Cao, Ping 2; Dong, Zhao3 ; Liu, Ke2
	2010-05-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	59 期号:10 页码:3245-3285
摘要	Software reliability testing is concerned with the quantitative relationship between software testing and software reliability. Our previous work develops a mathematically rigorous modeling framework for software reliability testing. However the modeling framework is confined to the case of perfect debugging, where detected defects are removed without introducing new defects. In this paper the modeling framework is extended to the case of imperfect debugging and two models are proposed. In the first model it is assumed that debugging is imperfect and may make the number of remaining defects reduce by one, remain intact, or increase by one. In the second model it is assumed that when the number of remaining defects reaches the upper bound, the probability that the number of remaining defects is increased by one by debugging is zero. The expected behaviors of the cumulative number of observed failures and the number of remaining defects in the first model show that the software testing process may induce a linear or nonlinear dynamic system, depending on the relationship between the probability of debugging introducing a new defect and that of debugging removing a detected defect. The second-order behaviors of the first model also show that in the case of imperfect debugging, although there may be unbiased estimator for the initial number of defects remaining in the software under test, the cumulative number of observed failures and the current number of remaining defects are not sufficient for precisely estimating the initial number of remaining defects. This is because the variance of the unbiased estimator approaches a non-zero constant as the software testing process proceeds. This may be treated as an intrinsic principle of uncertainty for software testing. The expected behaviors of the cumulative number of observed failures and the number of remaining defects in the second model show that the software testing process may induce a nonlinear dynamic system. However theoretical analysis and simulation results show that, if defects are more often removed from than introduced into the software under test, the expected behaviors of the two models tend to coincide with each other as the upper bound of the number of remaining defects approaches infinity. (C) 2010 Elsevier Ltd. All rights reserved.
关键词	Software testing Software reliability Imperfect debugging The principle of uncertainty Markovian property
DOI	10.1016/j.camwa.2010.03.011
语种	英语
资助项目	Natural Science Foundation of China[60633010] ; Natural Science Foundation of China[6398100] ; Natural Science Foundation of China[70731003] ; Natural Science Foundation of China[70971125] ; Science Fund for Creative Research Groups[10721101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000278629700003
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10284
专题	应用数学研究所
通讯作者	Cai, Kai-Yuan
作者单位	1.Beijing Univ Aeronaut & Astronaut, Dept Automat Control, Beijing 100191, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Appl Math, MADIS, Beijing 100190, Peoples R China 3.Chinese Acad Sci, AMSS, Inst Appl Math, Lab Random Complex Struct & Data Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Cai, Kai-Yuan,Cao, Ping,Dong, Zhao,et al. Mathematical modeling of software reliability testing with imperfect debugging[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2010,59(10):3245-3285.
APA	Cai, Kai-Yuan,Cao, Ping,Dong, Zhao,&Liu, Ke.(2010).Mathematical modeling of software reliability testing with imperfect debugging.COMPUTERS & MATHEMATICS WITH APPLICATIONS,59(10),3245-3285.
MLA	Cai, Kai-Yuan,et al."Mathematical modeling of software reliability testing with imperfect debugging".COMPUTERS & MATHEMATICS WITH APPLICATIONS 59.10(2010):3245-3285.