The classical, meta-heuristic and EM algorithms for the estimation of the KM-Weibull distribution under progressively first-failure censoring

Sert, Sümeyra; Abusaif, Ihab; Pekgör, Ahmet; Karakaya, Kadir; Kuş, Coşkun

doi:10.47974/JSMS-1199

Open Access Research Article

The classical, meta-heuristic and EM algorithms for the estimation of the KM-Weibull distribution under progressively first-failure censoring

^*Sümeyra SertCorresponding authorsumeyra.sert@selcuk.edu.trDepartment of Statistics Faculty of Science Selçuk UniversityKonya, 42250, Turkey0000-0002-4647-1583View full profile → , Ihab Abusaifcenstat@gmail.comDepartment of Statistics Faculty of Science Selçuk UniversityKonya, 42250, Turkey0000-0002-6255-1268View full profile → , Ahmet Pekgörapekgor@erbakan.edu.trDepartment of Statistics Faculty of Science Necmettin Erbakan UniversityKonya, 42090, Turkey0000-0001-9446-7960View full profile → , Kadir Karakayakkarakaya@selcuk.edu.trDepartment of Statistics Faculty of Science Selçuk UniversityKonya, 42250, Turkey0000-0002-0781-3587View full profile → , Coşkun Kuşcoskun@selcuk.edu.trDepartment of Statistics Faculty of Science Selçuk UniversityKonya, 42250, Turkey0000-0002-7176-0176View full profile →

* Corresponding author · click or hover a name for details

pp. 277–307Vol. 28Issue 2March 2025DOI: 10.47974/JSMS-1199XML

Received:: 08 Feb 2023
Published Online:: 01 Mar 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1199
Pages:: 277–307

Abstract

In life testing, collecting data is difficult for high-technology products since they are too expensive and have long lifetimes. From this perspective, some censoring schemes are introduced, and the most popular one is the progressive censoring scheme. Recently, this scheme has also been modified and called a progressively-first-failure censoring scheme. This scheme allows lifetimes in short time intervals, even if the products are highly reliable. On the other hand, the maximum likelihood estimation cannot be obtained explicitly in many cases when the data are censored. Therefore, the estimates are obtained via numerical methods. One of the most important problems is determining the initial values for these numerical searching methods. Nowadays, meta-heuristic algorithms become popular for the optimization of a function. In this regard, these algorithms are being used to maximize the likelihood functions in the statistical theory. In this study, we considered the estimation problem for the KM-Weibull distribution under a progressively-first-failure censoring scheme. The fixed point iteration and Expectation-Maximization (EM) algorithms are also derived. Meta-heuristic algorithms and classical methods like Nelder-Mead, BFGS, etc. are employed to maximize the likelihood estimation of unknown parameters. The performances of all methods are compared with a simulation study. The methodology is exemplified through the inclusion of a numerical illustration.

Keywords

EM algorithm First-failure censoring sampling plan KM-Weibull distribution Maximum likelihood estimator Meta-heuristic algorithms Optimization

Subject Classifications

62N0265K9968W50

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