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Article

Monitoring the Weibull Scale Parameter Based on Type I Censored Data Using a Modified EWMA Control Chart

by
Dan Yu
,
Li Jin
,
Jin Li
,
Xixi Qin
,
Zhichuan Zhu
and
Jiujun Zhang
*
School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(5), 487; https://doi.org/10.3390/axioms12050487
Submission received: 29 March 2023 / Revised: 13 May 2023 / Accepted: 16 May 2023 / Published: 17 May 2023
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications)
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Abstract

In industrial production, the exponentially weighted moving average scheme is widely used to monitor shifts in product quality, especially small-to-moderate shifts. In this paper, we propose a modified one-sided EWMA scheme for Type I right-censored Weibull lifetime data for detecting shifts in the scale parameter with the shape parameter fixed. A comparative analysis with existing cumulative sum and exponentially weighted moving average results from the literature is provided. The zero-state and steady-state behaviour of the new scheme are considered with regard to the average run length, the standard deviation of the run length, and other performance measures. Our simulation shows stronger power in detecting changes in the censored lifetime data using the modified scheme than that using the traditional exponentially weighted moving average scheme, and the new scheme is superior to the cumulative sum scheme in most situations. A real-data example further demonstrates the effectiveness of the proposed method.
Keywords: exponentially weighted moving average; Weibull distribution; censored data; statistical process monitoring exponentially weighted moving average; Weibull distribution; censored data; statistical process monitoring

Share and Cite

MDPI and ACS Style

Yu, D.; Jin, L.; Li, J.; Qin, X.; Zhu, Z.; Zhang, J. Monitoring the Weibull Scale Parameter Based on Type I Censored Data Using a Modified EWMA Control Chart. Axioms 2023, 12, 487. https://doi.org/10.3390/axioms12050487

AMA Style

Yu D, Jin L, Li J, Qin X, Zhu Z, Zhang J. Monitoring the Weibull Scale Parameter Based on Type I Censored Data Using a Modified EWMA Control Chart. Axioms. 2023; 12(5):487. https://doi.org/10.3390/axioms12050487

Chicago/Turabian Style

Yu, Dan, Li Jin, Jin Li, Xixi Qin, Zhichuan Zhu, and Jiujun Zhang. 2023. "Monitoring the Weibull Scale Parameter Based on Type I Censored Data Using a Modified EWMA Control Chart" Axioms 12, no. 5: 487. https://doi.org/10.3390/axioms12050487

APA Style

Yu, D., Jin, L., Li, J., Qin, X., Zhu, Z., & Zhang, J. (2023). Monitoring the Weibull Scale Parameter Based on Type I Censored Data Using a Modified EWMA Control Chart. Axioms, 12(5), 487. https://doi.org/10.3390/axioms12050487

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