Single and group acceptance sampling plans for Weibull and Pareto distribution

Year 2018, Volume: 11 Issue: 2, 143 - 155, 31.12.2018

Canan Hamurkaroğlu Ayten Yiğiter Yasemin Gençtürk

Abstract

One of the most important statistical tools in production sector is the acceptance sampling plans. Because the producers want the protection of the quality of the products and minimum variability between the products. Acceptance sampling plans are not only preserving the producers’ benefit but also looking out for the consumers’ interest. The expected lifetime may be an important quality characteristic for some products. Then, the quality control sufficiency of the products can be controlled using a suitable survival test based on the acceptance sampling plans. In the industry, the acceptance sampling plans based on the survival test of the products’ lifetime are also called as reliability sampling plans. As the cost and time are limited, it might be impossible to continue the trial until the failure time of all products are observed. Therefore, the acceptance sampling plan based on survival test truncated with a censored scheme is used.

In this study, single and group acceptance sampling plans based on truncated survival test using Type-I censoring are investigated for Weibull and Pareto distributions. Optimal sampling size and acceptance number are determined for some parameter values.

Keywords

Acceptance sampling plan, truncated survival test, producer’s risk, consumer’s risk, operation characteristic curve, Weibull distribution, Pareto distribution.

Weibull ve Pareto dağılımları için tip-I sansürleme düzeninde kesilmiş yaşam testine dayalı tek katlı ve grup kabul örnekleme planlar

Abstract

Üretim sektöründe kullanılan önemli istatistiksel araçlardan biri kabul örnekleme planlarıdır. Çünkü üreticiler ürünlerin kalitesinin korunmasını ve ürünler arasındaki değişkenliğin minimum olmasını isterler. Kabul örnekleme planları üreticinin çıkarlarını koruduğu gibi tüketicinin de çıkarlarını gözeten planlardır. Bazı ürünler için kullanım ömrü önemli bir kalite karakteristiği olabilir. Bu durumda, ürünlerin kalite kontrol yeterliliği yaşam testine dayalı uygun bir kabul örneklem planı ile test edilebilir. Endüstride ürün ömrünün yaşam testine dayalı kabul örnekleme planları güvenilirlik planları olarak da adlandırılır. Maliyet ve zamanın kısıtlı olması nedeniyle, tüm ürünlerin başarısızlık zamanı gözlenene kadar denemeye devam etmek mümkün olmayabilir. Bu nedenle bir sansürleme düzeni ile kesilmiş yaşam testine dayalı kabul örnekleme planı uygulanır.

Bu çalışmada, Weibull ve Pareto dağılımları için Tip-I sansürleme düzeni kullanılarak kesilmiş yaşam testlerine dayalı tek katlı ve grup kabul örnekleme planları incelenmiştir. Belirlenen plan parametreleri için optimal örneklem büyüklüğü ve kabul sayısı elde edilmiştir.

Keywords

Kabul örnekleme planı, kesilmiş yaşam testi, üretici riski, tüketici riski, işlem karakteristik eğrisi, Weibull dağılım, Pareto dağılımı.

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