From: Reliability analysis of subway vehicles based on the data of operational failures
Subsystem | Failure density function | Cumulative distribution function |
---|---|---|
Running gear | \( f(t)=\frac{0.9124}{13.5450}{\left(t/13.5450\right)}^{\hbox{-} 0.0876}\exp \left[-{\left(t/13.5450\right)}^{0.9124}\right] \) | F(t) = 1 − exp[−(t/13.5450)0.9124] |
Traction system | \( f(t)=\frac{0.9940}{10.6495}{\left(t/10.6495\right)}^{-0.006}\exp \left[-{\left(t/10.6495\right)}^{0.9940}\right] \) | F(t) = 1 − exp[−(t/10.6495)0.9940] |
Brake system | \( f(t)=\left\{\begin{array}{l}\frac{1}{1.3003\sqrt{2\pi }t}{e}^{\frac{{\left(\ln t-2.3693\right)}^2}{2\times {1.3003}^2}},t>0\\ {}0,t=0\end{array}\right. \) | \( F(t)=\Phi \left(\frac{\ln t-2.3693}{1.3003}\right) \) |
Control and diagnostic system | \( f(t)=\left\{\begin{array}{l}\frac{1}{1.3581\sqrt{2\pi }t}{e}^{\frac{{\left(\ln t-2.5573\right)}^2}{2\times {1.3581}^2}},t>0\\ {}0,t=0\end{array}\right. \) | \( F(t)=\Phi \left(\frac{\ln t-2.5573}{1.3581}\right) \) |
Auxiliary system | \( f(t)=\left\{\begin{array}{l}\frac{1}{0.9349\sqrt{2\pi }t}{e}^{\frac{{\left(\ln t-1.4915\right)}^2}{2\times {0.9349}^2}},t>0\\ {}0,t=0\end{array}\right. \) | \( F(t)=\Phi \left(\frac{\ln t-1.4915}{0.9349}\right) \) |