Reliability models based on bivariate exponential distributions

On the mean remaining strength at the system level for some bivariate survival models based on exponential distribution

“…The reliability of a two-component coherent systems in a stress-strength model has a considerable interest in the literature. We refer for the reliability of a system with bivariate models subject to a random stress Y in the stress-strength setting, for example, [6][7][8][9][10]. Kotz, Lumelskii and Pensky [11] have given an explicit review about the stress-strength models.…”

Testing for a class of bivariate exponential distributions

“…Since its introduction by Moran and Downton, several authors have studied analytical and inferential properties of this distribution. For example, the papers by Al-Saadi and Young [3], Balakrishnan and Ng [8,9], Shi and Lai [33], Iliopulos [21] and Iliopulos and Karlis [22] deal with point estimation; Nadarajah and Kotz [28] derive the exact distribution of X 1 + X 2 and X 1 /X 1 + X 2 ; and Gupta and Nadarajah [19] derive an explicit expression for the product moment E(X m 1 X n 2 ), m, n ≥ 1, among others. Nevertheless, in the applications of the MD distribution to real data sets, the adequacy of the model is concluded from the fitted marginals and from the observed correlation [14,19].…”