Sains Malaysiana 53(12)(2024): 3437-3462

http://doi.org/10.17576/jsm-2024-5312-24

 

The One-Sided Variable Sampling Interval Exponentially Weighted Moving Average X̅ Charts Under the Gamma Distribution

(Carta Purata Bergerak Berpemberat Eksponen Selang Pensampelan Berubah-ubah Satu Hala X̅ di Bawah Taburan Gamma)

 

KAI LE GOH^1, WEI LIN TEOH^1,2,*, JING WEI TEOH¹, ZHI LIN CHONG³ & XINYING CHEW⁴

 

¹School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, 62200 Putrajaya, Malaysia
²International Chair in Data Science & Explainable Artificial Intelligence, International Research Institute for Artificial Intelligence and Data Science, Dong A University, Danang, Vietnam
³Department of Electronic Engineering, Faculty of Engineering and Green Technology, Universiti Tunku Abdul Rahman, 31900 Kampar, Perak, Malaysia
⁴School of Computer Science, Universiti Sains Malaysia, 11800 Gelugor, Pulau Pinang, Malaysia

 

Received: 26 July 2024/Accepted: 25 October 2024

 

Abstract

Recently, adaptive quality control charts have been frequently utilised in diverse production and manufacturing industries to ensure process stability and maintain a desirable level of product quality. Among these charts, the variable sampling interval (VSI) exponentially weighted moving average (EWMA) X̅ chart is known for its sensitivity and efficiency in monitoring the process mean shifts. However, the existing literature on the design of the VSI EWMA X̅ chart is predicated on the presumption that the underlying process adheres to a normal distribution. This normality assumption is often violated in manufacturing settings, where many practical processes tend to follow non-normal or skewed distributions. Therefore, this paper investigates the performance of one-sided VSI EWMA X̅ charts designed under the normal distribution model, when the quality characteristics of interest follow a gamma distribution. Our findings indicate that the in-control average time to signal and the standard deviation of the time to signal for the one-sided VSI EWMA X̅ charts are significantly deteriorated under the gamma distribution. To tackle this problem, this paper proposes new charting parameters specifically derived for the one-sided VSI EWMA X̅ charts under the gamma distribution. Besides, comparative analyses show that the proposed one-sided VSI EWMA X̅ charts exhibit the best detection speed compared to the one-sided Shewhart X̅ and EWMA X̅ charts, when the process follows a gamma distribution. An illustrative application of the one-sided VSI EWMA X̅ chart for monitoring the weight of bias tires in scooter manufacturing is provided at the end of this paper.

 

Keywords: Average time to signal; exponentially weighted moving average control chart; gamma distribution; statistical process control; variable sampling interval scheme

 

Abstrak

Baru-baru ini, carta kawalan kualiti beradaptif sering digunakan dalam pelbagai industri pengeluaran dan pembuatan untuk memastikan kestabilan proses dan mengekalkan tahap kualiti produk yang diinginkan. Antara carta ini, carta kawalan purata bergerak berpemberat eksponen selang pensampelan berubah-ubah (VSI EWMA) X̅ dikenali kerana kepekaan dan kecekapannya dalam memantau perubahan min proses. Walau bagaimanapun, kepustakaan sedia ada yang mengenai reka bentuk carta VSI EWMA X̅ adalah berdasarkan andaian bahawa proses asas mematuhi taburan normal. Andaian kenormalan ini sering tidak dipenuhi dalam persekitaran perbuatan dengan kebanyakan proses praktikal cendurung mengikuti taburan yang tidak normal atau taburan yang condong. Oleh itu, kertas ini mengkaji prestasi carta VSI EWMA X̅ satu hala yang direka di bawah model taburan normal, apabila ciri kualiti yang diminati mengikuti taburan gamma. Hasil kajian menunjukkan bahawa purata masa untuk isyarat dan sisihan piawai masa untuk isyarat dalam kawalan bagi carta VSI EWMA X̅ satu hala merosot dengan ketara di bawah taburan gamma. Untuk menangani masalah ini, kertas ini mencadangkan parameter carta baharu yang khususnya diperoleh untuk carta VSI EWMA X̅ satu hala di bawah taburan gamma. Selain itu, analisis perbandingan menunjukkan bahawa carta VSI EWMA X̅ satu hala yang dicadangkan mempunyai kelajuan pengesanan terbaik berbanding dengan carta Shewhart X̅ dan EWMA X̅ satu hala, apabila proses mengikuti taburan gamma. Satu aplikasi ilustrasi bagi carta VSI EWMA X̅ satu hala untuk memantau berat tayar bias dalam pembuatan skuter disediakan pada bahagian akhir kertas ini.

 

Kata kunci: Carta kawalan purata bergerak berpemberat eksponen; kawalan proses statistik; purata masa untuk isyarat; skim selang pensampelan berubah-ubah; taburan gamma

 

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*Corresponding author; email: wei_lin.teoh@hw.ac.uk