Question 2.5: The reliability function for a system is assumed to be an ex......
The reliability function for a system is assumed to be an exponential distribution (see Chapter 3) and is given by
R(t)=e^{-\lambda_o t},
where \lambda_{0} is a constant (i.e., a constant hazard rate).
Calculate the reliability of the system for mission time, t, given that the system has already been used for 10 years
Step-by-Step
Using Equation 2.39
R(t, 10)=\frac{R(t+10)}{R(10)}=\frac{e^{-\lambda_0(t+10)}}{e^{-\lambda_0 10}}=e^{-\lambda_0 t}=R(t) .R\left(t, t_1\right)=\frac{R\left(t+t_1\right)}{R\left(t_1\right)} (2.39)
That is, the system reliability is “as good as new,” regardless of the age of the system.
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