On properties of the phase-type mixed Poisson process and its applications to reliability shock modeling

DOI10.1007/S11009-022-09961-2OpenAlexW4283010993MaRDI QIDQ2684950

Nil Kamal Hazra, Dheeraj Goyal, Maxim Finkelstein

Publication date: 17 February 2023

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-022-09961-2

zbMATH Keywords

phase-type distributionshock modelsnon-homogeneous Poisson processmixed Poisson process

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Probability distributions: general theory (60E05) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

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• On the exact solution of a generalized Pólya process
• The structure distribution in a mixed Poisson process
• Stochastic orders
• Semi-Markov chains and hidden semi-Markov models toward applications. Their use in reliability and DNA analysis.
• Point processes with finite-dimensional conditional probabilities
• Reliability evaluation of a system under a mixed shock model
• Some results and applications of geometric counting processes
• Nonstationary shock models
• A shock model for the maintenance problem of a repairable system
• Poisson Lindley process and its main properties
• Realistic variation of shock models
• Life behavior of \(\delta\) -shock model
• Shocks, runs and random sums
• Fundamentals of Matrix-Analytic Methods
• Characterization of the Generalized Pólya Process and its Applications
• General shock models associated with correlated renewal sequences
• Distribution properties of the system failure time in a general shock model
• Stochastic Processes in Science, Engineering and Finance
• Cumulative shock models
• A versatile Markovian point process
• Renewal Approximations of the Switched Poisson Processes and Their Applications to Queueing Systems
• Repairable models with operating and repair times governed by phase type distributions
• On a Terminating Shock Process with Independent Wear Increments
• On New Classes of Extreme Shock Models and Some Generalizations
• Extreme shock models
• Semi-Markov processes and reliability

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