Multivariate Statistical Modeling on the 3-State (Up, Derated, Down) Availability of Repairable Hardware Units and Networks with the Sahinoglu- Libby Probability Distribution using Monte Carlo Simulation

摘要

The principal author in response to then-in-2007-unsolved homework question from his Wiley textbook proposes to generate the multivariate probability distribution model of an important pillar of the trustworthiness employing simulation techniques by proper modeling of the problem. Namely, the availability of a component (unit) is studied when the units have three states with a derated state included beyond the usual 2-state assumption. It is usually assumed that repairable units 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 units from routers or servers in cyber systems 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. Due to lack of a closed-form solution of the 3-State SL model as opposed to a closed-form of the 2-State model, the analysis can only be conducted by Monte Carlo simulations using the empirical Bayesian principles to estimate the full and derated availability of a repairable hardware unit. Industrial applications for units and networks will be numerically illustrated.