AQL Sampling Plan Proposal Based on Two-Stage Cluster Sampling in Production Systems with High Unit Product Amount

Year 2024, EARLY VIEW, 1 - 1

Mustafa Deste , Ezgi Günaydın , Aziz Yurttaş

https://doi.org/10.2339/politeknik.1228663

Abstract

In this study, a proposal has been developed aimed at the establishment of an AQL sampling plan in enterprises that produce lots type with a high number of unit products and group packaging. In the developed model, two different sampling approaches were tested comparatively, based on the two-stage cluster sampling method approach. The application of the proposed model was carried out in a high-volume lots type bolt factory. In the first approach, the boxes (clusters) to be sampled were determined based on the number of boxes in the determined lot. In the second stage, the sample amount was determined by calculating the AQL over the unit number of products in the randomly selected boxes and an equal amount of sample was taken from the selected boxes. In the second approach, the boxes to be sampled were determined again based on the number of boxes in the determined lot, and the sample amount to be taken from the determined boxes was calculated based on the number of unit products in the whole lot. Trials were made for the acceptance quality limits of 2.5, 4 and 6.5 for both approaches and the acceptance/rejection statuses were compared.

Bu çalışmada, birim ürün adedi yüksek ve grup paketlemeli parti tipi üretim yapan işletmelerde AQL örnekleme planı oluşturulmasına yönelik bir öneri geliştirilmiştir. Geliştirilen modelde, iki aşamalı küme örnekleme yöntemi yaklaşımı temel alınarak iki farklı numune alma yaklaşımı karşılaştırmalı olarak test edilmiştir. Önerilen modelin uygulaması yüksek hacimli parti tipi üretim yapan bir cıvata fabrikasında gerçekleştirilmiştir. Birinci yaklaşımda, belirlenen partideki kutu adedi baz alınarak örneklem alınacak kutular (kümeler) belirlenmiştir. İkinci aşamada ise, rassal olarak seçilen kutulardaki birim ürün adedi üzerinden AQL hesaplaması yapılarak numune miktarı belirlenmiş ve seçilen kutulardan eşit miktarda örnek alınmıştır. İkinci yaklaşımda ise, yine belirlenen partideki kutu adedi baz alınarak örneklem alınacak kutular belirlenmiş olup belirlenen kutulardan alınacak numune miktarı partinin tamamındaki birim ürün adedi baz alınarak hesaplanmıştır. Her iki yaklaşım için 2.5, 4 ve 6.5 kabul kalite sınırları için denemeler yapılmış ve kabul/red durumları karşılaştırılmıştır.

Keywords

Acceptance Quality Limit, Two-Stage Cluster Sampling, High Unit Production, Kabuledilebilir-Kalite Limiti, İki-Aşamalı Küme Örneklemesi, Yüksek Birim Üretimi

AQL Sampling Plan Proposal Based on Two-Stage Cluster Sampling in Production Systems with High Unit Product Amount

Abstract

In this study, a proposal has been developed aimed at the establishment of an AQL sampling plan in enterprises that produce lots type with a high number of unit products and group packaging. In the developed model, two different sampling approaches were tested comparatively, based on the two-stage cluster sampling method approach. The application of the proposed model was carried out in a high-volume lots type bolt factory. In the first approach, the boxes (clusters) to be sampled were determined based on the number of boxes in the determined lot. In the second stage, the sample amount was determined by calculating the AQL over the unit number of products in the randomly selected boxes and an equal amount of sample was taken from the selected boxes. In the second approach, the boxes to be sampled were determined again based on the number of boxes in the determined lot, and the sample amount to be taken from the determined boxes was calculated based on the number of unit products in the whole lot. Trials were made for the acceptance quality limits of 2.5, 4 and 6.5 for both approaches and the acceptance/rejection statuses were compared.
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Bu çalışmada, birim ürün adedi yüksek ve grup paketlemeli parti tipi üretim yapan işletmelerde AQL örnekleme planı oluşturulmasına yönelik bir öneri geliştirilmiştir. Geliştirilen modelde, iki aşamalı küme örnekleme yöntemi yaklaşımı temel alınarak iki farklı numune alma yaklaşımı karşılaştırmalı olarak test edilmiştir. Önerilen modelin uygulaması yüksek hacimli parti tipi üretim yapan bir cıvata fabrikasında gerçekleştirilmiştir. Birinci yaklaşımda, belirlenen partideki kutu adedi baz alınarak örneklem alınacak kutular (kümeler) belirlenmiştir. İkinci aşamada ise, rassal olarak seçilen kutulardaki birim ürün adedi üzerinden AQL hesaplaması yapılarak numune miktarı belirlenmiş ve seçilen kutulardan eşit miktarda örnek alınmıştır. İkinci yaklaşımda ise, yine belirlenen partideki kutu adedi baz alınarak örneklem alınacak kutular belirlenmiş olup belirlenen kutulardan alınacak numune miktarı partinin tamamındaki birim ürün adedi baz alınarak hesaplanmıştır. Her iki yaklaşım için 2.5, 4 ve 6.5 kabul kalite sınırları için denemeler yapılmış ve kabul/red durumları karşılaştırılmıştır.

Keywords

Acceptance Quality Limit, Two-Stage Cluster Sampling, High Unit Production, Kabuledilebilir-Kalite Limiti, İki-Aşamalı Küme Örneklemesi, Yüksek Birim Üretimi

References

• [1] Govindaraju, K. and Bebbington, M., “The consumer’s risk and costs in zero-acceptance number sampling”, Commun. Stat.-Theory Methods, 44: 2933–2944, (2015).
• [2] Luca, S., Vandercappellen, J. and Claes, J., “A web-based tool to design and analyze single-and double-stage acceptance sampling plans”, Quality Engeenering, 32: 58–74, (2020).
• [3] Balakrishnan, N., Leiva, V. and Lopez, G., “Acceptance sampling plan based on the truncated life test in generalized Birnbaum- Saunders distribution”, Commun. Stat.-Simul. Comput., 36: 643–656, (2007).
• [4] Montgomery, D.C., “Introduction to Statistical Quality Control”, Sixth ed., John Wiley and Sons, Inc, (2009).
• [5] Rao, B.S. and Rao, G.S., “A two-stage group acceptance sampling plan based on life tests for half logistic distribution”, Model Assisted Statistics and Applications, 11: 203–211, (2016).
• [6] Gaspers, V., “Lean Six Sigma for Manufacturing and Service Industries”, Jakarta: PT Gramedia Pustaka Utama, (2007).
• [7] Chien-Wei, W. and Pearn, W.L., “A variables sampling plan based on Cpmk for product acceptance determination”, European Journal of Operational Research, 184: 549–560, (2008).
• [8] Muhammad, A., Muhammad, A. Saminathan, B. and Affifa, J., “Two stage group acceptance sampling plan for half normal percentiles”, Journal of King Saud University – Science, 27: 239-243, (2015).
• [9] Fallahnezhad, M.S. and Qazvini, E., “Transactions of the Institute of Measurement and Control”, 39(7): 1097–1103, (2017).
• [10] Alpar, R., “Uygulamalı Çok Değişkenli İstatistiksel Yöntemler”, Üçüncü Baskı, Detay Yayıncılık, Ankara, (2011).
• [11] Tkaczynski, A."Segmentation Using Two-Step Cluster Analysis-Segmentation in Social Marketing”, Editors: Dietrich, T., Rundle-Thiele, S. and Kubacki, K., Springer, Singapore, 109–125, (2017).
• [12] Taşkın, Ç. and Emel, G.G., "Veri madenciliğinde kümeleme yaklaşımları ve kohonen ağları ile perakendecilik sektöründe bir uygulama", Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 15(3): 395-409, (2010).
• [13] Yamane, T. “Temel Örnekleme Yöntemleri”, Translators: Esin, A., Aydın, C., Bakır, M.A. and Gürbüzel, E., Literatür Yayınları, ISBN 975-8431-34-X, İstanbul, 450-509. (2001).
• [14] Sherman, R.E., “Design and evaluation of repetitive group sampling plan”, Technometrics, 7: 11-21, (1965).
• [15] Stephens, K.S. and Dodge, H.F., “Two-stage chain sampling inspection plans with different sample sizes in the two-stages”, Journal of Quality Technology, 8(4): 209-224, (1976).
• [16] Soundararajan, V. and Ramaswamy, M.M., “Designing repetitive group sampling (RGS) plan indexed by AQL and LQL”, IAPQR Trans., 9(1): 9-14, (1984).
• [17] Rivest, L.P., Helene, C. and Michel, C., “A two-phase sampling plan for the estimation of the size of a moose population”, Biometrics, 46: 163-176, (1990).
• [18] Choi, W., Shah, P. and Das, S.K., "A framework for energy-saving data gathering using two-phase clustering in wireless sensor networks", Proceedings of the First Annual International Conference on Mobile and Ubiquitous Systems: Networking and Services (MobiQuitous’04), Bostan, USA, (2004).
• [19] Namvar, M., Gholamian, M.R. and Abi, S.K., "A two phase clustering method for ıntelligent customer segmentation". International Conference on Intelligent Systems, Modelling and Simulation (ISMS), Liverpool, United Kingdom, (2010).
• [20] Çetin, H. and Irmak, S., "Elektronik Alışverişte Akademisyenlerin Güvenlik ve Risk Algılarının Belirlenmesi", Yönetim Bilimleri Dergisi, 12(24): 275-294, (2014).
• [21] Arı, E.S., Özköse, H., Doğan, A. and Calp, M.H., "İstanbul Borsası'nda İşlem Gören Firmaların Performanslarının Kümeleme Analizi İle Değerlendirilmesi", Bilişim Teknolojileri Dergisi, 9(1): 33-39, (2016).
• [22] Ishak, A. and Zalukhu, N. E., “Bolt Product Quality Control Using Six Sigma DMAIC Method (Case study: PT XYZ Company)”, IOP Conf. Series: Materials Science and Engineering 1003, 012094: 1-10, (2020).
• [23] Syaefulloh, H., Fitriana, R. and Harahap, E.F., “Quality Improvement of Bolt Welding M6 X 12 With Six Sigma Method and Multi-Attribute Failure Mode Analysis (MAFMA)”, In PT. A Proceedings of the Second Asia Pacific International Conference on Industrial Engineering and Operations Management, Surakarta, Indonesia, September, 14-16, (2021),