Table 3 The reliability characteristic functions of each subsystem
From: Reliability analysis of subway vehicles based on the data of operational failures
Subsystem | Reliability function | Failure rate function | Average life (days) |
|---|---|---|---|
Running gear | R(t) = exp[−(t/13.5450)0.9124] | \( \lambda (t)=\frac{0.9124}{13.5450}{\left(t/13.5450\right)}^{\hbox{-} 0.0876} \) | 14 |
Traction system | R(t) = exp[−(t/10.6495)0.9940] | \( \lambda (t)=\frac{0.9940}{10.6495}{\left(t/10.6495\right)}^{-0.006} \) | 11 |
Brake system | \( R(t)=1\hbox{-} \Phi \left(\frac{\ln t-2.3693}{1.3003}\right) \) | \( \lambda (t)=\frac{\frac{1}{1.3003\sqrt{2\pi }t}{e}^{\frac{{\left(\ln t-2.3693\right)}^2}{2\times {1.3003}^2}}}{1-\Phi \left(\frac{\ln t-2.3693}{1.3003}\right)} \) | 25 |
Control and diagnostic system | \( R(t)=1\hbox{-} \Phi \left(\frac{\ln t-2.5573}{1.3581}\right) \) | \( \lambda (t)=\frac{\frac{1}{1.3581\sqrt{2\pi }t}{e}^{\frac{{\left(\ln t-2.5573\right)}^2}{2\times {1.3581}^2}}}{1-\Phi \left(\frac{\ln t-2.5573}{1.3581}\right)} \) | 32 |
Auxiliary system | \( R(t)=1\hbox{-} \Phi \left(\frac{\ln t-1.4915}{0.9349}\right) \) | \( \lambda (t)=\frac{\frac{1}{0.9349\sqrt{2\pi }t}{e}^{\frac{{\left(\ln t-1.4915\right)}^2}{2\times {0.9349}^2}}}{1-\Phi \left(\frac{\ln t-1.4915}{0.9349}\right)} \) | 7 |