针对现有测试性增长模型忽略了测试性设计缺陷的修正延时过程，进而导致测试性增长模型（TGM）跟踪与预计精度低的问题，提出了一种考虑测试性设计缺陷修正延时的测试性增长模型建模理论与方法。首先分析测试性设计缺陷识别与修正之间的延时机理，得到剩余测试性设计缺陷（TDL）具有先增后减的铃形变化趋势；在此基础上，分别以Gamma、Raleigh和Delay-S 3种曲线拟合剩余测试性设计缺陷（RTDL）变化趋势，研究建立基于以上3种曲线考虑修正延时的测试性增长模型；最后，以某机载稳定跟踪平台测试性增长试验数据验证测试性增长模型拟合、跟踪及预计效能。研究结果表明：基于该测试性增长试验数据，Gamma曲线可以精确地拟合剩余测试性设计缺陷变化规律，测试性增长模型跟踪和预计精度可达到10-2数量级。
For existing testability growth models ignores the rectifying process of testability design limitations, causes the testability growth process describes incompletely, and the tracking and projecting imprecise, a Testability Growth Model (TGM) which considers the rectifying delay based on Bell-shaped curve are proposed. Firstly, the mechanism relation between the discovering process of Testability Design Limitation (TDL) and the rectifying process of TDL is analyzed. And on the basis, three bell-shaped curves are used to describe the variation tendency of remaining testability design limitations, the three bell-shaped curves are Rayleigh curve and Delay-S curve, then, TGMs which consider bell-shaped TDL rectifying delay process are founded. Finally, a data set is used to verify the fitting, estimation and prediction of TGM. Result shows that:Gamma curve is more accurate to fit the number of Remaining Testability Design Limitation (RTDL) and that TGM considering the rectifying delay can give good result in fitting, estimation and prediction, and the accuracy of estimation can reach 10-2 order of magnitude.
[1] 全国量和单位标准化技术委员会.装备测试大纲:GJB2547-1995[S].北京:中国标准出版社, 1995:68-108. National Technical Committee on Quantity and Unit Standardization. Testability program for materiel:GJB2547-1995[S]. Beijing:Standards Press of China, 1995:68-108(in Chinese).
[2] 田仲, 石君友.系统测试性设计分析与验证[M].北京:北京航空航天大学出版社,2003:361-396. TIAN Z, SHI J Y. Design,analysis and demonstration of system testability[M]. Beijing:Beihang University Press, 2003:361-396(in Chinese).
[3] LI T M, XU C Q, QIU J, et al. The assessment and foundation of bell-shaped testability growth effort functions dependent system testability growth models based on NHPP[J]. Mathematical Problems in Engineering, 2015,27(1):1-18.
[4] ZHAO C X, QIU J, LIU G J, et al. A testability growth model and its application[C]//IEEE Autotestcon. Piscataway, NJ:IEEE Press, 2014:121-128.
[5] ZHAO C X, KRISHINA P, LIU G J, et al. A Markov Chain-based testability growth model with a cost-benefit function[J]. IEEE Transactions on Systems, Man and Cybernetics:Systems, 2016, 46(4):524-534.
[6] SCHNEIDEWIND N. Modeling the fault correction process[C]//Proceddings of the 12th International Conference on Software Reliability Engineering, 2001:185-190.
[7] PHAM H, ZHANG X M. NHPP software reliability and cost models with testing coverage[J].European Journal of Operational Research, 2003, 145(6):443-454.
[8] 舒艳君. 故障检测与修正过程的NHPP类软件可靠性增长模型研究[D].哈尔滨:哈尔滨工业大学, 2009:50-102. SHU Y J. Research on NHPP software reliability growth models of fault detection and correction processes[D]. Harbin:Harbin Institute of Technology, 2009:50-102(in Chinese).
[9] PHAM H, NORDMANN L, ZHANG X M. A general imperfect software debugging model with s-shaped fault-detection rate[J]. IEEE Transaction on Power Systems, 1999, 48(2):169-176.
[10] LI Q Y, LI H F, LU M Y, et al. Software reliability growth model with s-shaped testing effort function[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011,37(2):149-160.
[11] PHAM H, ZHANG X M. NHPP software reliability and cost models with testing coverage[J].European Journal of Operational Research, 2003, 145(8):443-454.
[12] PHAM H. Software reliability and cost models:Perspectives, comparison and practice[J]. European Journal of Operational Research, 2003,149(6):475-489.
[13] PENG R, LI Y F, ZHANG W J, et al. Testing effort dependent software reliability model for imperfect debugging considering both detection and correction[J].Reliability Engineering and System Safety,2014, 126(4):37-43.
[14] KAPUR P K, PHAM H, GUPTA A, et al. Software reliability assessment with applications[M]. London:Springer-Verlag, 2011:315-386.
[15] HUANG C, LIN C. Software reliability analysis by considering fault dependency and debugging time lag[J]. IEEE Transaction on Reliability, 2006, 55(3):436-450.
CJA