Unification of Software Reliability Models Using Markovian Arrival Processes

This paper proposes an unified modeling framework of Markov-type software reliability models (SRMs) using Markovian arrival processes (MAPs). The MAP is defined as a point process whose inter-arrival time follows a phase-type distribution incorporating the correlation between successive two arrivals. This paper presents MAP representation of Markov-type SRMs, called MAP-based SRMs. This framework enables us to use generalized formulas for several reliability measures such as the expected number of failures and the software reliability which can be applied to all the Markov-type SRMs. In addition, we discuss the parameter estimation for the MAP-based SRMs from grouped failure data and find maximum likelihood estimates of all the Markov-type SRMs. The resulting MAP-based SRM is a novel approach to unifying the model-based software reliability evaluation using failure data.

[1]  Tadashi Dohi,et al.  Gompertz software reliability model: Estimation algorithm and empirical validation , 2009, J. Syst. Softw..

[2]  Tadashi Dohi,et al.  Estimating Markov Modulated Software Reliability Models via EM Algorithm , 2006, 2006 2nd IEEE International Symposium on Dependable, Autonomic and Secure Computing.

[3]  Shigeru Yamada,et al.  Software Reliability Management: Techniques and Applications , 2003 .

[4]  Süleyman Özekici,et al.  Reliability of Complex Devices in Random Environments. , 1987 .

[5]  J. G. Shanthikumar.  A general software reliability model for performance prediction , 1981 .

[6]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[7]  Tadashi Dohi,et al.  Application of Deterministic Annealing EM Algorithm to Markovian Arrival Process Parameter Estimation , 2010, 2010 7th International Conference on Ubiquitous Intelligence & Computing and 7th International Conference on Autonomic & Trusted Computing.

[8]  Amrit L. Goel,et al.  Time-Dependent Error-Detection Rate Model for Software Reliability and Other Performance Measures , 1979, IEEE Transactions on Reliability.

[9]  Süleyman Özekici,et al.  Complex Systems in Random Environments , 1996 .

[10]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[11]  Tadashi Dohi,et al.  An infinite server queueing approach for describing software reliability growth: unified modeling and estimation framework , 2004, 11th Asia-Pacific Software Engineering Conference.

[12]  S. Özekici,et al.  Reliability of software with an operational profile , 2003, Eur. J. Oper. Res..

[13]  Tadashi Dohi,et al.  An iterative scheme for maximum likelihood estimation in software reliability modeling , 2003, 14th International Symposium on Software Reliability Engineering, 2003. ISSRE 2003..

[14]  Roger C. Cheung,et al.  A User-Oriented Software Reliability Model , 1978, IEEE Transactions on Software Engineering.

[15]  Jean-Claude Laprie,et al.  Dependability Evaluation of Software Systems in Operation , 1984, IEEE Transactions on Software Engineering.

[16]  Antonio Puliafito,et al.  From UML to Petri Nets: The PCM-Based Methodology , 2011, IEEE Transactions on Software Engineering.

[17]  Myron Hlynka,et al.  Queueing Networks and Markov Chains (Modeling and Performance Evaluation With Computer Science Applications) , 2007, Technometrics.

[18]  K Okumoto,et al.  Bayesian Software Prediction Models. Volume 1. An Imperfect Debugging Model for Reliability and other Quantitative Measures of Software Systems , 1978 .

[19]  B. Littlewood.  Software Reliability Model for Modular Program Structure , 1979, IEEE Transactions on Reliability.

[20]  Tadashi Dohi,et al.  Faster Maximum Likelihood Estimation Algorithms for Markovian Arrival Processes , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[21]  Z. Jelinski,et al.  Software reliability Research , 1972, Statistical Computer Performance Evaluation.

[22]  Nozer D. Singpurwalla,et al.  A Unification of Some Software Reliability Models , 1985 .

[23]  Michael R. Lyu,et al.  A Unified Scheme of Some Nonhomogenous Poisson Process Models for Software Reliability Estimation , 2003, IEEE Trans. Software Eng..

[24]  Dietmar Pfeifer.  THE STRUCTURE OF ELEMENTARY PURE BIRTH PROCESSES , 1982 .

[25]  Paul B. Moranda.  Event-Altered Rate Models for General Reliability Analysis , 1979, IEEE Transactions on Reliability.

[26]  Nozer D. Singpurwalla,et al.  Unification of Software Reliability Models by Self-Exciting Point Processes , 1997, Advances in Applied Probability.

[27]  Aditya P. Mathur,et al.  Comparison of architecture-based software reliability models , 2001, Proceedings 12th International Symposium on Software Reliability Engineering.

[28]  Katerina Goseva-Popstojanova,et al.  Assessing uncertainty in reliability of component-based software systems , 2003, 14th International Symposium on Software Reliability Engineering, 2003. ISSRE 2003..

[29]  Tadashi Dohi,et al.  An Architecture-based Software Reliability Model with Finite Number of Faults , 2005, IASTED Conf. on Software Engineering.

[30]  Xuemei Zhang,et al.  An NHPP Software Reliability Model and Its Comparison , 1997 .

[31]  J. Ledoux,et al.  A counting model for software reliability analysis , 1997 .

[32]  Hany H. Ammar,et al.  Architectural-Level Risk Analysis Using UML , 2003, IEEE Trans. Software Eng..

[33]  Tadashi Dohi,et al.  EM algorithms for logistic software reliability models , 2004, IASTED Conf. on Software Engineering.

[34]  Swapna S. Gokhale,et al.  A time/structure based software reliability model , 1999, Ann. Softw. Eng..

[35]  Bev Littlewood,et al.  A Reliability Model for Systems with Markov Structure , 1975 .

[36]  H. Okamura,et al.  Markovian Arrival Process Parameter Estimation With Group Data , 2009, IEEE/ACM Transactions on Networking.

[37]  Douglas R. Miller.  Exponential order statistic models of software reliability growth , 1986, IEEE Transactions on Software Engineering.

[38]  B. Conolly.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1991 .

[39]  Gunter Bolch,et al.  Queueing Networks and Markov Chains - Modeling and Performance Evaluation with Computer Science Applications, Second Edition , 1998 .

[40]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[41]  J. Ledoux,et al.  Availability modeling of modular software , 1999 .

[42]  Katerina Goseva-Popstojanova,et al.  Architecture-based approach to reliability assessment of software systems , 2001, Perform. Evaluation.