Exponential approximation for maintained Weibull distributed component

Abstract

Exponential distribution is widely used in reliability and maintainability studies although it is well known that the constant failure rate assumption may not be valid. The purpose of this paper is to investigate the use of exponential distribution as an approximation. In fact, for components undergoing regular maintenance or replacement, the exponential assumption can be acceptable. In this paper, the exponential approximation for regularly maintained Weibull component is studied. The approximated exponential distribution using the average failure rate is compared with the exact reliability. The asymptotic relative error is derived, which can be used to adjust the exponential approximation when needed. Based on the framework of exponential approximation for Weibull distributed components, the problems of decision-making regarding the optimal maintenance time and spare allocation are also addressed.