Computer Science ›› 2025, Vol. 52 ›› Issue (6): 21-34.doi: 10.11896/jsjkx.240300061

• Computer Software • Previous Articles     Next Articles

Modeling Mechanism and Review of Imperfect Debugging Reliability Model Related to the Total Number of Faults in Software

ZHANG Ce1, SUN Zhichao2, JI Kexing1, WANG Jinyong3, WANG Yubin1   

  1. 1 School of Computer Science and Technology,Harbin Institute ofTechnology,Weihai,Weihai,Shandong 264209,China
    2 Huawei Nanjing Research Institute,Nanjing 210000,China
    3 School of Automation and Software Engineering,Shanxi University,Taiyuan 030006,China
  • Received:2024-03-09 Revised:2024-08-17 Online:2025-06-15 Published:2025-06-11
  • About author:ZHANG Ce,born in 1978,Ph.D,professor,master supervisor,is a senior member of CCF(No.12696S).His main research interests include reliability mo-deling and evaluation,security analysis in the Internet of Things, trusted computing and so on.
  • Supported by:
    National Natural Science Foundation of China(61473097),Shandong Province Natural Science Foundation(ZR2021MF067),Shanxi Province Basic Research Program(201801D121120) and Weihai Science and Technology Development Plan Project(ITEAZMZ001807).

Abstract: In the reliability research,the total number of software faults is crucial for allocating testing resources,assessing reliability changes,and determining optimal release times.However,there has been limited research from the perspective of total faults counts thus far.This study delves deeply into reliability growth models related to the total number of faults in software,particularly in environments that closely mimic real testing scenarios,including imperfect debugging.Initially,the study reviews the software reliability growth model(SRGM),outlining its main themes,essence,and technical content,and introduces analysis of total failures in software.It incorporates models that introduce new faults from the perspective of imperfect debugging,and establishes an imperfect debugging model to categorize the dynamics of total failures and cumulative detected failures under various conditions.Subsequently,from the perspectives of imperfect debugging and the introduction of new faults,a unified binary first-order imperfect debugging system of differential equations is developed to describe the software testing process.Solutions are derived for expressions of total failures and cumulative detected failures.The performance of these models is validated against multiple real-world computer engineering system faults datasets,analyzing their fit and predictive capabilities,thereby assessing the impact of total failures on reliability variations.The results indicate that the total number of failures significantly influences the reliability models and supports the growth and performance enhancement of reliability.Finally,this paper highlights forthcoming research challenges and pressing issues that need to be addressed.

Key words: Reliability, Software reliability growth model, Reliability modeling, Total number of faults, Imperfect debugging

CLC Number: 

  • TP311
[1]ZHANG J,LU Y,ZHANG B H,et al.Reliability analysis algebraic approach to software evolution[J].Acta Automatica Sinica,2021,47(1):148-160.
[2]Academician Forum丨MEI HONG academician:entering the era of software definition[EB/OL].https://m.thepaper.cn/baijiahao_6956608.
[3]MEI H.Future world defined by software[J].Satellite & Network,2018(6):28-33.
[4]MEI H.Everything can be interconnected and everything can be programmed[J].Fangyuan Magazine,2018(12):58-59.
[5]XU Y,SUN L F,ZHANG T H R,et al.Examining the Quality of Bug Report Titles:An Empirical Study[J].Computer Science,2023,50(12):14-23.
[6]JIANG J J,CHEN J J,XIONG Y F.Survey of automatic program repair techniques[J].Journal of Software,2021,32(9):2665-2690.
[7]CAO X D,HUANG Z Q,CHEN Y J,et al.An Overview of Research on Vulnerability Database Construction and Application[J].Chinese Journal of Computers,2024,47(5):1082-1119.
[8]SU XH,ZHENG W N,JIANG Y,et al.Research and Progress on Learning-Based Source Code Vulnerability Detection[J].Chinese Journal of Computers,2024,47(2):337-374.
[9]FUJ M,JIANG Y Q,HE J,et al.Cryptocurrency Mining Malware Detection Method Based on Sample Embedding[J].Computer Science,2024,51(1):327-334.
[10]GU J X,SUN H Y,HAN D,et al.Software security vulnerability mining based on deep learning[J].Journal of Computer Research and Development,2021,58(10):2140-2162.
[11]ZHANG F,XU M D,ZHAO H J,et al.Real-time trust measurement of software:behavior trust analysis approach based on noninterference[J].Journal of Software,2019,30(8):2268-2286.
[12]YADAV S S,KUMAR A,JOHRI P,et al.Testing effort-de-pendent software reliability growth model using time lag functions under distributed environment[M]//System Assurances.2022:85-102.
[13]PRADHAN V,KUMAR A,DHAR J.Modelling software reliability growth through generalized inflection S-shaped fault reduction factor and optimal release time[J].Journal of Risk and Reliability,2022,236.(1):18-36.
[14]DUAN W X,HU M,ZHOU Q,et al.Reliability in cloud computing system:a review[J].Journal of Computer Research and Development,2020,57(1):102-123.
[15]WU Y J,CHEN H B,BAO Y G,et al.Preface to the topic of Frontier progress of system software[J].Journal of Software,2020,31(10):2981-2982.
[16]WANG J,ZHANG C.Software reliability prediction using adeep learning model based on the RNN encoder-decoder[J].Reliability Engineering & System Safety,2018(170):73-82.
[17]AGGARWAL A G,GANDHI N,VERMA V,et al.Multi-Release software reliability growth assessment:An approach incorporating fault reduction factor and imperfect debugging[J].International Journal Mathematics in Operational Research,2019,15(4):446-463.
[18]SONG K Y,CHANG I H,PHAM H.A three-parameter fault-detection software reliability model with the uncertainty of operating environments[J].Journal of Systems Science and Systems Engineering,2017,26(1):121-132.
[19]KAPUR P K,SINGH V B,ANAND S,et al.Software reliability growth model with change-point and effort control using a power function of the testing time[J].International Journal of Production Research,2008,46(3):771-787.
[20]PHAM H,NORDMANN L,ZHANG Z.A general imperfect-software-debugging model with S-shaped fault-detection rate[J].IEEE Transactions on Reliability,1999,48(2):169-175.
[21]NAGARAJU V,WANDJI T,FIONDELLA L.Improved algorithm for non-homogeneouspoisson process software reliability growth models incorporating testing-effort[J].International Journal of Performability Engineering.2019,15(5):1265-1272.
[22]PENG R,MA X Y,ZHAI Q Q,et al.Software reliability growth model considering first-step and second-step fault dependency[J].Journal of Shanghai Jiaotong University(Science),2019,24:477-479.
[23]SARAF I,LQBAL J.Generalized multi-release modelling ofsoftware reliability growth models from the perspective of two types of imperfect debugging and change point[J].Quality & Reliability Engineering International.2019,35(7):2358-2370.
[24]SARAF I,LQBAL J.Generalized software fault detection and correction modeling framework through imperfect debugging,error generation and change point[J].International Journal of Information Technology,2019,11(4):751-757.
[25]ERTO P,GIORGIO M,LEPORE A.The generalized inflection S-shaped software reliability growth model[J].IEEE Transactions on Reliability,2020,69(1):228-244.
[26]LEE T Q,YEH C W,FANG C C.Bayesian software reliability prediction based on yamada delayed s-shaped model[J].Applied Mechanics and Materials,2014,490:1267-1278.
[27]HAQUE M A,AHMAD N.An effective software reliabilitygrowth model[J].Safety and Reliability,2021(2):1-12.
[28]MUNDE A.An empirical validation for predicting bugs andthe release time of open source software using entropy measures-Software reliability growth models[M]//System Assurances.2022:41-49.
[29]ZHU M,PHAM H.A generalized multiple environmental factors software reliability model with stochastic fault detection process[J].Annals of Operations Research,2022,311:525-546.
[30]MINAMINO Y,INOUE S,YAMADA S.Extension of software reliability growth models by several testing-time functions[M]//System Assurances.2022:155-174.
[31]AHMAD N,BOKHARI M U,QUADRI S M K,et al.The exponentiated Weibull software reliability growth model with various testing-efforts and optimal release policy:a performance analysis[J].International Journal of Quality & Reliability Management,2008,25(2):211-235.
[32]MANJULA T,JAIN M,GULATI T R.Cost optimization of a software reliability growth model with imperfect debugging and a fault reduction factor[C]//Proceedings Engineering Mathematics and Applications Conference.2014:182-196.
[33]LI H F,LI Q Y,LU M Y.Software reliability modeling with logistic test coverage funtion[J].Journal of Computer Research and Development,2011,48(2):232-240.
[34]LI H F,WANG S Q,LIU C,et al.Software reliability modelconsidering both testing effort and testing coverage[J].Journal of Software,2013(4):749-760.
[35]WANG J Y,ZHANG C,MI X P,et al.Software reliability growth model based on weibull distribution introduced faults[J].Journal of Software,2019,30(6):1759-1777.
[36]ZHANG C,YI W M,BAI R,et al.Utility and verification of failure data set in SRGM[J].Computer Engineering & Science,2020,42(6):1012-1020.
[37]GOEL L,OKUMOTO K.Time-dependent error-detection rate model for software reliability and other performance measures[J].IEEE Transactions on Reliability,1979,R-28(3):206-211.
[38]YAMADA S,HISHITANI J,OSAKI S.Software-reliabilitygrowth with a Weibull test-effort:a model and application[J].IEEE Transactions on Reliability,1993,42(1):100-106.
[39]PHAM T,PHAM H.A generalized software reliability model with stochastic fault-detection rate[J].Annals of Operations Research,2019,277(1):83-93.
[40]WANG J,MI X.Open Source Software reliability model with the decreasing trend of fault detection rate[J].The Computer Journal,2019,62(9):1301-1312.
[41]WANG J Y,WU Z B,SHU Y J,et al.A Software reliability model with irregular changes of fault detection rate[J].Journal of Software,2015,26(10):2465-2484.
[42]ZHANG C,LIU H W,BAI R,et al.Review on fault detection rate in reliability model[J].Journal of Software,2020,31(9):2802-2825.
[43]ZHANG C,MENG F C,KAO Y G,et al.Survey of software reliability growth model[J].Journal of Software,2017,28(9):2402-2430.
[44]ZHANG C,MENG F C,WAN K,et al.Analysis on SRGMmodeling categories and performances[J].Journal of Harbin Institute of Technology,2016,48(8):171-178.
[45]ZHANG C,LYU W G,QIU Z Y,et al.Testing coverage software reliability model under imperfect debugging[J].Journal of Hunan University(Natural Sciences),2021,48(4):26-35.
[46]YAMADA S,OHBA M,OSAKI S.S-shaped reliability growth modeling for software error detection[J].IEEE Transactions on Reliability,1983,32(5):475-484.
[47]HUANG C,LYU M,KUO S.A unified scheme of somenonhomogenous poisson process models for software reliability estimation[J].IEEE Transactions on Software Engineering,2003,29(3):261-269.
[48]PHAM H,ZHANG X.An NHPP software reliability model and its comparison[J].International Journal of Reliability,Quality and Safety Engineering,1997,4(3):269-282.
[49]PHAM H.System software reliability[M].London:Springer,2007.
[50]YAMADA S,TOKUNO K,OSAKI S.Imperfect debuggingmodels with fault introduction rate for software reliability assessment[J].International Journal of Systems Science,1992,23(12):2241-2252.
[51]PHAM H,ZHANG X.NHPP software reliability and cost models with testing coverage[J].European Journal of Operational Research,2003,145(2):443-454.
[52]PHAM H.An imperfect-debugging fault-detection dependent-parameter software[J].International Journal of Automation and Computing,2007,4(4):325-328.
[53]AHMAD N,KHAN M,RAFI L.A study of testing-effort dependent inflection s-shaped software reliability growth models with imperfect debugging[J].International Journal of Quality & Reliability Management,2010,27(1):89-110.
[54]HUANG C,KUO S,LYU M.An assessment of testing-effort de-pendent software reliability growth models[J].IEEE Transactions on Reliability,2007,56(2):198-211.
[55]PENG R,HU Q P,NG S H,et al.Testing effort dependent software FDP and FCP models with consideration of imperfect debugging [C]//2010 Fourth International Conference on Secure Software Integration and Reliability Improvement.IEEE,2010:141-146.
[56]ZHANG X,TENG X,PHAM H.Considering fault removal efficiency in software reliability assessment[J].IEEE Transactions on Systems,Man,and Cybernetics-Part A:Systems and Humans,2003,33(1):114-120.
[57]SAMEERA M S,KANCHARLA G R,PRASAD R S.Software reliability measurement using combined Goel OKUMOTO and ANOM perfect debugging model[J].Journal of Advanced Research in Dynamical and Control Systems,2019,11:780-787.
[58]ZHANG C,CUI G,MENG F C,et al.A study of optimal release policy for SRGM with imperfect debugging[J].Journal of Engineering Science and Technology Review,2013,6(3):111-118.
[59]LIN C T.Analyzing the effect of imperfect debugging on software fault detection and correction process via a simulation framework[J].Mathematical and Computer Modelling,2011,54:3046-3064.
[60]JAIN M,MANJULA T,GULATI T R.Imperfect debuggingstudy of SRGM with fault reduction factor and multiple change point[J].International Journal of Mathematics in Operational Research,2014,6(2):155-175.
[61]PENG R,LI Y F,ZHANG W J,et al.Testing effort dependent software reliability model for imperfect debugging process considering both detection and correction[J].Reliability Enginee-ring & System Safety,2014,126:37-43.
[62] ZHANG C,CUI G,BIAN Y L,et al.Component-based software reliability process simulation considering imperfect debugging[J].High Technology Letters,2014,20(1):9-15.
[63]WANG J.An imperfect software debugging model considering irregular fluctuation of fault introduction rate[J].Quality Engineering,2017,29(3):377-394.
[64]WANG J,WU Z.Study of the nonlinear imperfect software debugging model[J].Reliability Engineering & System Safety,2016,153:180-192.
[65]WANG J,WU Z,SHU Y,et al.An imperfect software debugging model considering log-logistic distribution fault content function[J].Journal of Systems & Software,2015,100:167-181.
[66]KAPUR P K,PHAM H,ANAND S,et al.A unified approach for developing software reliability growth models in the presence of imperfect debugging and error generation[J].IEEE Transactions on Reliability,2011,60(1):331-340.
[67]HUANG C Y,LYU M R.Optimal release time for software systems considering cost,testing-effort,and test efficiency[J].IEEE Transactions on Reliability,2005,54(4):583-591.
[68]HUANG C Y,LO J H.Optimal resource allocation for cost and reliability of modular software systems in the testing phase[J].Journal of Systems and Software,2006,79(5):653-664.
[69]HUANG C Y.Cost-reliability-optimal release policy for soft-ware reliability models incorporating improvements in testing efficiency[J].Journal of Systems and Software,2005,77(2):139-155.
[70]HUANG C Y,LYU M R.Estimation and analysis of some generalized multiple change-point software reliability models[J].IEEE Transactions on Reliability,2011,60(2):498-514.
[71]KUO S Y,HUANG C Y,LYU M R.Framework for modeling software reliability,using various testing-efforts and fault-detection rates[J].IEEE Trans on Reliability,2001,50(3):310-320.
[72]WANG J,WU Z,SHU Y,et al.An optimized method for software reliability model based on nonhomogeneous Poisson process[J].Applied Mathematical Modelling,2016,40(13/14):6324-6339.
[73]EHRLICH W,PRASANNA B,STAMPFEL J,et al.Determi-ning the cost of a stop-test decision(softwarereliability)[J].IEEE Software,1993,10(2):33-42.
[74]WOOD A.Predicting software reliability[J].Computer,1996,29(11):69-77.
[75]STRINGFELLOW C,ANDREWS A A.An Empirical methodfor selecting software reliability growth models[J].Empirical Software Engineering,2002,7(4):319-343.
[76]ZHANG X,PHAM H.A software cost model with warranty cost,error removal times and risk costs[J].IIE Transactions,1998,30(12):1135-1142.
[77]MISRA P N.Software reliability analysis[J].IBM SystemsJournal,1983,22(3):262-270.
[78]HOSSAIN S A,DAHIYA R C.Estimating the parameters of a non-homogeneous Poisson-process model for software reliability[J].IEEE Transactions on Reliability,1993,42(4):604-612.
[79]BAI C G,HU Q P,XIE M,et al.Software failure predictionbased on a Markov Bayesian network model[J].Journal of Systems and Software,2005,74(3):275-282.
[80]ZHANG X,PHAM H.Software field failure rate prediction before software deployment[J].Journal of Systems and Software,2006,79(3):291-300.
[81]WANG J,ZHANG C.An Open-SourceSoftware ReliabilityModel Considering Learning Factors and Stochastically Introduced Faults[J].Applied Sciences,2024,14(2):708-742.
[82]OHBA M,CHOU X M.Does imperfect debugging affect software reliability growth? [C]//Proceedings of the 11th International Conference on Software Engineering.ACM,1989:237-244.
[83]ZHANG C,CUI G,LIU H W,et al.Software test resources and cost control and optimal release policy[J].Journal of Harbin Institute of Technology,2014,46(5):51-58.
[1] ZHAO Jihong, MA Jian, LI Qianwen, NING Lijuan. Service Function Chain Deployment Method Based on VNF Divided Backup Mechanisms [J]. Computer Science, 2025, 52(7): 287-294.
[2] LIU Wenfei, LIU Jiafei, WANG Qi, WU Jingli, LI Gaoshi. Component Reliability Analysis of Interconnected Networks Based on Star Graph [J]. Computer Science, 2025, 52(7): 295-306.
[3] WANG Dongyu, MO Ran, ZHAN Wenjing, JIANG Yingjie. Analysis of the Code Quality of Code Automatic Generation Tool Github Copilot [J]. Computer Science, 2025, 52(7): 37-49.
[4] ZHANG Shihao, LENG Ming. Study on t/s Diagnosability and t/s Diagnostic Algorithm of (n,k)-Arrangement Graphs [J]. Computer Science, 2025, 52(6A): 240700180-9.
[5] JIN Jiaobo, ZHU Tiantian. Circuit Module Reliability Calculation Method for Multi-target Tracking [J]. Computer Science, 2025, 52(6A): 240800094-6.
[6] WANG Tian, SHEN Wei, ZHANG Gongxuan, XU Linli, WANG Zhen, YUN Yu. Soft Real-time Cloud Service Request Scheduling and Multiserver System Configuration for ProfitOptimization [J]. Computer Science, 2024, 51(6A): 230900099-10.
[7] LIANG Jingyu, MA Bowen, HUANG Jiwei. Reliability-aware VNF Instance Placement in Edge Computing [J]. Computer Science, 2024, 51(6A): 230500064-6.
[8] ZHANG Hao, GUO Oufan, ZHOU Feifei, MA Tao, HE Yingli, YAO Subin. Study on Dynamic Redundancy Mechanism of Time Sensitive Networks Based on Segmented Frame Copy and Elimination [J]. Computer Science, 2024, 51(11A): 240300085-7.
[9] BING Ying’ao, WANG Wenting, SUN Shengze, LIU Xin, NIE Qigui, LIU Jing. Network Reliability Analysis of Power Monitoring System Based on Improved Fuzzy ComprehensiveEvaluation Method [J]. Computer Science, 2023, 50(6A): 220400293-7.
[10] LI Honghui, CHEN Bo, LU Shuyi, ZHANG Junwen. Study on Reliability Prediction Model Based on BASFPA-BP [J]. Computer Science, 2023, 50(5): 31-37.
[11] WEN Haolin, DI Peng, CHEN Tong. Design of Ship Mission Reliability Simulation System Based on Agent [J]. Computer Science, 2023, 50(11A): 220800272-7.
[12] LI Jinliang, LIN Bing, CHEN Xing. Reliability Constraint-oriented Workflow Scheduling Strategy in Cloud Environment [J]. Computer Science, 2023, 50(10): 291-298.
[13] XU Miaomiao, CHEN Zhenping. Incentive Mechanism for Continuous Crowd Sensing Based Symmetric Encryption and Double Truth Discovery [J]. Computer Science, 2023, 50(1): 294-301.
[14] ZHANG Zhi-long, SHI Xian-jun, QIN Yu-feng. Diagnosis Strategy Optimization Method Based on Improved Quasi Depth Algorithm [J]. Computer Science, 2022, 49(6A): 729-732.
[15] WANG Xin, ZHOU Ze-bao, YU Yun, CHEN Yu-xu, REN Hao-wen, JIANG Yi-bo, SUN Ling-yun. Reliable Incentive Mechanism for Federated Learning of Electric Metering Data [J]. Computer Science, 2022, 49(3): 31-38.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!