Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps.

Area of Science:

• Reliability Engineering
• Stochastic Processes
• Degradation Modeling

Background:

• Degradation trajectories often exhibit multi-phase features with abrupt jumps due to changing operating conditions or physical mutations.
• Traditional lifetime estimation methods are inadequate for processes with such complex degradation patterns.

Purpose of the Study:

• To develop a robust method for estimating the lifetime of multi-phase degradation processes with abrupt jumps.
• To extend existing models to account for unit-to-unit variability and complex multi-phase behaviors.

Main Methods:

• Formulation of a multi-phase degradation model with jumps based on the Wiener process.
• Derivation of a closed-form expression for lifetime in a two-phase model with fixed jumps.
• Extension of the model to incorporate random effects and further phases.
• Development of a model identification method using Expectation Maximization (EM) algorithm and Bayesian rule.

Main Results:

• A novel Wiener process-based model effectively describes multi-phase degradation with abrupt jumps.
• Closed-form lifetime expressions were derived for simplified and extended cases.
• An effective model identification method was proposed for practical implementation.

Conclusions:

• The proposed approach provides a reliable framework for lifetime estimation in complex degradation scenarios.
• The methods are applicable to systems with unit-to-unit variability and multi-phase degradation patterns.
• Demonstrated utility through numerical case studies and a practical gyro example.