On Constrained Multicriteria‐Based Planning for a Two‐Parameter Exponential Distribution

In this article, we propose to plan an optimal life‐testing experimental design under hybrid censoring scheme based on multicriteria optimization, where two objectives are simultaneously optimized. In order to do this, we outline a strategy for simultaneously optimizing two objectives as follows: the cost‐ and variance‐based objective models. We present a methodology and algorithm for implementing the multicriteria optimization subject to two constraints. We consider first constraint on the overall budget to set up a life‐testing experiment, and the second constraint is on the efficiency of lifetime model parameters' estimates based on the experimental design. In particular, a Type II hybrid censoring scheme with a two‐parameter exponential distribution as the lifetime model is illustrated. Afterwards, a sensitivity analysis regarding the constraints, model parameters, and cost coefficients is performed. Furthermore, we examine the effects of model parameter mis‐specification on the optimal designs and demonstrate the applicability of the proposed approach using a real lifetime data set. Finally, it is shown that the proposed algorithm converges in a finite number of steps.