A.2. Example of a Multi-State Deterioration model with three states 201 By replacing u(t)=1/R(t), and considering that R(t =0)=1 and SB(t =0)= SB(0) we find that C↓ =SB(0). Also, considering ϖA,B(t)=→R↑A,B(t)/RA,B(t) and SA(t)=SA(0)RA,B(t), we get: SB(t)=RB,C(t) t 0 1 RB,C(ϱ) ϖA,B(ϱ)SA(ϱ)dϱ +SB(0) SB(t)=RB,C(t)→SA(0) t 0 1 RB,C(ϱ) R↑A,B(ϱ) RA,B(ϱ) RA,B(ϱ)dϱ +SB(0) SB(t)=RB,C(t)SB(0) →SA(0) t 0 R↑A,B(ϱ) RB,C(ϱ) dϱ (A.15a) Finally, we find SC(t) following a similar process, we provide below the result: SC(t)= t 0 R↑B,C(ϱ)SA(0) t 0 R↑A,B(u) RB,C(u) du→SB(0)dϱ +SC(0) (A.16)
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