Prediction intervals for load‐sharing systems in accelerated life testing

Abstract

Based on accelerated lifetime experiments, we consider the problem of constructing prediction intervals for the time point at which a given number of components of a load‐sharing system fails. Our research is motivated by lab experiments with prestressed concrete beams where the tension wires fail successively. Due to an audible noise when breaking, the time points of failure could be determined exactly by acoustic measurements. Under the assumption of equal load sharing between the tension wires, we present a model for the failure times based on a birth process. We provide a model check based on a Q‐Q plot including a simulated simultaneous confidence band and four simulation‐free prediction methods. Three of the prediction methods are given by confidence sets where two of them are based on classical tests and the third is based on a new outlier‐robust test using sign depth. The fourth method uses the implicit function theorem and the δ‐method to get prediction intervals without confidence sets for the unknown parameter. We compare these methods by a leave‐one‐out analysis of the data on prestressed concrete beams. Moreover, a simulation study is performed to discuss advantages and drawbacks of the individual methods.