Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
system reliability; semi-Markov chain; usage model
system reliability; semi-Markov chain; usage model
Summary:
Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first and second moments of the single-use reliability. The model and the validity of the results are illustrated through a numerical example.
References:
[1] Barbu, V., Boussemart, M., Limnios, N.: Discrete-time semi-Markov model for reliability and survival analysis. Commun. Stat., Theory Methods 33 (2004), 2833-2868. DOI 10.1081/STA-200037923 | MR 2138658 | Zbl 1089.60525
[2] Barbu, V., Limnios, N.: Semi-Markov Chains and Hidden Semi-Markov Models toward Applications. Their Use in Reliability and DNA Analysis. Lecture Notes in Statistics 191 Springer, New York (2008). MR 2452304 | Zbl 1208.60001
[3] Blasi, A., Janssen, J., Manca, R.: Numerical treatment of homogeneous and non-homogeneous semi-Markov reliability models. Commun. Stat., Theory Methods 33 (2004), 697-714. DOI 10.1081/STA-120028692 | MR 2056962 | Zbl 1114.60327
[4] Ciardo, G., Marie, R. A., Sericola, B., Trivedi, K. S.: Performability analysis using semi-Markov reward processes. IEEE Trans. Comput. C-39 (1990), 1251-1264. DOI 10.1109/12.59855
[5] D'Amico, G.: The crossing barrier of a non-homogeneous semi-Markov chain. Stochastics 81 (2009), 589-600. DOI 10.1080/17442500903278892 | MR 2589413 | Zbl 1196.60147
[6] D'Amico, G.: Age-usage semi-Markov models. Appl. Math. Modelling 35 (2011), 4354-4366. DOI 10.1016/j.apm.2011.03.006 | MR 2801959 | Zbl 1225.90034
[7] D'Amico, G., Petroni, F., Prattico, F.: Reliability measures of second-order semi-Markov chain applied to wind energy production. Journal of Renewable Energy 2013 (2013), Article ID 368940, 6 pp.
[8] Janssen, J., Manca, R.: Semi-Markov Risk Models for Finance, Insurance and Reliability. Springer, New York (2007). MR 2301626 | Zbl 1144.91027
[9] Limnios, N.: Reliability measures of semi-Markov systems with general state space. Methodol. Comput. Appl. Probab. 14 895-917 (2012). DOI 10.1007/s11009-011-9211-5 | MR 2993738 | Zbl 1259.60106
[10] Limnios, N., Oprişan, G.: Semi-Markov Processes and Reliability. Statistics for Industry and Technology Birkhäuser, Basel (2001). MR 1843923 | Zbl 0990.60004
[11] Prowell, S. J., Poore, J. H.: Computing system reliability using Markov chain usage models. J. Systems Software 73 (2004), 219-225. DOI 10.1016/S0164-1212(03)00241-3
[12] Sayre, K. D.: Improved Techniques for Software Testing Based on Markov Chain Usage Models. PhD Thesis, The University of Tennessee, Knoxville, Tennessee (1999).
[13] Sayre, K. D., Poore, J. H.: Stopping criteria for statistical testing. Information and Software Technology 42 (2000), 851-857. DOI 10.1016/S0950-5849(00)00110-5
[14] Whittaker, J. A., Poore, J. H.: Markov analysis of software specifications. ACM Transactions on Software Engineering and Methodology (1993), 93-106. DOI 10.1145/151299.151326
[15] Whittaker, J. A., Thomason, M. G.: A Markov chain model for statistical software testing. IEEE Transactions on Software Engineering 30 (1994), 812-824. DOI 10.1109/32.328991
Search
Partner of
