Interval Enclosures for Reliability Metrics

Abstract

ABSTRACT. The computation of reliability metrics, that are reliability function, mean time to failure, hazard rate function, involves real numbers. Therefore, numerical problems are generated due to the limitation of representing and operating with real numbers in computers. This paper is focused on computing intervals that bound numeric errors introduced during computation process of reliability metrics in digital machines for Exponential, Weibull and Normal failure distributions. Interval functions were proposed for controlling numeric errors in the computation of reliability metrics values of complex systems, based on interval mathematics and high accuracy arithmetic. The interval functions calculate interval enclosures, using Intlab toolbox, for real values of reliability metrics and the SHARPE software was used to validate the results. Analysis of the numerical results obtained with the proposed functions showed that the intervals really enclose the real numbers calculated by the SHARPE software, indicating that these functions, in fact, are an alternative for auto-validating representation of these reliability values of complex systems.