On estimation procedures of stress-strength reliability for Weibull distribution with application

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 maxi...

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Bibliographic Details
Published in:PloS one 2020-08, Vol.15 (8), p.e0237997-e0237997
Main Authors: Almarashi, Abdullah M, Algarni, Ali, Nassar, Mazen
Format: Article
Language:English
Subjects:
Confidence intervals
Datasets
Engineering and Technology
Estimators
Least squares
Maximum likelihood method
Methods
Monte Carlo methods
Parameter estimation
Physical Sciences
Random variables
Reliability
Research and Analysis Methods
Simulation
Statistical analysis
Stress analysis (Engineering)
Studies
Weibull distribution
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0237997