PARAMETER-ESTIMATION FOR WEIBULL PROBABILITY-DISTRIBUTION FUNCTION OFINITIAL FATIGUE QUALITY

This paper considers the problem of determining the parameters of a We ibull distribution when a limited set of experimental data of such a d istribution is available, The problem is of particular interest in the probabilistic approach to durability analysis of flight structures, i n which the distribution of time to crack initiation for a given crack length as well as the equivalent initial flaw size distribution are u sually described through a three parameter Weibull distribution. The a ims of this paper are the determination of a high-quality estimation p rocedure and the solution of the problem of the determination of the n umber of experimental data that are necessary to estimate, with a give n confidence level, the parameters of the distribution and some relate d statistics. The maximum likelihood and the least square methods are compared with regard to the estimation quality, It is shown, by Monte Carlo simulations, that the maximum likelihood approach gives better r esults than the least square approach. The problem of obtaining confid ence intervals for the number of cracks with greater length than the r eference one for a fixed service time on a single sample basis is addr essed and solved through the bootstrap method.