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Operations Management and Econometrics

Optimal Sample Size Allocation for Multi-Stress Tests using Extreme Value Regression

Associate Professor H. K. Tony Ng, Dept. of Statistical Science, Southern Methodist University, USA

22nd Jun 2010  11:00 am - Room 498 Merewether Building

In this talk, I will discuss the optimal sample size allocation in a multi-group life-testing experiment for complete sample and Type-II censored sample. The extreme value regression model is commonly used for statistical analysis of data arising from such a multi-stress experiment, for example, the books by Nelson (1982) and Meeker and Escobar (1998).  By considering this situation, we will derive the maximum likelihood estimators (MLEs), expected Fisher information and the asymptotic variance-covariance matrix of the MLEs. Three optimality criteria will be introduced and the optimal allocation of units for two- and k-stress level situations will then be determined. Then I will demonstrate the efficiency of this optimal allocation rule by using the real experimental situation considered earlier by Nelson and Meeker (1978). Finally, I will present some Monte Carlo simulations to show that the optimality results hold for small sample sizes as well.