Discrete time shock model with varying success probability

Objective & Hypothesis:Let us consider a system fails when the time between two consecutive shocks falls below a fixed threshold $\delta \in N$ and the system's lifetime is measured as the time up to the occurrence of this event.

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Key Findings & Data:In this paper, we consider the interarrival times between $(i-1)$ i-th and $i$- th successive shocks follow a geometric distribution with mean 1/pi ,where pi =theta*pi-1, i=1,2,..., ,0<theta<1, 0<p<1.

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Conclusion & Impact:A numerical example is also presented buy using real data.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:q-distributions · delta-Shock model · probabilty generating function

Abstract

Let us consider a system fails when the time between two consecutive shocks falls below a fixed threshold $\delta \in N$ and the system's lifetime is measured as the time up to the occurrence of this event. In this paper, we consider the interarrival times between $(i-1)$ i-th and $i$- th successive shocks follow a geometric distribution with mean 1/pi ,where pi =theta*pi-1, i=1,2,..., ,0<theta<1, 0<p<1. Under the above considerations, the distribution of system lifetime is obtained. Probability generating function and than also moments of system are derived. The proportion estimates of distribution parameters are studied. A numerical example is also presented buy using real data.

Keywords

q-distributions delta-Shock model probabilty generating function

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Cite This Article

KARAKAYA, K., AKDOĞAN, Y., ŞAHİN, F., KINACI, İ., KUŞ, C. (2019). Discrete time shock model with varying success probability. Türkiye İstatistik Derneği İstatistik Dergisi, Cilt: 12 - Sayı: 1, 13–24. https://ajindex.com/articles/812556

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