An Ameliorated Improvement Factor Model for Imperfect Maintenance and Its Goodness of Fit

ABSTRACT

Maintenance actions can be classified, according to their efficiency, into three categories: perfect maintenance, imperfect maintenance, and minimal maintenance. To date, the literature on imperfect maintenance is voluminous, and many models have been developed to treat imperfect maintenance. Yet, there are two important problems in the community of maintenance that still remain wide open: how to give practical grounds for an imperfect-maintenance model, and how to test the fit of a real dataset to an imperfect-maintenance model. Motivated by these two pending problems, this work develops an imperfect-maintenance model by taking a physically meaningful approach. For the practical implementation of the developed model, we advance two methods, called QMI method and spacing-likelihood algorithm, to estimate involved unknown parameters. The two methods complete each other and are widely applicable. To offer a practical guide for testing fit to an imperfect-maintenance model, this work promotes a bootstrapping approach to approximating the distribution of a test statistic. The attractions and dilemmas of QMI method and spacing-likelihood algorithm are revealed via simulated data. The utility of the developed imperfect-maintenance model is evidenced via a real dataset. This article has a supplementary material online.

KEYWORDS:

• Censored data
• Maximum spacing estimation
• Model selection
• Parametric bootstrap
• Quasi-Monte Carlo integration

Supplementary Materials

• Technical details: In the PDF file, we provided a further discussion on the ameliorated improvement factor model and a short review of chi-square goodness-of-fit tests. We extended QMI method and spacing-likelihood algorithm for dealing with censored data. The PDF file also includes parameter-estimation results for τ = 0.5 and τ = 1, and the performance of the S step of spacing-likelihood algorithm was examined. A real dataset was analyzed (PDF file).

• Source code: The zipped package contains R codes for the two parameter-estimation methods (ZIP file).

Acknowledgments

The authors are very grateful to the editor, the associate editor, and two referees for their comments for improvements. The work described in this article was partially supported by a grant from City University of Hong Kong (Project No. 9380058) and also National Natural Science Foundation of China (Project No. 71371163).