Bivariate reliability and availability modeling

Abstract

Equipment longevity is a resource that is consumed in device operation. For many types of equipment, the resource can be reasonably represented in terms of two (or more) measures. We construct a general framework for specifying bivariate longevity models and incorporating them in availability models. Following an introduction to the domain of study a short taxonomy of model types is provided and indicates which types of models have not been studied. For two classes of bivariate models, their construction is shown, along with how they should be interpreted in relation to commonly used univariate concepts such as hazard functions. Several example models illustrate these points. The construction of bivariate renewal models is shown and their inclusion in basic and preventive maintenance-based availability models is explained. All of these analyses show the development of the bivariate Laplace transforms of the probability measures being studied. Unfortunately, in nearly all cases, the inverse transforms are not yet available. The chief contributions of the paper are the definition of a structure for classifying bivariate problems, description of methods for building and analyzing bivariate models, general presentation of a new domain of research in equipment reliability. Potential extensions and improvements to this work are numerous and the resulting realism in reliability and maintenance models will be important.