The Optimal Design Of Life Test With Competition Risk Under Progressive Interval Censoring

Traditional life test models generally assume that only one mechanism cause product failure.However,product failure could be caused by many mechanisms in reality and each mechanism alone could lead to product failure.This phenomenon is called competing risk.The lifetime of the product with competing risk is determined by the time of the earlist happened failure mechanism.Ignoring the cause of product failure may lead to wrong inference.This thesis assumes that the lifetime of the product follows the exponential distribution with competing risk and studies the optimal design of the life test under progressive type I interval censoring with cost constraints.It is assumed that failure mechanisms that are independent of each other and all follow the exponential distribution with different parameters.The number of products randomly removed in the experiment is assumed random and follows a binomial distribution with probabilityp.The likelihood function under these conditions is derived and the maximum likelihood estimation is obtained numerically.The cost model is set up.Given the upper limit of the experiment expenditure,the number of the product,the number of inspection and the interval length between two inspections are optimized by minimizing the determinant of varaince of covariance matrix.The robustness of the optimal plans is investigated for different lifetime of parameters of the model by Monte-carlo simulation.This research results provide valuable reference for the experimenter to carry out this kind of experiment.