Robust Optimum Life-Testing Plans under Progressive Type-I Interval Censoring Schemes with Cost Constraint

Abstract

This paper considers optimal design problems for the Weibull distribution, which can be used to model symmetrical or asymmetrical data, in the presence of progressive interval censoring in life-testing experiments. Two robust approaches, Bayesian and minimax, are proposed to deal with the dependence of the D-optimality and c-optimality on the unknown model parameters. Meanwhile, the compound design method is applied to ensure a compromise between the precision of estimation of the model parameters and the precision of estimation of the quantiles. Furthermore, to make the design become more practical, the cost constraints are taken into account in constructing the optimal designs. Two algorithms are provided for finding the robust optimal solutions. A simulated example and a real life example are given to illustrate the proposed methods. The sensitivity analysis is also studied. These new design methods can help the engineers to obtain robust optimal designs for the censored life-testing experiments.

Keywords

• Weibull distribution
• progressive interval censoring
• Bayesian design
• minimax design
• particle swarm optimization