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Markov chain sampling is an important part of the Monte Carlo technique through which random multivariable samples are obtained that serve as a basis for producing estimates of unknown parameters. The product estimator is one result of the successful incorporation of Markov chain sampling into an experimental design that exploits the problem's special structural characteristics. The product estimator has been used for estimating the distribution of first-passage time for a positive recurrent Markov chain. Other applications are the estimation of a convex body's volume and the permanent of a matrix. Given its flexibility, the product estimator is a practical approach to Monte Carlo experimentation. An analysis of its properties given data obtained from a Markov chain beginning from an arbitrary initial state is undertaken. Factor relations, interval lengths and the required number of independent replications are described.

Computations of system reliability are predicated upon available numerical values for the reliability of the system's components. Computations of system reliability generally rely on estimates of component reliabilities that are calculated from test data since the numerical values of the reliabilities of the system components are not typically known with exact precision. However, the substitution of system component reliability adds another source of error, leading to research seeking a confidence interval for true system reliability for specified systems. A related problem arises during the computation of system reliabilities in sequenced systems that employ increasing number of components 'k' of the same type for which component reliability estimates based on 'n' independent test points are based, since the situation leads to an overstatement when k increases. The limit (k to the power of 2/n) = 0 is necessary for sample system reliability for the probability to converge in true system reliability.

An analysis of the reliability of large-scale systems whose components are subject to failure indicates that system reliability varies as a function of component reliability. Considerations of system design changes focusing on system deterioration and the extent to which sampling errors of component reliability affect system reliability reveal that the computation of system reliability becomes increasingly difficult as the system size grows. Sensitivity analysis is important when considering component replacement and alternative system designs. A Monte Carlo sampling plan can be used to estimate the sensitivity of s-t reliability for a set of alternative component reliability vectors. The Monte Carlo plan reduces the cost of evaluating the sensitivity of s-t reliability as a function of component reliability.

A sampling plan for estimating the distribution of maximum flow in a network is described. The arcs of the network have random capacities, and the network can be used to represent a multistate system. Procedures for interval estimation and assessing when the experiment has reached specified accuracy are also described.

A relatively complete and comprehensive description is presented of a general class of Monte Carlo sampling plans for estimating 'g = g(s, T)', the probability that a specified node 's' is connected to all nodes in a node set 'T' for an undirected network 'G= (V, E)', whose arcs are subject to random failure. Procedures are provided for implementing the plans, each of which uses known lower and upper bounds ('B', 'A') on 'g' to produce an estimator of 'g' that has a smaller variance '(A - g)(g - B) - K' on 'K' independent replications than that obtained for crude Monte Carlo sampling ('B = 0, A = 1'). Worst-case bounds on sample sizes 'K', in relation to 'B' and 'A', for satisfying absolute and relative error criteria are given. Also provided is the worst-case bound on the amount of variance reduction that can be anticipated when compared with crude Monte Carlo sampling.

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Organized Labor - Key player for better education When President Bush sat down with the Governors to discuss the need for educational reform, not a single trade union representative was [...]