PARAMETER ESTIMATION FOR A K-UNIT SERIES SYSTEM BASED ON THE PROGRESSIVELY CENSORED ERLANG-TRUNCATED EXPONENTIAL DATA WITH BINOMIAL REMOVALS

Yıl 2021, Cilt: 3 Sayı: 1, 59 - 71, 30.06.2021

Çağatay Çetinkaya

https://doi.org/10.51541/nicel.904461

Öz

This study deals with point and interval estimations for the scale and shape parameters of the component lifetime distribution of a k-component series system when the component lifetimes are assumed to be independently and identically Erlang-truncated exponential distributions. It is assumed that the components are exposed to progressive Type-II censoring scheme. Each failure in this censoring plan is assumed to be random and subject to the binomial distribution. Parameter estimations are obtained by using the maximum likelihood method and their approximate confidence intervals are obtained by using the bootstrap method. The simulations are performed to evaluate the performances of the theoretical outcomes.

Anahtar Kelimeler

Bootstrap, Erlang-Truncated Exponential Distribution, Maximum Likelihood, Progressive Censoring, Series system

BİNOM KALDIRMALAR İLE AŞAMALI SANSÜRLENMİŞ ERLANG-KESİLMİŞ ÜSTEL VERİLERE DAYALI BİR K-BİRİMLİ SERİ SİSTEM İÇİN PARAMETRE TAHMİNİ

Öz

Bu çalışma, bileşen ömürlerinin bağımsız ve özdeş Erlang kesilmiş üstel dağılımına sahip olduğu varsayıldığında, bir k-bileşenli seri sistemin bileşen ömrü dağılımının ölçek ve şekil parametrelerinin parametre tahminlerini ele almaktadır. Bileşenlerin aşamalı Tip-II sansürleme şemasına maruz kaldığı varsayılmaktadır. Bu sansürleme planındaki her bir başarısızlığın rastgele olduğu ve binom dağılımına sahip olduğu varsayılır. Parametre tahminleri, maksimum olabilirlik yöntemi kullanılarak, yaklaşık güven aralıkları ise bootstrap yöntemi kullanılarak elde edilmiştir. Teorik sonuçların performanslarını değerlendirmek için simülasyon çalışmaları uygulanmıştır.

Anahtar Kelimeler

Bootstrap, Erlang Kesilmiş Üstel Dağılım, En Çok Olabilirlik, Aşamalı Sansürleme, Seri Sistem

Kaynakça

• Balakrishnan, N. and Sandhu, R. A. (1995), A simple simulational algorithm for generating progressive Type-II censored samples, The American Statistician, 49(2), 229-230.
• El-Alosey, A. R. (2007), Random sum of new type of mixture of distribution, International Journal of Statistics and Systems, 2(1), 49-57.
• Elbatal, I. and Elgarhy, M. (2020), A new generalization of erlang-truncated exponential distribution: properties and applications. Advances and Applications in Statistics, 64(1), 63-74.
• Efron, B. and Tibshirani, R. J. (1994), An introduction to the bootstrap, CRC press.
• Epstein, B. (1954), Truncated life tests in the exponential case, The Annals of Mathematical Statistics, 555-564.
• Gadde, S. R. (2017), Reliability estimation in multicomponent stress-strength based on Erlang-truncated exponential distribution. International Journal of Quality & Reliability Management.
• Jimoh, H., Oluyede, B. O., Wanduku, D. and Makubate, B. (2019), The gamma log-logistic Erlang truncated exponential distribution with applications, Afrika Statistika, 14(4), 2141-2164.
• Khan, R. U., Kumar, D. and Athar, H. (2010), Moments of generalized order statistics from Erlang-truncated exponential distribution and its characterization, International Journal of Statistics and System, 5(4), 455-464.
• Kulshrestha, A., Khan, R. U. and Kumar, D. (2013), On moment generating functions of generalized order statistics from Erlang-truncated exponential distribution, Open J. Statist, 2, 557-564.
• Kumar, D. (2014a), Quotient Moments of the Erlang-truncated Exponential Distribution Based on Record Values and a Characterization. Journal of applied mathematics & informatics, 32(1_2), 7-16.
• Kumar, D. (2014b), Relations of generalized order statistics from Erlang-Truncated exponential distribution, Pacific Journal of Applied Mathematics, 6(1), 53.
• Malik, M. R. and Kumar, D. (2017), Relations for moments of progressively type-II Right censored order statistics from Erlang-truncated exponential distribution, Statistics, 651.
• Mohsin, M. (2009), Recurrence relation for single and product moments of record values from Erlang-truncated exponential distribution, World Applied Science Journal, 6(2), 279-282.
• Mubarak, M. (2012), Parameter estimation based on the Frechet progressive type II censored data with binomial removals, Journal of Quality and Reliability Engineering, 2012.
• Nasiru, S., Luguterah, A. and Iddrisu, M. M. (2016), Generalized Erlang-truncated exponential distribution.
• Okorie, I. E., Akpanta, A. C., Ohakwe, J. and Chikezie, D. C. (2017a), The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data, Heliyon, 3(6), e00296.
• Okorie, I. E., Akpanta, A. C. and Ohakwe, J. (2017b), Marshall-Olkin generalized Erlang-truncated exponential distribution: Properties and applications, Cogent Mathematics & Statistics, 4(1), 1285093.
• Okorie, I. E., Akpanta, A. C. and Ohakwe, J. (2016), Transmuted Erlang-truncated exponential distribution. Stochastics and Quality Control, 31(2), 71-84.
• Rao, G. S. (2013), One-sided cumulative sum (CUSUM) control charts for the Erlang-truncated exponential distribution, Computational Methods in Science and Technology, 19(4), 229-234.
• Sarana, J., Vermaa, K. and Pushkarnaa, N. (2018), Relationships for moments of generalized order statistics from Erlang-truncated exponential distribution and related inference. In ProbStat Forum (11), 91-103.
• Smith, P. J. (2017), Analysis of failure and survival data. CRC Press.
• Tse, S. K., Yang, C. and Yuen, H. K. (2000), Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals. Journal of Applied Statistics, 27(8), 1033-1043.
• Yan, W., Shi, Y., Song, B. and Mao, Z. (2011), Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals, Journal of Systems Engineering and Electronics, 22(4), 707-714.
• Wu, S. J. and Chang, C. T. (2002). Parameter estimations based on exponential progressive type II censored data with binomial removals. International journal of information and management sciences, 13(3), 37-46.