Nonlinear regression models have widespread applications across diverse scientific disciplines‎. ‎Achieving precise fitting of the optimal nonlinear model is essential‎, ‎taking into account the biases inherent in Bayesian optimal design‎. ‎This study introduces a Bayesian optimal design utilizing the Dirichlet process as a prior‎. ‎The Dirichlet process is a fundamental tool in exploring Nonparametric Bayesian inference‎, ‎providing multiple well-suited representations‎. ‎The research paper presents a novel one-parameter model‎, ‎termed the ``unit-exponential distribution"‎, ‎specifically designed for the unit interval‎. ‎Additionally‎, ‎a representation is employed to approximate the D-optimality criterion‎, ‎considering the Dirichlet process as a functional tool‎. ‎Through this approach‎, ‎the aim is to identify a nonparametric Bayesian optimal design.

Providing the citizens with drinking water is one of the most important undertakings of the governments requiring huge amount of investments. Piping and pumping costs constitutes a major part of the water distribution network costs. It is obvious that any reduction in these costs amounts to a considerable savings in particular for large scale projects. A constrained nonlinear programming formulation for the optimal design of pipe networks is presented in this paper enabling optimal sizing of the network pipes and pumping heads if required. Two general purpose optimization codes namely DOT & DOC are used to solve the resulting optimization problem. Different numerical examples are considered and results are compared with other methods to verify the capabilities and versatility of the proposed method. Further researches are underway to improve the proposed method and the early results are encouraging.

This paper considers the progressively Type-II censoring and determines the optimal sample size using a Bayesian prediction approach. To this end, two criteria, namely the Bayes risk function of the point predictor for a future progressively censored order statistic and the designing cost of the experiment are considered. In the Bayesian prediction, the general entropy loss function is applied. We find the optimal sample size such that the Bayes risk function and the cost of the experiment do not exceed two pre-fixed values. To show the usefulness of the results, some numerical computations are presented.