High-dimensional generation of Bernoulli random vectors

Discrete and continuous reliability models for systems with identically distributed correlated components

“…Multivariate Bernoulli distributions [13,14] model the component reliability as a vector of correlated success probabilities. Fiondella and Gokhale [15] developed Taylor series approximations to characterize the impact of correlation on system reliability with a multivariate Bernoulli distribution encoded as a multivariate normal distribution.…”

On parametric families for sampling binary data with specified mean and correlation

“…We set a i = Φ −1 (m i ) for i ∈ D to adjust the mean. In order to compute the parameter Σ that yields the desired cross-moments M, we may use a fast series approximations (Drezner and Wesolowsky, 1990) Modarres (2011) suggests the bivariate Plackett (1965) distribution as a proxy for ϕ σ ij which might provide a good starting value σ 0 ij ∈ (−1, 1). While we always obtain a solution in the bivariate case, it is well-known that the resulting matrix Σ is not necessarily positive definite due to the range of the Gaussian copula which allows to attain the bounds (2) for d ≤ 2, but not for higher dimensions.…”

Reliability Model and Sensitivity Analysis for General Electronic Systems with Failure Types based on Non-identical Correlated Components

“…The correlation model was first shown in life distributions studies [1,16,17]. Modeling by using Multivariable Bernoulli distribution [13] another method used by defining the vector of failure and success situations of dependent components. The other model is presented by using properties of Taylor series [8] and statistical distributions.…”