Journal
IEEE TRANSACTIONS ON RELIABILITY
Volume 69, Issue 4, Pages 1178-1194Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TR.2019.2957503
Keywords
Maintenance engineering; Hazards; Warranties; Stochastic processes; Delays; Data models; Nonhomogeneous media; Delayed reporting; probability distributions; warranty claims
Categories
Funding
- Victoria University of Wellington Research Fund [206200]
- Waseda University Grant for Special Research Projects [2015B-441, 2016B-267]
- Waseda University [2016B-267, 2017B-325, 2018K-383]
- Kaken [18K04621]
- Waseda Institute for Advanced Study Visiting Scholars
- FY2018 Grant Program for Promotion of International Joint Research, Waseda University
- Fulbright New Zealand: Fulbright Scholar Award
- Grants-in-Aid for Scientific Research [18K04621] Funding Source: KAKEN
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In this article, we present a model for delayed reporting of faults: multiple nonfatal faults are accumulated and then simultaneously reported and repaired. The reporting process is modeled as a stochastic process dependent on the underlying stochastic process generating the faults. We derive the joint distribution of the reporting times and numbers of reported faults, giving general results and results specific to faults generated by a Poisson process. We investigate a number of extensions to the basic model, including multiple fault types (including invisible and fatal faults), preventative maintenance, and customer rush. We show how to simulate from the model and implement maximum likelihood parameter estimation in a simulated dataset and a real dataset of warranty claims from a car manufacturer.
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