Α new mixed δ-shock model with a change in shock distribution

• Published in: TOP Vol. 31; no. 3; pp. 491 - 509
• Main Authors: Chadjiconstantinidis, Stathis, Tuncel, Altan, Eryilmaz, Serkan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023; Springer Nature B.V
• Subjects: Business and Management; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Industrial and Production Engineering; Insurance; Management; Operations Research/Decision Theory; Optimization; Original Paper; Statistics for Business; Delta shock model; Matrix-geometric distributions; Mixed shock model; Matrix-exponential distributions; Primary 62N05; Reliability; Secondary 62E15
• ISSN: 1134-5764; 1863-8279; 1863-8279
• DOI: 10.1007/s11750-022-00649-x

In this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.