A Data-Driven Reliability Estimation Approach for Phased-Mission Systems

Algorithm 1

Kalman filtering algorithm.

Step  1. Initialize 𝜆₀, 𝑃₀.

Step  2. State estimation at time 𝑡_𝑖

       𝑃_{𝑖∣𝑖−1}=𝑃_{𝑖−1∣𝑖−1}+𝑄

       𝐾_𝑖=(𝑡_𝑖−𝑡_𝑖−1)²𝑃_{𝑖∣𝑖−1}+𝜎²(𝑡_𝑖−𝑡_𝑖−1)

       𝜆_𝑖=𝜆_𝑖−1+𝑃_{𝑖∣𝑖−1}𝑡_𝑖−𝑡_𝑖−1𝐾_𝑖⁻¹𝑦_𝑖−𝑦_𝑖−1−𝜆_𝑖−1𝑡_𝑖−𝑡_𝑖−1

Step  3. Updating variance 𝑃_𝑖∣𝑖=𝑃_{𝑖∣𝑖−1}−𝑃_{𝑖∣𝑖−1}(𝑡_𝑖−𝑡_𝑖−1)²𝐾_𝑖⁻¹𝑃_{𝑖∣𝑖−1}