Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life-testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two- and k-stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life-testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well.