The Hazard Potential
This is an expository article directed at reliability theorists, survival analysts, and others interested in looking at life history and event data. Here we introduce the notion of a hazard potential as an unknown resource that an item is endowed with at inception. The item fails when this resource becomes depleted. The cumulative hazard is a proxy for the amount of resource consumed, and the hazard function is a proxy for the rate at which this resource is consumed. With this conceptualization of the failure process, we are able to characterize accelerated, decelerated, and normal tests and are also able to provide a perspective on the cause of interdependent lifetimes. Specifically, we show that dependent life lengths are the result of dependent hazard potentials. Consequently, we are able to generate new families of multivariate life distributions using dependent hazard potentials as a seed. For an item that operates in a dynamic environment, we argue that its lifetime is the killing time of a continuously increasing stochastic process by a random barrier, and this barrier is the item's hazard potential. The killing time perspective enables us to see competing risks from a process standpoint and to propose a framework for the joint modeling of degradation or cumulative damage and its markers. The notion of the hazard potential generalizes to the multivariate case. This generalization enables us to replace a collection of dependent random variables by a collection of independent exponentially distributed random variables, each having a different time scale.