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Dergiler / Journal of Universal Mathematics / 2019 / Cilt: 2 - Sayı: 1

AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL

Mustafa TEKİN
Serkan ERYILMAZ
Sayfa
16–21
Yayın Tarihi
2019-01-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Optimal replacement time is also studied.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Phase-type distributions have been found to be very useful in reliability, queueing theory, and some other operational research applications.
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Temel Bulgular & Veri:The system under concern fails upon the occurrence of k consecutive shocks of size at least d1 or a single large shock of size at least d2, d1 < d2.
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Sonuç & Katkı:Optimal replacement time is also studied.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:. Reliability · Shock models · Phase type distribution

Abstract

Phase-type distributions have been found to be very useful in reliability, queueing theory, and some other operational research applications. In this work, we de_ne a new mixed shock model and study lifetime properties of the corresponding system using phase-type distributions. The system under concern fails upon the occurrence of k consecutive shocks of size at least d1 or a single large shock of size at least d2, d1 < d2. In particular, using closure properties of phase-type distributions, we obtain survival function and mean time to failure of the system. Optimal replacement time is also studied.

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Bu Makaleye Atıf Yap

TEKİN, M., ERYILMAZ, S. (2019). AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. Journal of Universal Mathematics, Cilt: 2 - Sayı: 1, 16–21. https://ajindex.com/articles/782224

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Kaynakça (5)

  1. Neuts, M. F., Meier, K. S., On the use of phase type distributions in reliability modelling of systems with two components. OR Spektrum, 2(4), 227-234, 1981Ahmad R., Kamarudin S., An overview of time-based and condition-based maintenance in industrial application, Computers & Industrial Engineering 63(1), 135-149, 2012
  2. Gut, A. Mixed shock models, Bernoulli 7(3), 541-555, 2001.
  3. He, Q. M., Fundamentals of Matrix-Analytic Methods. NewYork: Springer, 22-43, 2014
  4. Eryilmaz, S., Computing optimal replacement time and mean residual life in reliability shock models Computers & Industrial Engineering, 103, 40-45, 2017.
  5. Eryilmaz, S. and Tekin, M., Reliability evaluation of a system under a mixed shock model, 2018, submitted for publication.