Sigmoid functions in reliability based management

Abstract

This paper introduces the theoretical background of a few possible applications of the so-called sigmoid-type functions in manufacturing and service management. An extended concept of reliability, derived from fuzzy theory, is discussed here to illustrate how reliability based management decisions can be made consistent, when handling of weakly defined concepts is needed. I demonstrate how performance growth can be modelled using an aggregate approach with support of sigmoid-type functions. Suitably chosen parameters of sigmoid-type functions allow these to be used as failure probability distribution and survival functions. If operation time of an item has a given sigmoid-type failure probability distribution function, then its hazard function is proportional to the failure probability distribution function. Furthermore, this hazard function can be a model of the third part of the bathtub failure rate curve.