Constant Test Statistics. Mixture Distribution Analysis

With the development of science technology and economy, accelerated life test becomes an important method in the field of reliability. However, when the life distribution is a mixture distribution, i.e., there are many reasons cause the products to be failure, which problem has not been studied. But it is more useful in practice. In this dissertation, life-testing with mixture distribution is discussed and problems are solved as follows:1. Suppose the life distribution of the products is a mixture distribution, the component distributions of which come from a same distribution family but with different parameters. We studies the backgrounds of constant stress accelerated life testing, set up the basic model to analysis the test data, and give the maximum likelihood estimates (MLE) for model parameters when the samples are full or censored respactly. The asymptotic properties of the estimation are discussed too.2. We have mixture exponential distribution and mixture lognormal distribution as examples, discuss the details of the model and the method. The estimation is proved to be practicable and effective through simulation.3. For mixture distribution F(x) = (1 - a)F1 (x) + aF2 (x), we assume that there are K (K > 2) i.i.d. samples coming from(1-ai)F1(x) + aiF2(x), i = 1,...,K, respectively, where ai are known but F1, F2 are not. We give the estimations of F1, F2 when the observations are censored by a i.i.d. r.v. sequence and prove their properties. For the mixture density function f(x) = (1 - a)f1 (x) + a2 (x) , we givethe estimations of f1, f2 when the observations are full or censored and prove theasymptotic properties of the estimation.