TY - JOUR
T1 - Bootstrap control charts for quantiles based on log-symmetric distributions with applications to the monitoring of reliability data
AU - Leiva, Víctor
AU - Santos, Rafael A.dos
AU - Saulo, Helton
AU - Marchant, Carolina
AU - Lio, Yuhlong
N1 - Funding Information:
The authors would like to thank the Editors and Reviewers for their constructive comments on an earlier version of this manuscript which led to an improved version. The research was partially funded by FONDECYT, project grant numbers 1200525 (V. Leiva) and 11190636 (C. Marchant) from the National Agency for Research and Development (ANID) of the Chilean government under the Ministry of Science, Technology, Knowledge, and Innovation; and by ANID‐Millennium Science Initiative Program‐NCN17‐059 (C. Marchant). Helton Saulo acknowledges CNPq for financial support.
Publisher Copyright:
© 2022 John Wiley & Sons Ltd.
PY - 2022
Y1 - 2022
N2 - In this work, a methodology to monitor a shift in the quantile of a distribution that is a member of the log-symmetric family is proposed. Because the sampling distribution of a quantile estimator is often not available, the parametric bootstrap method is used to determine this sampling distribution and to establish the control limits when the process measurements follow a log-symmetric distribution. The mentioned family is helpful for describing the behavior of data following a distribution with positive support and that is skewed to the right. Monte Carlo simulations are carried out to investigate the performance of the proposed bootstrap control charts for quantiles. An application regarding failure data due to stress on carbon fibers is presented for illustration when monitoring reliability data. This illustration shows that non-conventional models, other than the Birnbaum-Saunders, log-normal and Weibull distributions, have potential to be used in practice. Two model selection procedures are considered to assess adequacy to the data. To facilitate the public use of the proposed methodology, we have created an R package named chartslogsym whose main functions are detailed in this paper.
AB - In this work, a methodology to monitor a shift in the quantile of a distribution that is a member of the log-symmetric family is proposed. Because the sampling distribution of a quantile estimator is often not available, the parametric bootstrap method is used to determine this sampling distribution and to establish the control limits when the process measurements follow a log-symmetric distribution. The mentioned family is helpful for describing the behavior of data following a distribution with positive support and that is skewed to the right. Monte Carlo simulations are carried out to investigate the performance of the proposed bootstrap control charts for quantiles. An application regarding failure data due to stress on carbon fibers is presented for illustration when monitoring reliability data. This illustration shows that non-conventional models, other than the Birnbaum-Saunders, log-normal and Weibull distributions, have potential to be used in practice. Two model selection procedures are considered to assess adequacy to the data. To facilitate the public use of the proposed methodology, we have created an R package named chartslogsym whose main functions are detailed in this paper.
UR - http://www.scopus.com/inward/record.url?scp=85123703696&partnerID=8YFLogxK
U2 - 10.1002/qre.3072
DO - 10.1002/qre.3072
M3 - Article
AN - SCOPUS:85123703696
JO - Quality and Reliability Engineering International
JF - Quality and Reliability Engineering International
SN - 0748-8017
ER -