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Single and group acceptance sampling plans for Weibull and Pareto distribution

Yıl 2018, Cilt: 11 Sayı: 2, 143 - 155, 31.12.2018

Öz

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.

Kaynakça

  • [1] Amer Ibrahim Al-Omari (2018), Acceptance sampling plans based on truncated life tests for Sushila distribution J. Math. Fund. Sci., 50(1), 72-83.
  • [2] Aslam, M., Kundu, D. and Ahmad, M. (2010) Time truncated acceptance sampling plans for generalized exponential distribution, Journal of Applied Statistics, 37(4), 555-566.
  • [3] Aslam, M. and Jun, C.H. (2013) Designing of time truncated acceptance sampling plans by using two-point approach, Electronic Journal of Applied Statistical Analysis, 6(1), pp. 18-31.
  • [4] Balakrishnan, N., Leiva, V. and Lopez, J. (2007) Acceptance sampling plans for truncated life tests based on the generalized Birnbaum-Saunders distribution, Communications in Statistics-Simulation and Computation, 36, 643-656.
  • [5] Baklizi, A (2003). Acceptance sampling based on truncated life tests in the Pareto distribution of the second kind, Advances and Applications in Statistics, 3(1), 33-48.
  • [6] Epstein, B. (1954) Truncated life tests in the exponential case. Annals of Mathematical Statistics, 25, 555-564.
  • [7] Gui, W. and Shangli Zhang, S. (2014) Acceptance sampling plans based on truncated life tests for Gompertz Distribution, Journal of Industrial Mathematics, Vol. 2014, Article ID 391728, 7 pages. https://doi.org/10.1155/2014/391728 .
  • [8] Loganathan, A. and Gunasekaran, M. (2017) Determination of reliability single sampling plans based on exponentiated distribution, Global and Stochastic Analysis, 4(1), 111-118.
  • [9] Malathi, D. and Muthulakshmi, S. (2015) Acceptance sampling plan for the truncated life tests based on Gompertz distribution using mean, International Journal of Scientific and Engineering Research, 6(8), 1828-1841.
  • [10] Malathi, D. and Muthulakshmi, S. (2016) Truncated life test acceptance sampling plans assuring percentile life under Gompertz distribution, IOSR-Journal of Mathematics,12(2), 27-32.
  • [11] Malathi, D. and Muthulakshmi, S. (2015) Acceptance sampling plan for truncated life tests based on Frechet distribution using median, International Journal of Advancement in Research and Technology, 4(8), 1-13.
  • [12] Mughal, A.R. and Ismail, M. (2013) An Economic Reliability Efficient Group Acceptance Sampling Plans for Family Pareto Distributions, Research Journal of Applied Sciences, Engineering and Technology 6(24), 4646-4652.
  • [13] Rosaiah, K. and Kantam, R.R.L. (2005) Acceptance sampling based on the inverse Rayleigh distribution, Economic Quality Control, 20(2), 277-286.
  • [14] Rao, B.S., Kumar, S.C.H. and K. Rosaiah, S. (2013) Acceptance Sampling Plans from Life Tests Based on Percentiles of Half Normal Distribution, Journal of Quality and Reliability Engineering, Article ID 302469, 1-7.
  • [15] Srinivasa Rao, G. (2011) A Hybrid Group Acceptance Sampling Plans For Lifetimes Based On Log-Logistic Distribution, Journal of Reliability and Statistical Studies; 4(1), 31- 40.
  • [16] Singh, S. and Tripathi, Y.M. (2015) Acceptance sampling plan for inverse Weibull distribution based on truncated life tests, DOI:10.13140/RG.2.1.3984.0085.
  • [17] Sudamani A.R. and Anburajan, P. (2012) Group Acceptance Sampling Plans using Weighted Binomial on Truncated Life Tests for Inverse Rayleigh and Log-Logistic Distributions, Journal of Mathematics, 2(3), 33-38.

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

Yıl 2018, Cilt: 11 Sayı: 2, 143 - 155, 31.12.2018

Öz

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.

Kaynakça

  • [1] Amer Ibrahim Al-Omari (2018), Acceptance sampling plans based on truncated life tests for Sushila distribution J. Math. Fund. Sci., 50(1), 72-83.
  • [2] Aslam, M., Kundu, D. and Ahmad, M. (2010) Time truncated acceptance sampling plans for generalized exponential distribution, Journal of Applied Statistics, 37(4), 555-566.
  • [3] Aslam, M. and Jun, C.H. (2013) Designing of time truncated acceptance sampling plans by using two-point approach, Electronic Journal of Applied Statistical Analysis, 6(1), pp. 18-31.
  • [4] Balakrishnan, N., Leiva, V. and Lopez, J. (2007) Acceptance sampling plans for truncated life tests based on the generalized Birnbaum-Saunders distribution, Communications in Statistics-Simulation and Computation, 36, 643-656.
  • [5] Baklizi, A (2003). Acceptance sampling based on truncated life tests in the Pareto distribution of the second kind, Advances and Applications in Statistics, 3(1), 33-48.
  • [6] Epstein, B. (1954) Truncated life tests in the exponential case. Annals of Mathematical Statistics, 25, 555-564.
  • [7] Gui, W. and Shangli Zhang, S. (2014) Acceptance sampling plans based on truncated life tests for Gompertz Distribution, Journal of Industrial Mathematics, Vol. 2014, Article ID 391728, 7 pages. https://doi.org/10.1155/2014/391728 .
  • [8] Loganathan, A. and Gunasekaran, M. (2017) Determination of reliability single sampling plans based on exponentiated distribution, Global and Stochastic Analysis, 4(1), 111-118.
  • [9] Malathi, D. and Muthulakshmi, S. (2015) Acceptance sampling plan for the truncated life tests based on Gompertz distribution using mean, International Journal of Scientific and Engineering Research, 6(8), 1828-1841.
  • [10] Malathi, D. and Muthulakshmi, S. (2016) Truncated life test acceptance sampling plans assuring percentile life under Gompertz distribution, IOSR-Journal of Mathematics,12(2), 27-32.
  • [11] Malathi, D. and Muthulakshmi, S. (2015) Acceptance sampling plan for truncated life tests based on Frechet distribution using median, International Journal of Advancement in Research and Technology, 4(8), 1-13.
  • [12] Mughal, A.R. and Ismail, M. (2013) An Economic Reliability Efficient Group Acceptance Sampling Plans for Family Pareto Distributions, Research Journal of Applied Sciences, Engineering and Technology 6(24), 4646-4652.
  • [13] Rosaiah, K. and Kantam, R.R.L. (2005) Acceptance sampling based on the inverse Rayleigh distribution, Economic Quality Control, 20(2), 277-286.
  • [14] Rao, B.S., Kumar, S.C.H. and K. Rosaiah, S. (2013) Acceptance Sampling Plans from Life Tests Based on Percentiles of Half Normal Distribution, Journal of Quality and Reliability Engineering, Article ID 302469, 1-7.
  • [15] Srinivasa Rao, G. (2011) A Hybrid Group Acceptance Sampling Plans For Lifetimes Based On Log-Logistic Distribution, Journal of Reliability and Statistical Studies; 4(1), 31- 40.
  • [16] Singh, S. and Tripathi, Y.M. (2015) Acceptance sampling plan for inverse Weibull distribution based on truncated life tests, DOI:10.13140/RG.2.1.3984.0085.
  • [17] Sudamani A.R. and Anburajan, P. (2012) Group Acceptance Sampling Plans using Weighted Binomial on Truncated Life Tests for Inverse Rayleigh and Log-Logistic Distributions, Journal of Mathematics, 2(3), 33-38.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Canan Hamurkaroğlu 0000-0002-8537-513X

Ayten Yiğiter 0000-0001-8180-995X

Yasemin Gençtürk Bu kişi benim 0000-0002-8916-8509

Yayımlanma Tarihi 31 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 2

Kaynak Göster

IEEE C. Hamurkaroğlu, A. Yiğiter, ve Y. Gençtürk, “Weibull ve Pareto dağılımları için tip-I sansürleme düzeninde kesilmiş yaşam testine dayalı tek katlı ve grup kabul örnekleme planlar”, JSSA, c. 11, sy. 2, ss. 143–155, 2018.