Design optimization of a simple step-stress accelerated life test - Contrast between continuous and interval inspections with non-uniform step durations

Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long lifespans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. Although continuous inspection of the exact failure times is an ideal mode, the exact failure times of test units may not be available in practice due to technical limitations and/or budgetary constraints, but only the failure counts are collected at certain time points during the test (i.e., interval inspection). In this work, the design optimization of a simple step-stress accelerated life test under progressive Type-I censoring is studied with non-uniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D-optimality, T-optimality, C-optimality, A-optimality, and E-optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion on the design efficiency is compared between the continuous and interval inspection modes.