On the Existence of the Optimal Step-stress ALT under Progressive Type-I Censoring
On the Existence of the Optimal Step-stress ALTunder Progressive Type-I Censoring
David Han
The University of Texas at San Antonio
In reliability engineering, the accelerated life test is not only getting increasingly popular but also necessary as it quickly yields information on the lifetime distribution of a highly reliable product in a short period of time by conducting the life test at more extreme stress levels than normal operating conditions. Through extrapolation, the lifetime distribution at the usage stress is then estimated with an appropriate regression model. In this work, we revisit the problem of the design optimization for a general k-level step-stress accelerated life test under progressive Type-I censoring with an equi-spaced step duration for the design simplicity. Allowing the intermediate censoring to take place at each stress change time point (viz:, i, i = 1; 2; : : : ; k), the existence of the optimal stress duration is demonstrated under various design criteria including A-optimality and E-optimality in addition to D-optimality, T-optimality, and C-optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable.