PROPERTIES OF A MULTIVARIATE SURVIVAL DISTRIBUTION GENERATED BY A WEIBULL AND INVERSE-GAUSSIAN MIXTURE

In this paper, we consider the influence of the work environment on a system of non-renewable components. The failure times for the components are Weibull distributed and the work environment has an inverse-Gaussian distribution. A multivariate Weibull & inverse-Gaussian mixture distribution is derived. Several pertinent properties for this multivariate distribution are discussed that shed some tight on the nature of the distribution. We account for the operating environment and its changing nature by averaging over a parameter corresponding to the environment. The distribution is applied to find the mean number of components working at some mission time and the reliability for k-out-n components.