Design of experiments is a strategy used to identify the important factors which affect the response. A well-designed experiment plays a vital role in all disciplines of science since it can provide information to conduct time- and cost-efficient process. The ultimate goal of designing an experiment is to gain the maximum experimental outcome. Optimal designs are the designs that have best outcomes in pre-defined senses. Designs that are appropriate for one instance varies with another based on prior knowledge and available limited resources. Bayesian methods are ideal when prior information is available. Bayesian approach guides the experimenter to gain maximum outcome based on available prior information. It is well known that classical optimal designs depend on an assumed model which may not be a true model. To overcome this, Bayesian designs were introduced. For response surface experiments, the prediction of the response is an important task. Bayesian I-optimal design minimizes the average variance of prediction, thereby increases the prediction efficiency. Replication is an important technique in experimental designs. Since full replication is economically infeasible at most of the time, partial replication becomes an alternative to costly experiments. We introduce three new Bayesian optimality criteria for constructing partially replicated optimal designs that have high prediction efficiency and less dependence on an assumed model. Simulation studies are conducted to obtain optimal designs and to compare the performance of newly introduced criteria with existing criteria using graphical methods and some efficiency measures.