Physics-Based Gaussian Process Method for Predicting Average Product Lifetime in Design Stage

Residuals based process capability indices for two-stage processes

The manufacturing operations often involve multistage processes where the process capability of each stage is affected by the process capability of its precedent processes. This property is known as the cascade property. The purpose of this paper is to estimate the process capability of the second stage of two-stage process while the cascade property impact is removed using residuals analysis. ...

Product Trees for Gaussian Process Covariance in Sublinear Time

Gaussian process (GP) regression is a powerful technique for nonparametric regression; unfortunately, calculating the predictive variance in a standard GP model requires time O(n) in the size of the training set. This is cost prohibitive when GP likelihood calculations must be done in the inner loop of the inference procedure for a larger model (e.g., MCMC). Previous work by Shen et al. (2006) ...

Product Architecture Design Process for Model-based Knowledge Management

Matrix product approach for the asymmetric random average process

We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called beta densities, of all local interactions leading to steady states of product measure form are rigorously derived. This also completes an outstanding proof ...

Fast Gaussian Process Posteriors with Product Trees

Gaussian processes (GP) are a powerful tool for nonparametric regression; unfortunately, calculating the posterior variance in a standard GP model requires time O(n) in the size of the training set. Previous work by Shen et al. (2006) used a k-d tree structure to approximate the posterior mean in certain GP models. We extend this approach to achieve efficient approximation of the posterior cova...