Piecewise linear reliability data analysis with fuzzy sets

Abstract

The Weibull three-parameter model is widely used in the analysis of reliability data, since it provides a good fit to many, but not all, data cases. In this work an analysis is presented in which locally constant hazard rate functions are applied in the analysis. By defining concomitant fuzzy reliability functions as overlapping fuzzy sets, the limited ranges may be conjoined to provide an extensive continuous reliability function. The efficacy of this treatment is tested with three different typical cases of published physical data that were previously the subjects of Weibull graphical analysis. It is found that in each case the treatment is effective. Different phases of the failure pattern of each case are identified and characterized by ‘time’ constants. The treatment is not limited to three parameters, as in the Weibull case, and it is therefore more flexible. It provides a deeper insight into the underlying failure mechanisms and may be expected to provide a wider range of applications, both within reliability data analysis and in other fields, and can form part of a knowledge-based system.