Remarks on Renewal Theory when the Quality of Renewals Varies

摘要

In spite of its simple 'raw ingredients,' the theory of renewal processes has produced many very subtle mathematical investigations and supports a very elaborate structure of generalizations, extensions, and applications. The raw ingredients referred to consist of an infinite sequence of independent and identically distributed, non-negative random variables (X sub n); in the original renewal theory these random variables represent lifetimes of successive renewals of some industrial item subject to failure. This paper is primarily concerned with a mathematical model called the model of sequentially geometric improvement.