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by F Rigat, A Mira

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Hao-Wei Wang , Ke-Nan Teng
, 2016

"... Residual life pRediction foR highly ..."

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... σ( ) ( , , |) |=∆ ∆X X2 2 0 r rd d+∞ −∞ +∞ ∫∫ (7) π σ π µ σ µ( ) ( , , |)2 2 |=∆ ∆X Xr rd d −∞ +∞ −∞ +∞ ∫∫ (8) π π µ σ µ σ( ) ( , , |)r r |=∆ ∆X X2 2 0 d d −∞ +∞+∞ ∫∫ (9) Furthermore, the expectations of of µ|∆X , σ 2|∆X and r|∆X can be calculated as: |( |E( ) )dµ µ π µ µ+∞ −∞ ∆ = ⋅ ∆∫X X (10) E d( ) ( )σ σ π σ σ2 2 0 2 2 ||∆ ∆X X= +∞∫ (11) E d( ) ( )r r r r ||∆ ∆X X= ⋅ −∞ +∞ ∫ π (12) Generally, it is difficult to evaluate E( )µ|∆X , E( )σ 2|∆X and |E( )r ∆X through direct mathematical calculation. One alternative method is using Markov Chain Monte Carlo (MCMC) simulation with Gibbs sampling [16, 20], we implemented the method in WinBUGS. Replace µ σ, ,Λ with E( )µ|∆X , E( )σ 2|∆X and |E( )r ∆X in Eq. (4) and Eq. (5), the posterior PDF of RL and the posterior expectation of RL can be obtained. There will be more field degradation data available as the individual product works over time. Once new degradation data is available, E( )µ|∆X , E( )σ 2|∆X and E( )r|∆X are immediately updated. So the RL of an individual can be real-time predicted. 3. Evaluate the prior distributions of random parameters Before predicting RL using Bayesian method, the joint prior PDF π µ σ( , , )2 r need be evaluat...

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