The mixed exponential failure process

The 'mixed exponential failure process' is presently characterized by means of a time-dependent distribution from which the random hazard rate is obtained directly, rather than as the ratio of a given failure distribution to a corresponding reliability. Attention is given to the time-dependent distribution's 'characteristic function' (CF); the random hazard rate is shown to also be expressible as a singularity of the CF in the complex z-plane whose location is related to the random hazard rate. Also defined is a nonhomogeneous second-order differential equation for which the mixing distribution is a particular solution. Interdisciplinary applications of the mixing procedure are discussed.