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《Journal of Fujian Normal University(Natural Science Edition)》 1982-02
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Reliability Analysis of a Two-Unit Series System

Shi Dinghua Shanghai Inst. of Railway Techn.  
This paper deals with a two-unit series system with a single repair facility. It is assumed that: (1) Unit 1 has exponential failure distribution F_1(t)=1-e~(-λ)1~τ, and arbitrary repair time distribution G_1(t)=integral from n=0 to f(g_1(x)dx); (2) Unit 2 has arbitrary failure distribution F_2(t)=integral from n=0 (f2(x)dx), and arbitrary re- pair time distribution G_2(t)=integral n=0 to (g_2(x)dx). By using the supplementary variable method, the following operating characteris- tics are obtained: (1) expression for the Laplace transformation of availability A(s)==1/s+λ_1[1-g_1(s)]+[1-g_2(s)]H(s) (2) expression for the Laplace-Stieltjes transformation of the expected number of system failure in the interval(o, t) m(s)=[λ_1+H(s)]A(s) where H(s)[s+λ_1-λ_1g_1(s)]·f_2[s+λ_1-λ_1g_1(s)]/1-f_2[s+λ_1-λ_g_1(s)]
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