Source-item production laws for the case that items have multiple sources with fractional counting of credit

Abstract

This article extends two previous articles on the application of martingale theory to the well-known generalized ''success-breeds-success'' principle, generalized in order to comprise also other phenomena such as ''failure breeds failure'' and other production rhythms. The extension lies in the fact that items are allowed to have multiple sources, in which case fractional assignment of weights is taking place. In this sense this article differs from another one in which total counts are the assignment rule. Martingale properties of Y,(q), the number of sources with a weight q at time t are studied. In addition to that, applying a steady stare assumption, we develop formulae for E(P(t,q)), the expected fraction of sources with weight q at time t. We show that the irregular shapes of this function of q, which are encountered in practice, can be explained by this framework to a large extent.