Open AccessOn estimation procedures of stress-strength reliability for Weibull distribution with application
Author(s) -
Abdullah M. Almarashi,
Ali Algarni,
Mazen Nassar
Publication year - 2020
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0237997
Subject(s) - statistics , mathematics , percentile , frequentist inference , estimator , weibull distribution , mean squared error , sample size determination , point estimation , monte carlo method , parametric statistics , confidence interval , bayesian probability , bayesian inference
For the first time, ten frequentist estimation methods are considered on stress-strength reliability R = P ( Y < X ) when X and Y are two independent Weibull distributions with the same shape parameter. The start point to estimate the parameter R is the maximum likelihood method. Other than the maximum likelihood method, a nine frequentist estimation methods are used to estimate R , namely: least square, weighted least square, percentile, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, method of Cramér-von Mises, Anderson-Darling and Right-tail Anderson-Darling. We also consider two parametric bootstrap confidence intervals of R . We compare the efficiency of the different proposed estimators by conducting an extensive Mont Carlo simulation study. The performance and the finite sample properties of the different estimators are compared in terms of relative biases and relative mean squared errors. The Mont Carlo simulation study revels that the percentile and maximum product of spacing methods are highly competitive with the other methods for small and large sample sizes. To show the applicability and the importance of the proposed estimators, we analyze one real data set.