A practical approximation of Weibull renewal function for solving relevant optimization problems

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.

Keywords:

• Weibull distribution
• renewal function
• limiting relations
• approximation
• integral of renewal function

Acknowledgments

The authors would like to thank the two referees for their helpful comments and suggestions which have greatly enhanced the clarity of the paper.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China (No. 71771029).

Notes on contributors

R. Jiang

R. Jiang is a Professor of Changsha University of Science and Technology, China. He got his PhD at University of Queensland, Australia. His research interests are in various aspects of quality, reliability and maintenance. He is the author or coauthor of five reliability/maintenance related books and has published more than 200 papers.

Zhigao Chen

Zhigao Chen is a PhD candidate in Automotive Operation Engineering. His research interests include applied statistics and engineering asset management.