Sains Malaysiana 53(6)(2024): 1441-1461

http://doi.org/10.17576/jsm-2024-5306-17

A Robust Design for the Omnibus SPRT Control Chart Under Skewed Data Distributions

(Reka Bentuk Teguh untuk Carta Kawalan Omnibus SPRT di Bawah Taburan Data Pencong)

JING WEI TEOH¹, WEI LIN TEOH^1,2,*, ZHI LIN CHONG³, MING HA LEE⁴ & KHAI WAH KHAW⁵

¹School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, 62200 Putrajaya, Malaysia

²International Chair in DS & XAI, 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

⁴Faculty of Engineering, Computing and Science, Swinburne University of Technology Sarawak Campus, 93350 Kuching, Sarawak, Malaysia

⁵School of Management, Universiti Sains Malaysia, 11800 Gelugor, Pulau Pinang, Malaysia

Diserahkan: 18 Disember 2023/Diterima: 23 Mei 2024

Abstract

Control charts are widely used in manufacturing industries to ensure that production levels are stable and satisfactory. Recently, the omnibus sequential probability ratio test (OSPRT) control chart was developed for the purpose of monitoring the mean and variability of a process simultaneously. As the OSPRT chart was proposed for the first time in literature, its development relied entirely on the assumption that data follow the Normal distribution. Nonetheless, researchers are frequently reminded that the quality characteristics of manufacturing processes do not necessarily follow the Normal distribution, e.g., strengths of glass fibres, and lifetimes of products. In this paper, we investigate the extent to which the performances of the OSPRT chart designed for the Normal model deteriorate, in situations where the data distributions are Gamma and Lognormal. Results show that the in-control average run length (ARL) and standard deviation of the run length of the OSPRT chart designed for the Normal distribution deteriorate rapidly as skewness increases. To address this issue, we propose a robust design for the OSPRT chart by adjusting its control limits, known as the skewness correction method. It is shown that the skewness-corrected OSPRT chart enjoys a guaranteed in-control ARL, with a justifiable degradation in its out-of-control performances. Besides, we also show some insights into selecting the charting parameters for the skewness-corrected OSPRT chart in order to achieve an optimum out-of-control ARL performance over various shift sizes. The paper wraps up with an illustrative example of the skewness-corrected OSPRT chart for monitoring the weights of radial tyres.

Keywords: Average run length; joint monitoring control chart; sequential probability ratio test; skewed distributions; statistical process control

Abstrak

Carta kawalan telah digunakan secara meluas dalam sektor pembuatan untuk memastikan bahawa tahap pengeluaran adalah stabil dan memuaskan. Baru-baru ini, carta kawalan berdasarkan ujian nisbah kebarangkalian berjujukan (OSPRT) telah direka untuk tujuan memantau min dan variabiliti sesuatu proses industri secara serentak. Oleh sebab carta OSPRT baharu diusulkan, rekaannya bergantung sepenuhnya pada andaian bahawa data mengikuti taburan Normal. Walau bagaimanapun, para penyelidik sering diingatkan bahawa ciri mutu dalam proses pembuatan tidak semestinya mengikuti taburan Normal, seperti kekuatan serat kaca dan hayat produk. Dalam makalah ini, kami mengkaji sejauh mana prestasi carta OSPRT yang direka untuk taburan Normal merosot, dalam situasi yang mana taburan data adalah Gamma dan Lognormal. Hasil kajian menunjukkan bahawa purata panjang larian (ARL) dan sisihan piawai panjang larian carta OSPRT bagi kes terkawal merosot dengan laju apabila darjah pencongan meningkat. Untuk menyelesaikan masalah ini, kami membina reka bentuk yang teguh untuk carta OSPRT dengan mengubahsuaikan had kawalan, dikenali sebagai kaedah pembetulan pencongan. Carta OSPRT berdasarkan pembetulan pencongan didapati menghasilkan ARL terkawal yang terjamin, dan prestasinya dalam kes tidak terkawal juga kurang dijejaskan. Selain itu, kami memberikan beberapa garis panduan untuk memilih parameter carta OSPRT yang sesuai bagi mencapai prestasi ARL tidak terkawal yang optimum untuk pelbagai magnitud anjakan. Makalah ini diakhiri dengan contoh aplikasi carta OSPRT berdasarkan pembetulan pencongan untuk memantau berat tayar radial.

Kata kunci: Carta kawalan pemantauan serentak; kawalan proses statistik; purata panjang larian; taburan pencong; ujian nisbah kebarangkalian berjujukan

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*Pengarang untuk surat-menyurat; email: wei_lin.teoh@hw.ac.uk