Title: Goodness-of-fit test for generalised renewal process

Authors: Rajiv N. Rai; Garima Sharma

Addresses: Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology Kharagpur, West Bengal 721302, India ' Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology Kharagpur, West Bengal 721302, India

Abstract: Goodness-of-Fit (GOF) tests for the non-repairable systems as modelled through exponential, Weibull, normal and lognormal failure distributions are well touched upon in the literature. Substantial efforts have been made in developing GOF tests for non-repairable systems and Non-Homogeneous Poisson Process (NHPP) modelled through Power-Law Process (PLP). However, the literature is found to be limited in developing GOF models for imperfect repair modelled through Generalised Renewal Process (GRP). The paper, besides reviewing six trend tests, also develops a GOF test for repairable systems modelled through GRP based on Kijima I (KI) virtual age concept. KI takes into consideration the effect of repair effectiveness along with the shape and scale parameters. The developed GOF test model is a modification of the present Cramer-Von Mises (CVM) GOF test model available for PLP. The efficacy of the model is demonstrated with the help of three failure data sets.

Keywords: goodness-of-fit tests; virtual age; Kijima I; power-law process; generalised renewal process; repair effectiveness index; Cramer-Von Mises GOF test; maximum likelihood estimators; aero engine; statistic; significance level.

DOI: 10.1504/IJRS.2017.088552

International Journal of Reliability and Safety, 2017 Vol.11 No.1/2, pp.116 - 131

Accepted: 22 Sep 2017
Published online: 01 Dec 2017 *

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