The use of Weibull distribution for reliability assessment

Abstract

A method is proposed for estimation of the parameters of Weibull three-parameter distribution (based on the least squares method), and a method for the determination of confidence limits for the values of quantile and distribution functions. Testing of 90 random samples, computer-generated from a distribution with known parameters, has shown that the distribution of small samples often differed from the parent distribution by the position or slope. Thus, when determining quantiles or values of the distribution function, confidence intervals must also be determined. The proposed method for their obtaining (based on the decomposition of the total variance into the variance of the mean and slope of the sample distribution function) ensures a sufficient reliability especially for the estimates of the lower confidence limit for quantile function and upper limit for the values of distribution function.