New extended distribution-free homogenously weighted monitoring schemes for monitoring abrupt shifts in the location parameter
Loading...
Date
Authors
Letshedi, Tokelo Irene
Malela-Majika, Jean-Claude
Shongwe, Sandile Charles
Journal Title
Journal ISSN
Volume Title
Publisher
Public Library of Science
Abstract
A homogeneously weighted moving average (HWMA) monitoring scheme is a recently proposed memory-type scheme that gained its popularity because of its simplicity and superiority over the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)
schemes in detecting small disturbances in the process. Most of the existing HWMA
schemes are designed based on the assumption of normality. It is well-known that the performance of such monitoring schemes degrades significantly when this assumption is violated. Therefore, in this paper, three distribution-free monitoring schemes are developed
based on the Wilcoxon rank-sum W statistic. First, the HWMA W scheme is introduced. Secondly, the double HWMA (DHWMA) W scheme is proposed to improve the ability of the
HWMA W scheme in detecting very small disturbances in the location parameter and at last,
the hybrid HWMA (HHWMA) W scheme is also proposed because of its flexibility and better
performance in detecting shifts of different sizes. The zero-state performances of the proposed schemes are investigated using the characteristics of the run-length distribution. The
proposed schemes outperform their existing competitors, i.e. EWMA, CUSUM and DEWMA
W schemes, in many situations, and particularly the HHWMA W scheme is superior to these
competitors regardless of the size of the shift in the location parameter. Real-life data are
used to illustrate the implementation and application of the new monitoring schemes.
Description
DATA AVAILABILITY STATEMENT : The data used for the
illustration example are available from Mukherjee
et al. (2019) (10.1016/j.cie.2019.106059).
SUPPLEMENTARY MATERIAL : S1 Appendix. Properties of the HWMA W scheme. https://doi.org/10.1371/journal.pone.0261217.s001
S2 Appendix. Properties of the DHWMA W scheme. https://doi.org/10.1371/journal.pone.0261217.s002
S3 Appendix. Properties of the HHWMA W chart.
SUPPLEMENTARY MATERIAL : S1 Appendix. Properties of the HWMA W scheme. https://doi.org/10.1371/journal.pone.0261217.s001
S2 Appendix. Properties of the DHWMA W scheme. https://doi.org/10.1371/journal.pone.0261217.s002
S3 Appendix. Properties of the HHWMA W chart.
Keywords
Statistical distributions, Monte Carlo method, Data mining, Probability distribution, Normal distribution, Charts, Industrial processes, Test statistics, Homogeneously weighted moving average (HWMA), Exponentially weighted moving average (EWMA), Cumulative sum (CUSUM)
Sustainable Development Goals
Citation
Letshedi, T.I., Malela-Majika, J.-C. & Shongwe, S.C. (2022) New extended distribution-free
homogenously weighted monitoring schemes for
monitoring abrupt shifts in the location parameter.
PLoS One 17(1): e0261217. https://doi.org/10.1371/journal.pone.0261217.