Optimal experimental planning for constant-stress accelerated life-testing experiments based on coherent systems

Abstract

In this paper, we discuss the optimal experimental planning for multi-level stress testing with Type-II censoring when the test units can be put into coherent systems for the experiment. Based on the notion of system signatures of coherent systems and assuming the lifetimes of the test units follow a distribution in a general log-location-scale family of distributions, the maximum likelihood estimators of the model parameters and the Fisher information matrix are derived. For optimal experimental planning, in addition to some commonly used optimality criteria, such as D-optimality, A-optimality, and V-optimality, we also consider the total time of the experiment and the total time on test. Then, motivated by a real-life application in the reliability study of furniture joints, we focus on using series systems in multi-level stress experiments. The methodology is illustrated by considering lognormal and Weibull distributed test units. Numerical and Monte Carlo simulation studies are used to demonstrate the advantages and disadvantages of using series systems in life-testing experiments. A numerical example based on furniture joints with sensitivity analysis is used to elucidate how the proposed methods can be used in planning a life-testing experiment. Finally, some concluding remarks with some future research directions are provided.