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

Area of Science:

• Reliability Engineering
• Probability Theory
• Stochastic Processes

Background:

• Systems are often subject to sequences of random shocks.
• Understanding system failure under these conditions is crucial for design and maintenance.
• Existing models may not capture abrupt changes in shock behavior.

Purpose of the Study:

• To investigate the reliability properties of a system subjected to shock sequences.
• To introduce and analyze a novel change point model for shock magnitudes.
• To determine system survival functions under different inter-shock time distributions.

Main Methods:

• Development of a new change point model where shock distribution changes after a critical shock.
• Analysis of system failure conditions: time between shocks below a threshold or single shock magnitude above a threshold.
• Derivation of survival functions for both discrete and continuous inter-shock time distributions.

Main Results:

• The study provides a framework for analyzing system reliability under a dynamic shock environment.
• Matrix-based expressions are derived for reliability calculations in both discrete (matrix-geometric) and continuous (matrix-exponential) cases.
• The model captures the impact of critical shock events on system degradation.

Conclusions:

• The proposed change point model offers a more realistic approach to system reliability analysis under shocks.
• The derived matrix-based expressions facilitate quantitative assessment of system survival probabilities.
• This research contributes to the field of reliability engineering by providing new analytical tools for complex shock environments.