Multivariate Statistical Inference on the 3-State Availability of Repairable Sytems Using the Sahinoglu-Libby Probability Model
Mehmet Sahinoglu1, YangLin Yuan2, Sedat Capar3
1Informatics Institute, Auburn University, Montgomery, AL, United States; 2Computer Science, Troy University, Montgomery, AL, United States; 3Istatistik Bolumu, Dokuz Eylul Universitesi, Buca, Izmir, Turkey

The principal author, in resolution to an unsolved research project from his Wiley textbook (2007) entitled 'Trustworthy Computing' proposes to numerically generate the multivariate probability distribution model of an important pillar of the trustworthiness. Namely, the availability of a component (unit) when the components have three states now, with a derated state included beyond the usual 2-state assumption. It is usually assumed that repairable components reside in either up (operating) or down (non-operating) states where FOR (Forced Outage Rate) = down time/(up time + down time). On the contrary, many real-life grid components from routers or servers in cybersystems to the electric-power generating plants, and the water-supply networks or dams, as well as Markov state diagrams, do not operate in a dichotomously full or empty capacity. That is, the new FOR (Forced Outage Rate) = down time/(up time + down time + derated time) and DFOR (Derated Forced Outage Rate) = derated time/(up time + down time + derated time). Due to lack of a closed-form solution in the event of the 3-State Sahinoglu-Libby model as opposed to an existing closed-form solution of the 2-State model, the target analysis can only be conducted through Monte Carlo simulations. We have used the empirical Bayesian principles to estimate the full and derated availability of a repairable hardware component. Industrial component and network applications will be numerically illustrated using graphs and screenshots generated from a related software, which can be found on-line in the principal author's website.

Keywords: 3-State; Bayesian; Simulation; Sahinoglu-Libby

Biography: Dr. Sahinoglu is the founder Director of AUM's newly established Informatics Institute and 'Cybersystems and Information Security' program (2008). His Ph.D. is from Texas A&M (1981) in ECE/Statistics and MSEE from UMIST, England (1975) and BSEE from METU, Ankara (1973). He is jointly responsible for the original derivation of the Sahinoglu & Libby distribution (1981), innovator of “Compound Poisson Software Reliability Model” and “CP Stopping Rule” and “Security Meter” quantitative risk assessment software (patented). Among the 14 global Microsoft Trustworthy Computing Award recipients in 2006, he published 30+ journal papers, 110+ refereed proceedings and directed 10 national (in Turkey) and five international (United Nations, Europe and USA) technical grants. He is a Fellow of SDPS (Society of Design and Process Science), IEEE Senior, and Marquis Who's Who (1987), life-long honorary Cambridge Who's Who (2008), and an elected member of ISI (1995) and AFCEA, the Armed Forces Communications and Electronics Association.