Some Mathematical Models Useful in Reliability Analysis For Advanced Technologies

Abstract

This paper presents the mathematical foundations thought necessary to formalize properly most instances of stochastic variation that will be problematic in the construction industry. An emphasis is placed on clarifying those aspects which are frequently misunderstood. The paper reviews the concept of a distribution, its sample and parameter spaces, and compares several of those that have proved to be most useful in life and strength calculations. The problems of estimating the somewhat specialized quantities of engineering interest are discussed. The modern methods of maximum likelihood estimation for incomplete samples are explained and illustrated. The classification of a life length by the behavior of its hazard rate is shown. Cumulative damage is defined and such distributions are given and their properties explained. Some problems from the aero-space and (Hi-tech) Electronic industries are presented to illustrate the combination of these concepts arising in actual problems.