Optimal accelerated life tests under a cost constraint with non-uniform stress durations

To collect the information about the lifetime distribution of a product, a standard life testing method at normal working conditions is impractical when the product has a substantially long lifespan. Accelerated life testing solves this problem by subjecting the test units at higher stress levels for quicker and more failure data. Due to constrained resources in practice, several decision variables such as the allocation proportions and stress durations must be determined carefully at the design stage in order to run an accelerated life test efficiently. These decision variables directly affect the experimental cost as well as the estimate precision of the parameters of interest. This article investigates these optimal decision variables based on several well-known optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget. A general scale family of distributions is considered for the underlying lifetimes to accommodate different lifetime models at different stress levels for flexible modeling. The constant-stress and step-stress accelerated life tests are then studied in detail with linearly decreasing stress durations as the stress level progresses. Under the identical budget constraint, the efficiencies of these two stress loading schemes are compared using two case studies.