Control charts for monitoring the median in non-negative asymmetric data

Lucas O. F. Sales (), André L. S. Pinho (), Marcelo Bourguignon () and F. Moisés C. Medeiros ()
Additional contact information
Lucas O. F. Sales: Programa de Pós-Graduação em Matemática Aplicada e Estatística, Universidade Federal do Rio Grande do Norte
André L. S. Pinho: Universidade Federal do Rio Grande do Norte
Marcelo Bourguignon: Universidade Federal do Rio Grande do Norte
F. Moisés C. Medeiros: Universidade Federal do Rio Grande do Norte

Statistical Methods & Applications, 2022, vol. 31, issue 4, No 13, 1037-1068

Abstract: Abstract Control charts are commonly used for monitoring the mean of processes. However, there are practical applications in which asymmetric data are the standard. In these scenarios, the use of robust statistics, such as the median, is advantageous over the mean. Based on this, we propose an empirical control chart for monitoring the median of a wide class of distributions, known as the log-symmetric class. Closed-form estimators, which perform better than the maximum likelihood estimator, are considered. Simulation studies are carried out with the following objectives: to evaluate the in-control and the out-control average run length; to evaluate the behavior of the control limits; and to compare the proposed method with a naive method based on the asymptotic distribution of the three estimators. The results indicate that the proposed approach presents better in-control average run length than the naive method and better power of detection for negative shifts in the median. A practical use of the proposed approach is illustrated with a real engineering problem, followed by a goodness of fit based on AIC and BIC, considering the most common asymmetric distributions. We also perform a residual analysis with the chosen distribution to verify its fit. Finally, based on the chosen distribution the proposed method indicates that there is an out-of-control point in phase II, which is not detected by the naive approach. Therefore, showing a gain in using the proposed method.

Keywords: Closed-form estimators; Log-symmetric distribution class; Monte Carlo simulation; Shewhart chart (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10260-022-00624-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stmapp:v:31:y:2022:i:4:d:10.1007_s10260-022-00624-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10260/PS2

DOI: 10.1007/s10260-022-00624-7

Access Statistics for this article

Statistical Methods & Applications is currently edited by Tommaso Proietti

More articles in Statistical Methods & Applications from Springer, Società Italiana di Statistica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().