The Optimal Designs Of Accelerated Life Tests Under Exponential Distribution On The Theory Of Moore-Penrose Inverse

The Step-Stress ALT (Accelerated Life Test) is the most important method in Reliability Statistics. The problem of Optimal Design for Step-Stress ALT has been proposed early in the 60s of 20st century. R.Miller, W.Nelson and D.S.Bai, M.S.Kim, S.H.Lee, applying the theory of maximun likelihood estimator(MLE) respectively, discuss the Optimal Design problem for exponential distribution of two stress. ChengYingming generalized the result to the condition of k parameters and k stresses. This paper, considering the condition that the number of stress and parameter is not equal, using the principal of minmal MLE Asymptotic Variance,applying the theory of Moore-Penrose inverse, solves the optimum design for exponential distribution. This paper also generalizes the result to optimal design for Step-Stess ALT with competing causes of failure and Step-Stess ALT under linear restrict. Practical data simulations illustrate the proposed metheod is feasible and effective.