INFERENCE FOR A BIVARIATE SURVIVAL FUNCTION INDUCED THROUGH THE ENVIRONMENT (HAZARD)

A random environmental effects model for two component systems is proposed. The two components are part of a system which is exposed to an environment that may be more or less severe than that enviroment encountered by other systems. We assume that this random environmental effect simultaneously degrades or improves both components, and induces dependence between the component lifetimes.;Based on data from series systems collected in the operating environment and on component data collected under controlled conditions such as found in the laboratory, we obtain the usual estimators of the model parameters such as the method of moment estimators and maximum likelihood estimators assuming that the random environmental effect follows a gamma distribution, while the components have exponential lifetimes under the controlled conditions. We present new estimators using total time on test transform. A small scale Monte Carlo study is done to explore the properties of the estimators obtained.;In addition, we obtain an estimator of the degree of dependence based on this graphical approach and we study several tests of the hypothesis of no environmental effect. These tests are of interest in other areas where the property of no environmental effect can be considered as test of homogeneity.;Under the same setting as the above, we study the problem of combining the information from the component tests and of the system tests which are performed separately for a better inference about the distribution of the component lifetimes. We propose an optimal scheme for determining system sample sizes subject to the various cost constraints.;We model the dependent survival function for two component systems and discuss properties of the dependence structure induced through the common environment. We also investigate the effect of the random environment on system reliability by comparing reliability functions obtained with and without random environmental effect.