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Approximations to g‐renewal functions

Alagar Rangan (Department of Industrial Engineering, Eastern Mediterranean University, Famagusta, Cyprus)
Ehsan MoghimiHadji (Department of Industrial Engineering, Eastern Mediterranean University, Famagusta, Cyprus)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 2 August 2011

Abstract

Purpose

The purpose of the paper is to provide useful approximations for the computation of g‐renewal function, since no closed form solution of such a function is available

Design/methodology/approach

One of the methods uses a simple identity to obtain an approximation. The second method uses the Riemann sum to approximate the integrals to obtain a method of successive approximation.

Findings

The two methods provide satisfactory approximations with the relative errors in the computations are well within the acceptable limits. The accuracy of the successive approximation method could be improved with finer partition of the interval integration but at the cost of computational time.

Research limitations/implications

The computational time increases for the evaluation of the renewal function for increasing values of t.

Originality/value

The paper provides easy to evaluate approximations for g‐renewal functions, which do not have closed form analytical solutions.

Keywords

Citation

Rangan, A. and MoghimiHadji, E. (2011), "Approximations to g‐renewal functions", International Journal of Quality & Reliability Management, Vol. 28 No. 7, pp. 773-780. https://doi.org/10.1108/02656711111150841

Publisher

:

Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited