When developing a new product or process developers may conduct prototyping experiments to test the technical feasibility of design alternatives. We model product and process prototyping as combinations of Bernoulli experiments with known rewards, costs and success probabilities. Experimental outcomes are observed and the design with the highest observed reward is chosen. The model balances the...

<p>A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using Euler-Bernoulli beam equation. Given appropriate datasets, model can be used to regress analytical value structure’s bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed applied numerically simulated cantileve...

In this report, we study information propagation via inter-vehicle communication along two parallel roads. By identifying an inherent Bernoulli process, we are able to derive the mean and variance of propagation distance. A road separation distance of times the transmission range distinguishes two cases for approximating the success probability in the Bernoulli process. In addition, our results...

We give a characterization of the family of all probability measures on the extended line (−∞,+∞], which may be obtained as the distribution of the maximum of some linear Bernoulli process. On a probability space (Ω,P) consider a linear process

IEC 61508-7:2010 Annex D explicates some features of the statistical evaluation of software through its operational history. But it raises many questions. One is: how does the traditional urn model apply, if at all, to software? A second is: to what kinds of software does the reasoning in Annex D apply? A third is: do the confidence-interval numbers apply to all distributions of inputs? Recentl...

At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth–death process. Stop this process at time T > 0. It is known that the tree spanned by the N tips alive at time T of the t...

Testing a given matrix for membership in the family of Bernoulli matrices is a longstanding problem, the many applications of Bernoulli vectors in computer science, finance, medicine, and operations research emphasize its practical relevance. A novel approach towards this problem was taken by [Fiebig et al., 2017] for lowdimensional settings d ≤ 6. For the first time, they exploit the close rel...

When a photon is detected by a Geiger-mode avalanche photo-diode (GMAPD), the detector is rendered inactive, or blocked, for a certain period of time. In this paper we derive the blocking probability for a GMAPD whose input is either an unmodulated, Bernoulli modulated or pulse-position-modulated (PPM) Poisson process. We demonstrate how the PPM and Bernoulli cases differ, illustrating that the...