bayesian d-optimal design for regression-based stopping time of a system under the δ-shock model

‎according to the δ-shock model, the system fails when the inter-arrival time between two successive shocks falls below a given critical threshold, δ. therefore, the system's failure depends on both the probabilistic behavior of the inter-arrival times and the threshold δ. as a result, the factors affecting these two variables also influence the system's stopping time. in this paper, we consider a regression model with an explanatory factor for the system's stopping time and then apply the bayesian d-optimal criterion to obtain optimal designs. assuming a uniform prior, the obtained bayesian optimal designs all have a general form corresponding to the design space.