Table of Contents
Journal of Quality and Reliability Engineering
Volume 2014, Article ID 857437, 10 pages
Research Article

Renewal and Renewal-Intensity Functions with Minimal Repair

Department of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USA

Received 27 October 2013; Revised 2 January 2014; Accepted 16 January 2014; Published 19 March 2014

Academic Editor: Elio Chiodo

Copyright © 2014 Saeed Maghsoodloo and Dilcu Helvaci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The renewal and renewal-intensity functions with minimal repair are explored for the Normal, Gamma, Uniform, and Weibull underlying lifetime distributions. The Normal, Gamma, and Uniform renewal, and renewal-intensity functions are derived by the convolution method. Unlike these last three failure distributions, the Weibull except at shape does not have a closed-form function for the n-fold convolution. Since the Weibull is the most important failure distribution in reliability analyses, the approximate renewal and renewal-intensity functions of Weibull were obtained by the time-discretizing method using the Mean-Value Theorem for Integrals. A Matlab program outputs all reliability and renewal measures.