Novel estimations for lower confidence limits of population percentile and reliability by probability weighted moment in small number of test-sample

On the unbias of probability weighted moment (PWM) estimation in small number of test-sample, novel methods are presented lower confidence limit of population percentile (denoted by x̂_R) and that of reliability (denoted by R̂_L). In the traditional methods for estimating x̂_R and R̂_L, such as one-sided tolerance factor, improved one -sided tolerance factor and random sampling, moment method and maximum likelihood method are employed to estimate the distribution parameters of the population , while PWM is used to estimate the distribution parameters of the population in the presented novel methods. Since PWM possesses more excellent statistics prop erties than moment method and maximum likelihood method in small number of test -sample, x̂_R and R̂_L estimated by the novel methods are closer to real values than those estimated by the traditional methods, which is verified by a number of numerical simulations.