A moment-based estimation method for extreme probabilities

The performance analysis of highly reliable and fault tolerant systems requires the investigation of events with extremely low or high probabilities. This paper presents a simplified numerical method to bound the extreme probabilities based on the moments of the distribution. This simplified method eliminates some numerically sensitive steps of the general moments based bounding procedure. Numerical examples indicate the applicability of the proposed approach.

[1]  H. Hamburger,et al.  Über eine Erweiterung des Stieltjesschen Momentenproblems , 1921 .

[2]  G. Szegő.  Polynomials orthogonal on the unit circle , 1939 .

[3]  J. Shohat,et al.  The problem of moments , 1943 .

[4]  Edmundo de Souza e Silva,et al.  Calculating Cumulative Operational Time Distributions of Repairable Computer Systems , 1986, IEEE Transactions on Computers.

[5]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[6]  L. Donatiello,et al.  On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems , 1991, IEEE Trans. Computers.

[7]  Bruno Sericola,et al.  Performability Analysis: A New Algorithm , 1996, IEEE Trans. Computers.

[8]  E. D. S. E. Silva,et al.  An algorithm to calculate transient distributions of cumulative rate and impulse based reward , 1998 .

[9]  Miklós Telek,et al.  Numerical Analysis of Large Markov Reward Models , 1999, Perform. Evaluation.

[10]  Miklós Telek,et al.  Performability Analysis of Markov Reward Models with Rate and Impulse Reward , 1999 .

[11]  S. R'acz.  Numerical Analysis of Communication Systems through Markov Reward Models , 2002 .

[12]  Miklós Telek,et al.  On providing blocking probability and throughput guarantees in a multi-service environment , 2002, Int. J. Commun. Syst..

[13]  Gábor Horváth,et al.  Evaluation of reward analysis methods with MRMSolve 2.0 , 2004, First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings..

[14]  Miklós Telek,et al.  A moments based distribution bounding method , 2006, Math. Comput. Model..