Abstract:
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In mechanical engineering, it is important to estimate the amount of physical stress having a predetermined probability of system failure when developing new machine products. To estimate this stress most efficiently in terms of time and cost, c-optimal experimental design is considered. For simplicity, we assume that there are three serially dependent machine components, and that amount of damage to them given a stress follows a trivariate Weibull regression function. We assume that the amount of damage decreases sequentially as the stress progresses through the three components. The system is said to fail if the amount of damage for all three components exceeds predetermined thresholds. The target stress can be expressed in terms of a linear predictor function, and we evaluate c-optimal designs for optimizing the prediction of the target stress. Since locally optimal designs with nonlinear models depend on predetermined parameter values, misspecified parameter values can result in inefficient designs. To ameliorate the loss of efficiency from misspecified parameter values, we illustrate two-stage adaptive optimal designs, and then compare for efficacy with a single-stage design.
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