Weibull Dağılımının Parametrelerini Tahmin Etmek için Kaotik Parçacık Sürüsü Optimizasyon Algoritmasının Uygulanması

Öz

Güvenilirlik ve yaşam süresi çalışmaları gibi çeşitli disiplinlerde en iyi bilinen ve yaygın olarak kullanılan dağılımlardan biri olduğu için Weibull dağılımının parametrelerinin istatistiksel çıkarımları üzerine çok sayıda çalışma yapılmıştır. Maksimum olabilirlik, bilinmeyen parametrelerin tahmin sürecinde yaygın olarak kullanılan bir yöntem olmasına rağmen, üç parametreli Weibull dağılımı gibi bazı dağılımlar için, olabilirlik fonksiyonunu maksimize ederek parametreleri tahmin etmek oldukça zordur. Bu sorunu ele almak ve daha iyi sonuçlar elde etmek amacıyla Parçacık Sürü Optimizasyonu (PSO) algoritması incelenmektedir. Ancak, iyi sonuçlar elde etmek ve PSO’nun performansını artırmak için algoritma için farklı parametre değerlerinin ayarlanması gerekmektedir. Bu bağlamda, arama sürecini önemli ölçüde etkileyen atalet ağırlığının belirlenmesi oldukça önemlidir. Bu makalede bir yenilik olarak, PSO’nun yakınsamasını etkileyen faktör olan eylemsizlik ağırlığı için kaotik haritalarele alınmış ve üç parametreli Weibull dağılımının farklı parametre değerlerinin tahmini için ayrıntılı olarak incelenmiştir. Önerilen yöntemin etkinliği kapsamlı bir Monte-Carlo simülasyon analizi ile araştırılmıştır. Simülasyon bulguları, önerilen kaotik harita yaklaşımının klasik doğrusal azalan eylemsizlik ağırlıklarından daha iyi performansa sahip olduğunu göstermektedir.

Anahtar Kelimeler

• Kaotik harita
• parçacık sürüsü optimizasyonu
• weibull dağılımı
• maksimum olabilirlik

Implementation of a Chaotic Particle Swarm Optimization Algorithm to Estimate the Parameters of Weibull Distribution

Öz

Numerous studies on the statistical inferences of the Weibull distribution’s parameters have been performed because it is among the most well-known and widely applied distributions in several fields, including lifetime studies and reliability. Although maximum likelihood is a widely used method in the estimation process of unknown parameters, estimating the parameters by maximizing the likelihood function is very challenging for some distributions, like the three-parameter Weibull distribution. The Particle Swarm Optimization (PSO) algorithm is examined in order to address this issue and achieve improved outcomes. However, different parameter values for the algorithm need to be adjusted to achieve good results and increase the performance of PSO. In this context, it is very important to determine the inertia weight, which significantly affects the search process. As a novelty in this paper, chaotic maps for the inertia weight, which is the factor affecting the convergence of the PSO, are examined in detail for the estimation of different parameter values of the three-parameter Weibull distribution. The effectiveness of the suggested method is investigated by a thorough Monte-Carlo simulation analysis. The simulation findings demonstrate that the proposed chaotic map approach outperforms the classic linear decreasing inertia weights.

Anahtar Kelimeler

• Chaotic map
• particle swarm optimization
• weibull distribution
• maximum likelihood

Etik Beyan

The author(s) of this manuscript declare that the materials and methods used in their studies do not require ethics committee approval and/or legal-specific permission.

Teşekkür

The authors would like to thank Gazi University Academic Writing Application and Research Center for proofreading the article.

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