This research focuses on fourth-grade (9-year-old) students’ informal and intuitive conceptions of probability and distribution revealed as they worked through a sequence of tasks. These tasks were designed to study students’ spontaneous reasoning about distributions in different settings and their understanding of probability of various binomial random events that they explored with a set of p...

The design of acceptance sampling plans for hybrid exponential distribution under a truncated life test is considered in this paper. In this work, experimental values are treated as observed values of exponential random variables whose mean is assumed to be a fuzzy variable in the sense of Liu [25]. A new chance distribution called hybrid exponential distribution is considered in this paper and...

We study joint chance constraints where the distribution of the uncertain parameters is onlyknown to belong to an ambiguity set characterized by the mean and support of the uncertaintiesand by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic)ambiguous chance constraints, which require the corresponding classical chance constraints to bes...

In this paper we develop approximation algorithms for two-stage convex chance constrained problems. Nemirovski and Shapiro [18] formulated this class of problems and proposed an ellipsoid-like iterative algorithm for the special case where the impact function f(x,h) is bi-affine. We show that this algorithm extends to bi-convex f(x,h) in a fairly straightforward fashion. The complexity of the s...

This study presents a multimodal hub location problem which has the capability to split commodities by limited-capacity hubs and transportation systems, based on the assumption that demands are stochastic for multi-commodity network flows. In the real world cases, demands are random over the planning horizon and those which are partially fulfilled, are lost. Thus, the present study handles dema...

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project nontrivial probabilities for the events that they concern. And these probabilities play the chance role and so should be ...

Repairable system analysis is in nature an evaluation of repair effects. Recent tendency in reliability engineering literature was imposing repair regimes and estimate system repair effects or linking repair to certain covariate to extract repair impacts. Hinted by engineering tune up exercises, we propose a repair model in terms of random variable distribution with a fuzzy parameter because fu...

In this paper, a chance-constrained (CC) framework is developed to manage the voltage control problem of medium-voltage (MV) distribution systems subject model uncertainty. Such epistemic uncertainties are inherent in system analyses given that an exact network components not available. context, relying on simplified deterministic models can lead insufficient decisions. The CC-based proposed ta...