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Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Volume: 47 Issue: 6

Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution

M. Kh. Hassan
M. İ. Alohali
Pages
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Publication Date
2018-12-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Real data is used as a practical application of the proposed procedure.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we consider the problem of estimation reliability in multicomponent stress-strength model, when the system consists of $k$-components have strength are given by independently and identically distributed random variables $X_{1},...,X_{k}$ each component experiencing a random stress governed by a random variable $Y$.
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Key Findings & Data:The reliability such system is obtained when strength and stress variables are given by a generalized linear failure rate distribution.
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Conclusion & Impact:Real data is used as a practical application of the proposed procedure.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Generalized linear failure rate · stress-strength model · maximum likelihood method

Abstract

In this paper, we consider the problem of estimation reliability in multicomponent stress-strength model, when the system consists of $k$-components have strength are given by independently and identically distributed random variables $X_{1},...,X_{k}$ each component experiencing a random stress governed by a random variable $Y$. The reliability such system is obtained when strength and stress variables are given by a generalized linear failure rate distribution. The system is regarded as alive only if at least $s$ out of $k$ $(s<k)$ strength exceed the stress. The multicomponent reliability of the system is given by $R_{s,k}=P[$ at least $s$ of $X_{1},...,X_{k}$ exceed $Y]$. The maximum likelihood estimator $(MLE)$ and Bayes estimator of $R_{s,k}$ are obtained. A simulation study is performed to compare the different estimators of $R_{s,k}$. Real data is used as a practical application of the proposed procedure.

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Cite This Article

Hassan, M. K., Alohali, M. İ. (2018). Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 6. https://ajindex.com/articles/1402871

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