Estimation of P(X <= Y ) for a Bivariate Weibull Distribution

Source: OAI


Nous étudions ici l'estimation de R=P(X<Y), quand X et Y sont des variables aleatoires qui suivent la loi bivariate Weibull et X est censurée à Y. On obtient la loi marginale pour les données observées et on en tire MLE,UMVUE,MME de R. Ainsi on obtient les estimateurs de Bayes sur la fonction SEL. On a effectué une simulation de Monte-Carlo pour comparer ces estimateurs.

    • "The estimation of was discussed by Hanagal [11], and Jeevanad [12] when follow the bivariate Pareto distribution. When the stress is censored at the strength, and follow the Marshall-Olkin's bivariate exponential and Marshall-Olkin's Weibull distributions, estimation of was studied by Hanagal [13], and Davarzani et al. [14], respectively . When the strength variables follow the bivariate This article has been accepted for inclusion in a future issue of this journal. "
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    ABSTRACT: In this paper, we consider a system which has $k$ s-independent and identically distributed strength components, and each component is constructed by a pair of s-dependent elements. These elements $(X_{1},Y_{1}),(X_{2},Y_{2}),ldots ,(X_{k},Y_{k})$ follow a Marshall-Olkin bivariate Weibull distribution, and each element is exposed to a common random stress $T$ which follows a Weibull distribution. The system is regarded as operating only if at least $s$ out of $k (1leq sleq k)$ strength variables exceed the random stress. The multicomponent reliability of the system is given by $R_{s,k}=P$ (at least $s$ of the $(Z_{1},ldots ,Z_{k})$ exceed $T$) where $Z_{i}=min (X_{i},Y_{i})$, $i=1,ldots ,k$. We estimate $R_{s,k}$ by using frequentist and Bayesian approaches. The Bayes estimates of $R_{s,k}$ have been developed by using Lindley's approximation, and the Markov Chain Monte Carlo methods, due to the lack of explicit forms. The asymptotic confidence interval, and the highest probability density credible interval are constructed for $R_{s,k}$. The rel- ability estimators are compared by using the estimated risks through Monte Carlo simulations.
    No preview · Article · May 2015 · IEEE Transactions on Reliability