A Monte Carlo sampling plan for estimating network reliability
Abstract
This paper presents a relatively complete and comprehensive description of a general class of Monte Carlo sampling plans for estimating g = g(s,T), the probability that s is connected to all nodes in T. The paper also provides procedures for implementing these plans. Each plan uses known lower and upper bounds B,A on g to produce an estimator of g that has a smaller variance (Ag)(gB)/K than one obtains for crude Monte Carlo sampling (B=0, A=1) on K independent replications. The paper describes worst case bounds on sample sizes K, in terms of B and A, for meeting absolute and relative error criteria. It also gives the worst case bound on the amount of variance reduction that can be expected when compared with crude Monte Carlo sampling. An example illustrates the variance reductions achievable with these plans. The paper next shows how to assess the credibility that a specified error criterion for g is met as the Monte Carlo experiment progresses and then shows how confidence intervals can be computed for g.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 October 1984
 Bibcode:
 1984STIN...8522898F
 Keywords:

 Electric Networks;
 Errors;
 Monte Carlo Method;
 Probability Theory;
 Sampling;
 Algorithms;
 Chebyshev Approximation;
 Failure Analysis;
 Planning;
 Electronics and Electrical Engineering