A new multiple regression analysis method for Weibull distribution and extreme distribution is presented. The best unbiased integral estimation for regression parameters and their covariance are established by the method. The point estimators and confidence intervals of Weibull distribution

extreme distribution and normal distribution are also given. The present method extends the traditional multiple regression analysis that is only suitable to normal distribution and complete data to Weibull distribution

extreme distribution and censored data. Compared with the traditional group test method and best linear unbiased estimation

the present method can fully exploit and apply the crosswise information among the test data in different states; thus it reaches a better precision and a great number of specimens can be saved.