MODEL SELECTION IN THE NON-HOMOGENEOUS POISSON PROCESS FOR THE RELIABILITY OF A MACHINE

Yıl 2025, Cilt: 66 Sayı: 719, 239 - 252, 30.06.2025

Ayse T. Bugatekin

https://doi.org/10.46399/muhendismakina.1728546

Öz

Model selection plays an important role, especially in critical areas such as reliability analysis. Non-homogeneous Poisson process (NHPP) is a statistical approach widely used to model the frequency of time-dependent events. In such processes, correct model selection is vital to effectively evaluate the performance and reliability of the system. In this study, two basic models frequently used in NHPP, the power law model and the log-linear model, are compared. The research focuses on the reliability of ATM machines of a bank. The reliability performance and expected failure numbers of both models are calculated using the data between the failure times of ATMs. In the study, the predictive power and accuracy of the models are compared; their suitability to real data is evaluated with statistical methods. The obtained results are compared and it is decided which model is a better choice.

Anahtar Kelimeler

Distributions , maximum likelihood method , log-linear model , non-homogeneous , poisson process , power law model

BİR MAKİNENİN GÜVENİLİRLİĞİ İÇİN HOMOJEN OLMAYAN POİSSON SÜRECİNDE MODEL SEÇİMİ

Öz

Model seçimi, özellikle güvenilirlik analizi gibi kritik alanlarda önemli bir rol oynar. Homojen olmayan Poisson süreci (NHPP), zamana bağlı olayların sıklığını modellemek için yaygın olarak kullanılan istatistiksel bir yaklaşımdır. Bu tür süreçlerde doğru model seçimi, sistemin performansını ve güvenilirliğini etkili bir şekilde değerlendirmek için hayati önem taşır. Bu çalışmada, NHPP'de sıkça kullanılan iki temel model, kuvvet yasası modeli ve log-lineer model, karşılaştırılmıştır. Araştırma kapsamında bir bankanın ATM makinelerinin güvenilirliği üzerine odaklanılmıştır. ATM’lerin arıza süreleri arasındaki veriler kullanılarak her iki modelin güvenilirlik performansı ve beklenen arıza sayıları hesaplanmıştır. Çalışmada, modellerin tahmin gücü ve doğruluğu kıyaslanmış; gerçek verilere uygunlukları istatistiksel yöntemlerle değerlendirilmiştir. Elde edilen sonuçlar karşılaştırılarak hangi modelin daha iyi bir seçim olduğuna karar verilmiştir.

Anahtar Kelimeler

Dağılımlar , Maksimum olabilirlik metodu , log-lineer model , homojen olmayan poisson süreci , kuvvet yasası modeli.

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