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Bayesian Group Chain Sampling Plan for Poisson Distribution with Gamma Prior

Waqar Hafeez1, Nazrina Aziz1,2,*, Zakiyah Zain1,2, Nur Azulia Kamarudin1
1 School of Quantitative Sciences, Universiti Utara Malaysia, UUM Sintok, 06010, Kedah, Malaysia
2 Institute of Strategic Industrial Decision Modelling (ISIDM), Universiti Utara Malaysia, UUM Sintok, 06010, Kedah, Malaysia
* Corresponding Author: Nazrina Aziz. Email:

Computers, Materials & Continua 2022, 70(2), 3891-3902. https://doi.org/10.32604/cmc.2022.019695

Received 22 April 2021; Accepted 07 June 2021; Issue published 27 September 2021

Abstract

Acceptance sampling is a statistical quality control technique that consists of procedures for sentencing one or more incoming lots of finished products. Acceptance or rejection is based on the inspection of sampled products drawn randomly from the lot. The theory of previous acceptance sampling was built upon the assumption that the process from which the lots are produced is stable and the process fraction nonconforming is a constant. Process variability is inevitable due to random fluctuations, which may inadvertently lead to quality variation. As an alternative to traditional sampling plans, Bayesian approach can be used by considering prior information of the process. Using different combinations of design parameters, this study introduces a Bayesian group chain sampling plan (BGChSP). For the first time in group chain sampling plan, the probability of lot acceptance is derived by using Poisson distribution to estimate an average number of defectives. Gamma distribution is used as a prior distribution with Poisson distribution. Taking into account both consumer’s and producer’s risks, this research considers two quality regions namely, probabilistic quality region (PQR) and indifference quality region (IQR). By minimizing consumer’s and producer’s risks, BGChSP can be used to minimize the average number of defective products in industry.

Keywords

Bayesian; acceptance sampling; gamma; produce risk; consumer risk

Cite This Article

W. Hafeez, N. Aziz, Z. Zain and N. Azulia Kamarudin, "Bayesian group chain sampling plan for poisson distribution with gamma prior," Computers, Materials & Continua, vol. 70, no.2, pp. 3891–3902, 2022.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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