TY - JOUR
T1 - Delayed Reporting of Faults in Warranty Claims
AU - Arnold, Richard
AU - Chukova, Stefanka
AU - Hayakawa, Yu
N1 - Funding Information:
Manuscript received December 25, 2018; revised April 22, 2019; accepted December 1, 2019. Date of publication December 27, 2019; date of current version November 30, 2020. This work was supported in part by the Victoria University of Wellington Research Fund under Grant 206200 and in part by Waseda University Grant for Special Research Projects 2015B-441 and 2016B-267. This work was also supported in part by Waseda University for Special Research Projects under Grant 2016B-267, Grant 2017B-325, and Grant 2018K-383, in part by Kaken Grant-in-Aid for Scientific Research (C) under Grant 18K04621, in part by the Waseda Institute for Advanced Study Visiting Scholars 2018, in part by the FY2018 Grant Program for Promotion of International Joint Research, Waseda University, and in part by Fulbright New Zealand: Fulbright Scholar Award 2018. Associate Editor: S.-Y. Hsieh. (Corresponding author: Richard Arnold.) R. Arnold and S. Chukova are with the School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6012, New Zealand (e-mail: richard.arnold@vuw.ac.nz; stefanka.chukova@vuw.ac.nz).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2020/12
Y1 - 2020/12
N2 - 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.
AB - 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.
KW - Delayed reporting
KW - probability distributions
KW - warranty claims
UR - http://www.scopus.com/inward/record.url?scp=85083789756&partnerID=8YFLogxK
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U2 - 10.1109/TR.2019.2957503
DO - 10.1109/TR.2019.2957503
M3 - Article
AN - SCOPUS:85083789756
SN - 0018-9529
VL - 69
SP - 1178
EP - 1194
JO - IEEE Transactions on Reliability
JF - IEEE Transactions on Reliability
IS - 4
M1 - 8944016
ER -