A dynamic model for component testing

The authors consider the component testing problem of a system where the main feature is that the component failure rates are not constant parameters, but they change in a dynamic fashion with respect to time. More precisely, each component has a piecewise-constant failure-rate function such that the lifetime distribution is exponential with a constant rate over local intervals of time within the overall mission time. There are several such intervals, and the rates change dynamically from one interval to another. The authors note that these lifetime distributions can also be used in a more general setting to approximate arbitrary lifetime distributions. The optimal component testing problem is formulated as a semi-infinite linear program. The authors present an algorithmic procedure to compute optimal test times based on the column-generation technique and illustrate it with a numerical example.