A New Reliability Model Based on Weibull Distribution

Marwa KH. Hassan

doi:10.64060/JASRv2i34

Authors

Marwa KH. Hassan Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, 11566, Egypt Author https://orcid.org/0000-0003-3730-7869

DOI:

https://doi.org/10.64060/JASRv2i34

Keywords:

Mean remaining strength (MRS), Weibull distribution, Asymptotic Confidence Interval (A.C.I.), Bootstrap interval, Bayes estimator, Monte-Carlo simulation

Abstract

We examine the mean remaining strength of a parallel system under the stress-strength framework, utilizing the Weibull distribution. This distribution is selected due to its modeling flexibility, ability to represent symmetric data, and widespread application in reliability analysis, engineering, and life testing. The likelihood ratio ordering of the system’s remaining strength is analyzed for a two-component case. Both the maximum likelihood estimator and Bayesian estimator for the mean remaining strength are derived. Additionally, we develop both asymptotic and bootstrap confidence intervals for the mean remaining strength. A simulation study is conducted to evaluate and compare the performance of these estimators. The methodology is further illustrated using a real dataset related to breast cancer.

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