## JSM 2015 Online Program

#### Abstract Details

 Activity Number: 173 Type: Topic Contributed Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM Sponsor: Section on Risk Analysis Abstract #315806 Title: The Stress Strength Model for Moran-Downton's Downton's Bivariate Exponential Distribution Author(s): Yu-Jau Lin* and Yuhlong Lio and Hon Keung Tony Ng Companies: Chung Yuan Christian University and University of South Dakota and Southern Methodist University Keywords: MLE ; Monte Carlo method ; order statistics ; type II censoring Abstract: The estimation of the probability $\delta=P(X< Y)$ has been an important issue in the stress strength model. In the literature, X and Y are typically assumed independent. We consider possibly positively correlated Type II censored or unrestricted samples come from Moran-Downton's bivariate exponential (DBVE) distribution. The maximum likelihood estimators (MLE) of DBVE parameters are firstly calculated. Then the MLE of $\delta$ can thus be obtained by the invariant principle. Monte Carlo simulations are performed to approximate the confidence interval of $\delta$. An extensive simulation study is conducted to investigate the performance of the developed method. Finally, our proposed approach is applied to bivariate data sets for illustration.

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