Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process

Jing Jia Zhou, Kok Haur Ng, Kooi Huat Ng, Shelton Peiris and You Beng Koh
Additional contact information
Jing Jia Zhou: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Kooi Huat Ng: Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Sungai Long Campus, Universiti Tunku Abdul Rahman, Jalan Sungai Long, Bandar Sungai Long, Cheras, Kajang 43000, Malaysia
Shelton Peiris: School of Mathematics and Statistics, Faculty of Science, The University of Sydney, Sydney, NSW 2006, Australia
You Beng Koh: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2022, vol. 10, issue 22, 1-15

Abstract: Shewhart charts are the most commonly utilised control charts for process monitoring in industries with the assumption that the underlying distribution of the quality characteristic is normal. However, this assumption may not always hold true in practice. In this paper, the weighted-variance mean charts are developed and their population standard deviation is estimated using the three subgroup scale estimators, namely the standard deviation, median absolute deviation and standard deviation of trimmed mean for monitoring Weibull distributed data with different coefficients of skewness. This study aims to compare the out-of-control average run length of these charts with the pre-determined fixed value of the in-control ARL in terms of different scale estimators, coefficients of skewness and sample sizes via extensive simulation studies. The results indicate that as the coefficients of skewness increase, the charts tend to detect the out-of-control signal more rapidly under identical magnitude of shift. Meanwhile, as the size of the shift increases under the same coefficient of skewness, the proposed charts are able to locate the shifts quicker and the similar scenarios arise as a sample size raised from 5 to 10. A real data set from survival analysis domain which, possessing Weibull distribution, was to demonstrate the usefulness and applicability of the proposed chart in practice.

Keywords: weighted-variance; asymmetric control limits; mean chart; Weibull distribution; scale estimator; average run length (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/22/4380/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/22/4380/ (text/html)

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:gam:jmathe:v:10:y:2022:i:22:p:4380-:d:979124

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().