Weibull分布引进故障的软件可靠性增长模型
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摘要
软件调试是复杂过程,可能会受到很多种因素的影响,例如调试资源分配、调试工具的使用情况、调试技巧等.在软件调试过程中,当检测到的故障被去除时,新的故障可能会被引进.因此,研究故障引进的现象对建立高质量的软件可靠性增长模型具有重要意义.但是到目前为止,模拟故障引进过程仍是一个复杂和困难的问题.虽然有许多研究者开发了一些不完美调试的软件可靠性增长模型,但是一般都是假设故障内容(总数)函数为线性、指数分布或者是与故障去除的数量成正比.这个假设与实际的软件调试过程中故障引进情况并不完全一致.提出一种基于Weibull分布引进故障的软件可靠性增长模型,考虑故障内容(总数)函数服从Weibull分布,并用相关的实验验证了提出的模型的拟合和预测性能.在用两个故障数据集进行的模拟实验中,实验结果指出:提出的模型和其他模型相比,有更好的拟合和预测性能以及更好的鲁棒性.
Software debugging is a complex process and affected by many factors, such as debugging resources, debugging tools,debugging skills, etc. When detected faults were removed, new faults may be introduced. Therefore, it plays an important role to research an imperfect debugging phenomenon in the software debugging process. How to model fault introduction in building an imperfect debugging model is still an unresolved issue. So far, numerous software debugging models are developed by researchers, for example,assuming the fault content function is a linear, exponential distribution or proportional to the number of removed faults, etc. However,they can not entirely satisfy the realistic needs due to fault introduction complicated changes over time. In this study, an NHPP software reliability model is proposed based on Weibull distribution introduced faults and the fault content function following Weibull distribution is considered. The related experiment is carried out which validates the fitting and predictive power of the proposed model. The experimental results also show the proposed model has much better fitting and predictive performance than other models using two fault data sets, as well as better robustness.
Software debugging is a complex process and affected by many factors, such as debugging resources, debugging tools,debugging skills, etc. When detected faults were removed, new faults may be introduced. Therefore, it plays an important role to research an imperfect debugging phenomenon in the software debugging process. How to model fault introduction in building an imperfect debugging model is still an unresolved issue. So far, numerous software debugging models are developed by researchers, for example,assuming the fault content function is a linear, exponential distribution or proportional to the number of removed faults, etc. However,they can not entirely satisfy the realistic needs due to fault introduction complicated changes over time. In this study, an NHPP software reliability model is proposed based on Weibull distribution introduced faults and the fault content function following Weibull distribution is considered. The related experiment is carried out which validates the fitting and predictive power of the proposed model. The experimental results also show the proposed model has much better fitting and predictive performance than other models using two fault data sets, as well as better robustness.
引文
[1]Goel AL.Software reliability models:Assumptions,limitations and applicability.IEEE Trans.on Software Engineering,1985,SE-11:1411-1423.
[2]Ohba M,Chou XM.Does imperfect debugging effect software reliability growth.In:Proc.of the 11th Int’l Conf.of Software Engineering.1989.237-244.
[3]Kapur PK,Garg RB.Optimal software release policies for software reliability growth model under imperfect debugging.RAIRO,1990,24:295-305.
[4]Pham H,Nordmann L,Zhang X.A general Imperfect software debugging model with S-shaped fault detection rate.IEEE Trans.on Reliability,1999,R-48(2):169-175.
[5]Pham H.A software cost model with imperfect debugging,random life cycle and penalty cost.Int’l Journal of Systems Science,1996,27(5):455-463.
[6]Zhang X,Teng X,Pham H.Considering fault removal efficiency in software reliability assessment.IEEE Trans.on Systems,Man,and Cybernetics-Part A:Systems and Humans,2003,33(1):2241-2252.
[7]Kapur PK,Gupta D,Gupta A,Jha PC.Effect of introduction of faults and imperfect debugging on release time.Ratio Mathematica,2008,18:62-90.
[8]Kapur PK,Pham H,Anand S,Yadav K.A unified approach for developing software reliability growth models in the presence of imperfect debugging and error generation.IEEE Trans.on Reliability,2011,60(1):331-340.
[9]Wang JY,Wu ZB,Shu YJ,Zhang Z.A general imperfect software debugging model considering the nonlinear process of fault introduction.In:Proc.of the 14th Int’l Conf.on Quality Software(QSIC).2014.222-227.
[10]Wang JY,Wu ZB.Study of the nonlinear imperfect software debugging model.Reliability Engineering&System Safety,2016,153:180-192.
[11]Wang JY,Wu ZB,Shu YJ,Zhang Z.An imperfect software debugging model considering log-logistic distribution fault content function.Journal of Systems and Software,2015,100:167-181.
[12]Wang JY,Wu ZB,Shu YJ,Zhang Z.Software reliability model with irregular changes of fault detection rate.Ruan Jian Xue Bao/Journal of Software,2015,26(10):2465-2484(in Chinese with English abstract).http://www.jos.org.cn/1000-9825/4746.htm[doi:10.13328/j.cnki.jos.004746]
[13]Xie JY,An JX,Zhu JH.NHPP software reliability growth model considering imperfect debugging.Ruan Jian Xue Bao/Journal of Software,2010,21(5):942-949(in Chinese with English abstract).http://www.jos.org.cn/1000-9825/3539.htm[doi:10.3724/SP.J.1001.2010.03539]
[14]Yin Q,Li J,Bom KH,Guo P.A new cascade software reliability model.In:Proc.of the 3rd Int’l Conf.on Natural Computation(ICNC 2007).IEEE Press,2007.241-245.
[15]Yamada S,Tokuno K,Osaki S.Imperfect debugging models with fault introduction rate for software reliability assessment.Int’l Journal of System Science,1992,23(12):2253-2264.
[16]Pham H,Zhang X.An NHPP software reliability models and its comparison.Int’l Journal of Reliability,Quality and Safety Engineering,1997,4(3):269-282.
[17]Goel AL,Okumoto K.Time dependent error detection rate model for software reliability and other performance measures.IEEETrans.on Reliability,1979,R-28(3):206-211.
[18]Yamada S,Ohba M,Osaki S.S-shaped reliability growth modeling for software error detection.IEEE Trans.on Reliability,1983,32:475-484.
[19]Ohba M.Inflection S-shaped software reliability growth models.In:Osaki S,Hatoyama Y,ed.Proc.of the Stochastic Models in Reliability Theory.Berlin:Springer-Verlag,1984.144-162.
[20]Pham H.System Software Reliability.London:Springer-Verlag,2006.
[21]Sharma K,Garg R,Nagpal CK,Garg RK.Selection of optimal software reliability growth models using a distance based approach.IEEE Trans.on Reliability,2010,59(2):266-276.
[22]Tohma Y,Jacoby R,Murata Y,Yamamoto M.Hyper-geometric distribution model to estimate the number of residual software faults.In:Proc.of the COMPSAC’89.1989.610-617.
[23]Misra PN.Software reliability analysis.IBM Systems Journal,1986,22(3):262-270.
[24]Musa JD.Software Reliability Data,Cyber Security and Information Systems Information Analysis Center.1980.
[25]Li X,Xie M,Ng SH.Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points.Applied Mathematical Modelling,2010,34:560-3570.
[12]王金勇,吴智博,舒燕君,张展.故障检测率不规则变化的软件可靠性模型.软件学报,2015,26(10):2465-2484.http://www.jos.org.cn/1000-9825/4746.htm[doi:10.13328/j.cnki.jos.004746]
[13]谢景燕,安金霞,朱纪洪.考虑不完美排错情况的NHPP类软件可靠性增长模型.软件学报,2010,21(5):942-949.http://www.jos.org.cn/1000-9825/3539.htm[doi:10.3724/SP.J.1001.2010.03539]
[2]Ohba M,Chou XM.Does imperfect debugging effect software reliability growth.In:Proc.of the 11th Int’l Conf.of Software Engineering.1989.237-244.
[3]Kapur PK,Garg RB.Optimal software release policies for software reliability growth model under imperfect debugging.RAIRO,1990,24:295-305.
[4]Pham H,Nordmann L,Zhang X.A general Imperfect software debugging model with S-shaped fault detection rate.IEEE Trans.on Reliability,1999,R-48(2):169-175.
[5]Pham H.A software cost model with imperfect debugging,random life cycle and penalty cost.Int’l Journal of Systems Science,1996,27(5):455-463.
[6]Zhang X,Teng X,Pham H.Considering fault removal efficiency in software reliability assessment.IEEE Trans.on Systems,Man,and Cybernetics-Part A:Systems and Humans,2003,33(1):2241-2252.
[7]Kapur PK,Gupta D,Gupta A,Jha PC.Effect of introduction of faults and imperfect debugging on release time.Ratio Mathematica,2008,18:62-90.
[8]Kapur PK,Pham H,Anand S,Yadav K.A unified approach for developing software reliability growth models in the presence of imperfect debugging and error generation.IEEE Trans.on Reliability,2011,60(1):331-340.
[9]Wang JY,Wu ZB,Shu YJ,Zhang Z.A general imperfect software debugging model considering the nonlinear process of fault introduction.In:Proc.of the 14th Int’l Conf.on Quality Software(QSIC).2014.222-227.
[10]Wang JY,Wu ZB.Study of the nonlinear imperfect software debugging model.Reliability Engineering&System Safety,2016,153:180-192.
[11]Wang JY,Wu ZB,Shu YJ,Zhang Z.An imperfect software debugging model considering log-logistic distribution fault content function.Journal of Systems and Software,2015,100:167-181.
[12]Wang JY,Wu ZB,Shu YJ,Zhang Z.Software reliability model with irregular changes of fault detection rate.Ruan Jian Xue Bao/Journal of Software,2015,26(10):2465-2484(in Chinese with English abstract).http://www.jos.org.cn/1000-9825/4746.htm[doi:10.13328/j.cnki.jos.004746]
[13]Xie JY,An JX,Zhu JH.NHPP software reliability growth model considering imperfect debugging.Ruan Jian Xue Bao/Journal of Software,2010,21(5):942-949(in Chinese with English abstract).http://www.jos.org.cn/1000-9825/3539.htm[doi:10.3724/SP.J.1001.2010.03539]
[14]Yin Q,Li J,Bom KH,Guo P.A new cascade software reliability model.In:Proc.of the 3rd Int’l Conf.on Natural Computation(ICNC 2007).IEEE Press,2007.241-245.
[15]Yamada S,Tokuno K,Osaki S.Imperfect debugging models with fault introduction rate for software reliability assessment.Int’l Journal of System Science,1992,23(12):2253-2264.
[16]Pham H,Zhang X.An NHPP software reliability models and its comparison.Int’l Journal of Reliability,Quality and Safety Engineering,1997,4(3):269-282.
[17]Goel AL,Okumoto K.Time dependent error detection rate model for software reliability and other performance measures.IEEETrans.on Reliability,1979,R-28(3):206-211.
[18]Yamada S,Ohba M,Osaki S.S-shaped reliability growth modeling for software error detection.IEEE Trans.on Reliability,1983,32:475-484.
[19]Ohba M.Inflection S-shaped software reliability growth models.In:Osaki S,Hatoyama Y,ed.Proc.of the Stochastic Models in Reliability Theory.Berlin:Springer-Verlag,1984.144-162.
[20]Pham H.System Software Reliability.London:Springer-Verlag,2006.
[21]Sharma K,Garg R,Nagpal CK,Garg RK.Selection of optimal software reliability growth models using a distance based approach.IEEE Trans.on Reliability,2010,59(2):266-276.
[22]Tohma Y,Jacoby R,Murata Y,Yamamoto M.Hyper-geometric distribution model to estimate the number of residual software faults.In:Proc.of the COMPSAC’89.1989.610-617.
[23]Misra PN.Software reliability analysis.IBM Systems Journal,1986,22(3):262-270.
[24]Musa JD.Software Reliability Data,Cyber Security and Information Systems Information Analysis Center.1980.
[25]Li X,Xie M,Ng SH.Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points.Applied Mathematical Modelling,2010,34:560-3570.
[12]王金勇,吴智博,舒燕君,张展.故障检测率不规则变化的软件可靠性模型.软件学报,2015,26(10):2465-2484.http://www.jos.org.cn/1000-9825/4746.htm[doi:10.13328/j.cnki.jos.004746]
[13]谢景燕,安金霞,朱纪洪.考虑不完美排错情况的NHPP类软件可靠性增长模型.软件学报,2010,21(5):942-949.http://www.jos.org.cn/1000-9825/3539.htm[doi:10.3724/SP.J.1001.2010.03539]
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