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The most commonly discussed example in the area of static models in dependability analysis is the network reliability problem This concerns the evaluation of reliability metrics of large classes of multicomponent systems We will denote by E the set of components in the system (which will shortly be represented by the set of edges of the undirected graph modeling the system) In general, the structure of such a system is represented by a binary function of |E| binary variables The usual convention for the state of a component or for the whole system is that 1 represents the operational state (the device, component or system is operational or up) and 0 represents the failed or down state A state vector or system con guration is a vector x = (x1 , , x|E| ) where xi is a possible state, 0 or 1, of the ith component (ie, x is an element of [0, 1]|E| ) With this notation, (x) = 1 if the system is up when the con guration is x, and 0 otherwise We may have different structure functions associated with the same system, each addressing a speci c aspect of interest that must be evaluated (see below) Frequently (but not always) structure functions are coherent, corresponding to systems satisfying the following properties: (i) when all the components are down (up), the system is down (up); (ii) if the system is up (down) and we change the state of a component from 0 to 1 (from 1 to 0), the system remains up (down); (iii) all the components are relevant (a component i is irrelevant if the state of the system does not depend on the state of i) Formally, let us denote by 0 (by 1) a state vector having all its entries equal to 0 (equal to 1) We also denote by x y the relation xi yi for all i, by x < y the fact that x y with, for some j , xj < yj , and by (x, 0i ) (by (x, 1i )) the state vector constructed from x by setting xi to 0 (to 1) Then, is coherent if and only if (i) (0) = 0, (1) = 1; (ii) if x < y then (x) (y); and (iii) for each component i there exists some state vector x such that (x, 0i ) = (x, 1i ) (and thus, due to (ii), (x, 0i ) = 0 and (x, 1i ) = 1) After specifying the function , which de nes how the system provides the service for which it was designed, a probabilistic structure must be added to take the failure processes into account The usual framework is to assume that the state of the ith component is a random binary (Bernoulli) variable Xi with expectation E(Xi ) = ri , and that the |E| random variables X1 , , X|E| are independent The numbers ri = P(Xi = 1) (called the elementary reliabilities) are input data Sometimes we will also use the notation qi for the unreliability of link i, that is, qi = 1 ri The output parameter is the reliability R of the system, de ned by R = P( (X) = 1) = E( (X)) (71).

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where X = (X1 , , X|E| ), or its unreliability Q = 1 R Observe that this is a static problem, that is, time is not explicitly used in the analysis When time relations are considered, the context changes and the general framework in which the analysis is usually done is the theory of stochastic processes and, in particular,

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A nation s openness to trade greatly affects its ability to expand Trade policies that restrict and impede commerce between neighbors is typical of emerging nations Russia s openness to the world market has increased substantially in the postcrisis years, yet there still remain several obstacles to trade, such as its fragile legal system and impractical tariffs on foreign imports; therefore, Russia has received a neutral ranking in this regard First, Russia s legal system is obscure, subjective, and usually serves to protect state interests The lack of protection afforded to shareholders and property owners has been a common source of anxiety for foreign investors as well Third, high tariff rates and discriminatory licensing and approval procedures, aside from being a problem for investors, have been major sticking points in the government s prolonged World Trade Organization (WTO) negotiations The US government is one of many governments frequently criticizing Russia s trade practices, claiming the restrictions are excessive and protectionist, particularly in agriculture, manufacturing, and automobiles Since 1995, tariffs and other import restrictions have ranged between 5 percent and 30 percent, and despite the modest efforts of the Russian government to reverse that trend, it remains a problem In 2003, for instance, the government increased the customs duties on cars to 25 percent, preventing many foreign automakers from competing in its markets Similar protections for its aircraft industry overshadow restrictions on smaller-scale goods, such as alcohol, beef and poultry, televisions, and sugar Though the government has relied less on tariffs and import taxes for revenue in recent years, its tendencies from the Soviet era have proven dif cult to break Despite these barriers, Russia remains a major player in the world market, and investors have taken notice FDI, which had suffered mightily during the crisis in 1998, hit the $14 billion mark in 2005, and reached an estimated $30 billion in 2006 Though improvements have been made in this realm, investors should remain cautious about Russia s restrictive, and often one-sided, trade policies, as such practices inherently exclude free-market competition.

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