https://www.ise.ufl.edu/uryasev/files/2011/11/Modeling_and_Optimization_of_Risk.pdf

Modeling and optimization of risk

Issues of highway CCTV systems used in transport telematics systems were presented in this paper. Because those systems feature a vast range of electronic systems, they need to be tightly "packed" i.e. placed next to each other very closely. On one hand, integrated circuits bring down considerably dimensions of electric devices (and could also decrease power consumption), but on the other "packaging" them together in substantial amounts creates a danger of mutual interference (internal and external electromagnetic compatibility). Therefore, design of highway CCTV system needs to assure it both does not produce but also is resilient to external and internal electromagnetic interference (including overvoltage induced by atmospheric discharge).

Evaluation of Safety of Highway CCTV System’s Maintenance Process

A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distribution. The main result is proved by a geometric proof as well as by a probabilistic one.

/pdf/generating-uniform-random-vectors-over-a-simplex-with-5bz506imp6.pdf

Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes

This paper discusses issues related to reliability of uninterruptible power supplies equipped with automatic protection mechanisms (short circuit protection – SCP, overload protection – OLP, overvoltage protection – OVP) Relationships for determining probability of system states: full operational capability, partial capability and failure were derived The impact of time taken to restore the state of full operational capability on probability of different system states was also analysed

/pdf/modelling-reliability-of-uninterruptible-power-supply-units-2lx4840wcd.pdf

Modelling reliability of uninterruptible power supply units

In Poland, a problem of lack of radar coverage at certain flight levels over certain regions of the country is being observed. Therefore, the Polish Air Navigation Services Agency is looking for some better surveillance solutions for airspace and airport surface. Multilateration system (MLAT) are part of the technology used in aviation for many years. Originally developed for military purposes - to identify and determine the position of military airplanes in the air. In the system TDOA location method was used (Time Difference of Arrival) - the difference between flight time of the aircraft over the sensors.

Reliability Assessment of Cooperation and Replacement of Surveillance Systems in Air Traffic

Preliminaries The Poisson process and distribution Waiting time distributions for a Poisson process Statistical estimation theory Generating a Poisson process Nonhomogeneous Poisson process Binomial, geometric, and negative binomial distributions Statistical Life Length Distributions Stochastic life length models Models based on the hazard rate General remarks on large systems Reliability of Various Arrangements of Units Series and parallel arrangements Series-parallel and parallel-series systems Various arrangements of switches Standby redundancy Reliability of a One-Unit Repairable System Exponential times to failure and repair Generalizations Reliability of a Two-Unit Repairable System Steady-state analysis Time-dependent analysis via Laplace transform On model 2(c) Continuous-Time Markov Chains The general case Reliability of three-unit repairable systems Steady-state results for the n-unit repairable system Pure birth and death processes Some statistical considerations First Passage Time for Systems Reliability Two-unit repairable systems Repairable systems with three (or more) units Repair time follows a general distribution Embedded Markov Chains and Systems Reliability Computations of steady-state probabilities Mean first passage times Integral Equations in Reliability Theory Introduction Example 1: Renewal process with a general distribution Example 2: One-unit repairable system Example 3: Effect of preventive replacements or maintenance Example 4: Two-unit repairable system Example 5: One out of n repairable systems Example 6: Section 7.3 revisited Example 7: First passage time distribution References Index A Problems and Comments section appears at the end of each chapter.

Ishay Weissman

Papers

Mathematical Models for Systems Reliability