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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Optimal replacement time is also studied.
📌 3 Key Takeaways
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Objective & Hypothesis:Phase-type distributions have been found to be very useful in reliability, queueing theory, and some other operational research applications.
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Key Findings & Data: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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Conclusion & Impact:Optimal replacement time is also studied.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:. 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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Cite This Article
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