New extended distribution-free homogenously weighted monitoring schemes for monitoring abrupt shifts in the location parameter

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Authors

Letshedi, Tokelo Irene
Malela-Majika, Jean-Claude
Shongwe, Sandile Charles

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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.

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)

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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.