Testing exponentiality has long been an interesting issue in statistical infer-ences. The present article is based on a modified measure of distance between two distributions. The proposed new measure is similar to the Kullback-Leibler divergence and it is related to the Lin-Wong divergence applied on the residual lifetime data. A modified measure is developed here which is a consistent test statistic for testing the hypothesis of exponentiality against some alternatives. First, we consider a method similar to Vasicek’ s and Correa’ s techniques of estimating the density function in or-der to construct statistic for LW divergence. Then the critical values of the test are computed, using a Monte-Carlo simulation method. Also, we find the di erences of exponential distribution detection power between the proposed test and other tests. It is shown that the proposed test performs better than other tests of exponentiality when the hazard rate is in the form of an increasing function. Finally, a case of application of the proposed test is shown through two illustrative examples.

In this research, multi-state complex systems are analyzed in order to measure reliability and predict residual of systems’ lifetime under the effect of an out of control noise factor. Hence, the analytic method helps us to estimate multi-state system reliability, and then means residual lifetime that is calculated under normal conditions. Finally, the calculation is updated for out of control noisy condition using the accelerated method. To reveal the applied results, the proposed policy is implemented in a case study in a molding machine on SNJ Co. at Isfahan.

Recently attempts have been made to construct some measures to compute the local dependence between two random variables. Bairamov et al. (2003) introduced a measure of local dependence which is essentially an extension of Galton correlation coefficient. In the present paper, we give an extension of the measure of local dependence, given by the cited authors, and study some of its properties. In particular, we show that our measure of local dependence can be applied to measure the dependency between two residual lifetime random variables. In this case, we give an estimator of the proposed measure of local dependency based on the bivariate mean residual lifetime. The connections between different forms of local dependency measure given in this paper and some other concepts of dependency are also investigated.