A practical approximation of Weibull renewal function for solving relevant optimization problems. Issue Volume 32:Issues 3(2020) (2nd July 2020)

• Record Type: Journal Article
• Authors: Jiang, R.; Chen, Zhigao
• Is Part Of: Quality engineering. Volume 32:Issues 3(2020)
• Page Start: 333
• Page End: 341
• Publication Date: 2020-07-02
• Subjects: Weibull distribution -- renewal function -- limiting relations -- approximation -- integral of renewal function; Quality control -- Periodicals; Production management -- Quality control -- Periodicals; 658.5
• DOI: 10.1080/08982112.2020.1747628
• Languages: English
• ISSNs: 0898-2112

Abstract

Abstract: Some optimization problems in reliability and maintenance need to iteratively evaluate the renewal function (RF) of a lifetime distribution and/or its integral. For such problems, an accurate RF approximation with a closed-form expression is preferred to a numerical evaluation method. A number of RF approximations have been developed in the literature but few can simultaneously meet the requirements of simplicity, accuracy and integrability. This article aims to fill this gap by proposing such a RF approximation for the Weibull distribution. The proposed approximation is particularly useful for practitioners to solve the optimization problems that involve the RF and/or its integral.