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

Year 2021, Volume: 3 Issue: 1, 59 - 71, 30.06.2021

Çağatay Çetinkaya

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

Abstract

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.

Keywords

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

Abstract

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.

Keywords

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

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