Preventive replacement with defaulting

Alotaibi, NM; Cavalcante, CAV; Lopes, RS; Scarf, PA

Abstract

This paper models age replacement and block replacement when there is the possibility of defaulting on the planned maintenance. A default occurs when a planned preventive replacement is not executed, and we discuss how defaults can arise in practice. Our aim is to study the robustness of block replacement and age replacement, bearing in mind that (a) these policies are frequently used in practice, (b) in the standard scenario (no defaulting) age replacement has a lower economic cost rate than block-replacement and (c) block replacement is simple to manage because component age does not have to be monitored. We model defaults as independent Bernoulli trials. We prove that a cost-minimizing critical age for replacement in the age policy with defaulting exists if the time to failure distribution has an increasing failure rate. A numerical study of the policies indicates that: age replacement is effective if maintenance control is good, that is, when there is only a small chance of defaulting; block replacement is relatively robust to defaulting (postponement), but less so to lack of knowledge about component reliability.

Citation

Alotaibi, N., Cavalcante, C., Lopes, R., & Scarf, P. (2020). Preventive replacement with defaulting. IMA Journal of Management Mathematics, 31(4), 491-504. https://doi.org/10.1093/imaman/dpaa002

• Journal Article Type: Article
• Acceptance Date: Jan 26, 2020
• Online Publication Date: Apr 15, 2020
• Publication Date: Oct 1, 2020
• Deposit Date: Jul 16, 2020
• Journal: IMA Journal of Management Mathematics
• Print ISSN: 1471-678X
• Electronic ISSN: 1471-6798
• Publisher: Oxford University Press
• Volume: 31
• Issue: 4
• Pages: 491-504
• DOI: https://doi.org/10.1093/imaman/dpaa002
• Publisher URL: https://doi.org/10.1093/imaman/dpaa002
• Related Public URLs: http://imaman.oxfordjournals.org/
• Additional Information: Additional Information : ** Article version: VoR ** From Crossref via Jisc Publications Router **Journal IDs: pissn 1471-678X; eissn 1471-6798 **History: issued 15-04-2020; published_online 15-04-2020 **License for this article: starting on 15-04-2020, , https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model; Funders : Conselho Nacional de Desenvolvimento Científico e Tecnológico;Brazilian Research Council; Projects : unspecified