Sains Malaysiana 51(6)(2022): 1915-1926

http://doi.org/10.17576/jsm-2022-5106-26

Bayesian Two-Sided Complete Group Chain Sampling Plan for Poisson Distribution with Gamma Prior

(Pelan Persampelan Bayesian Kumpulan Berantai Dua Sisi Lengkap untuk Taburan Poisson dengan Prior Gamma)

WAQAR HAFEEZ¹ & NAZRINA AZIZ^1,2,*

¹School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia

²Institute of Strategic Industrial Decision Modelling (ISIDM), Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia

Diserahkan: 2 September 2021/Diterima: 17 November 2021

Abstract

For statistical quality assurance based on the inspection of a random sample, acceptance sampling plan help to decide whether the lot should be accepted or rejected. Most traditional plans only focus on minimizing the consumer’s risk, but producer’s risk also should not be ignored in acceptance sampling plan. Therefore, this study focuses on reducing both producer’s and consumer’s risks through the quality region. This study proposes a Bayesian two-sided complete group chain sampling plan (BTSCGChSP) for the average probability of lot acceptance. The Poisson distribution with gamma as prior distribution is used to derive the average probability of lot acceptance. Next, R programing language is used to obtain the average number of defectives according to average probability of acceptance and pre-specified values of design parameters. For selected design parameters in BTSCGChSP, the acceptable quality level (AQL) associated with producer’s risk and limiting quality level (LQL) associated with consumer’s risk are considered to estimate quality regions. In this paper, four quality regions are measured: (i) probabilistic quality region (PQR), (ii) quality decision region (QDR), (iii) limiting quality region (LQR) and (iv) indifference quality region (IQR). Operating characteristic curves (OC) are used for performance comparison with existing Bayesian group chain sampling plan (BGChSP) for the same probability of lot acceptance and other design parameter values. Findings validate that BTSCGChSP provides more ideal OC curve than BGChSP for the same probability of acceptance. For quality regions with the same values of consumer’s and producer’s risks, then the BTSCGChSP region will contain fewer defectives than in the BGChSP region. Hence, the proposed plan is a better substitute for existing BGChSP.

Keywords: Consumer’s risk; gamma distribution; producer’s risk; quality region

Abstrak

Bagi memastikan kualiti statistik berdasarkan pemeriksaan sampel secara rawak, pelan persampelan penerimaan dapat membantu memutuskan sama ada lot patut diterima atau ditolak. Kebanyakan pelan tradisional hanya menumpukan untuk meminimumkan risiko pengguna, tetapi risiko pengeluar juga tidak patut diabaikan dalam pelan persampelan penerimaan. Oleh itu, kajian ini memfokuskan pada pengurangan risiko pengeluar dan pengguna melalui wilayah kualiti. Kajian ini mencadangkan pelan pensampelan Bayesian kumpulan berantai dua sisi lengkap (BTSCGChSP) untuk purata kebarangkalian penerimaan lot. Taburan Poisson dengan gamma sebagai taburan prior digunakan untuk mendapatkan purata kebarangkalian penerimaan lot. Seterusnya, bahasa pengaturcaraan R digunakan untuk mendapatkan purata bilangan kecacatan berdasarkan purata kebarangkalian penerimaan dan nilai reka bentuk parameter yang telah ditetapkan. Bagi reka bentuk parameter yang terpilih dalam BTSCGChSP, tahap kualiti yang boleh diterima (AQL) yang berkait dengan risiko pengeluar dan tahap kualiti terbatas (LQL) yang berkaitan dengan risiko pengguna dipertimbangkan untuk menilai wilayah berkualiti. Dalam makalah ini, empat wilayah kualiti dinilai: (i) wilayah kualiti kebarangkalian (PQR), (ii) wilayah kualiti keputusan (QDR), (iii) wilayah kualiti terbatas (LQR) dan (iv) wilayah kualiti indiferens (IQR). Keluk ciri operasi (OC) digunakan untuk perbandingan prestasi dengan pelan persampelan Bayesian kumpulan berantai (BGChSP) sedia ada dengan kebarangkalian penerimaan lot yang sama dan nilai reka bentuk parameter yang lain. Hasil kajian mengesahkan bahawa BTSCGChSP memberikan keluk OC yang lebih ideal berbanding BGChSP untuk kebarangkalian penerimaan yang sama. Sekiranya wilayah kualiti mempunyai risiko pengguna dan pengeluar yang sama, maka wilayah BTSCGChSP akan mengandungi bilangan kerosakan yang lebih sedikit berbanding wilayah BGChSP. Oleh itu, pelan yang dicadangkan adalah pengganti yang lebih baik berbanding BGChSP.

Kata kunci: Risiko pengeluar; risiko pengguna; taburan gamma; wilayah kualiti

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^*Pengarang untuk surat-menyurat; email: nazrina@uum.edu.my