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Series Systems RBD |
This example validates the results for series systems in BlockSim's analytical and simulation diagrams.
Reference Case
The data set is from example 4.2 on page 69 in the book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.
Data
The lifetimes of the body, powertrain, electrical and chassis subsystems of a car are assumed to be exponentially distributed with the given lambdas in the table below. The reliability of the vehicle at 36,000 miles and the mean mileage to failure are calculated.
| Components of the vehicle | Number of failures, [math]\displaystyle{ \lambda }[/math] (per 1000 miles) |
|---|---|
| Body | 5.1 x 10-4 |
| Powertrain | 6.3 x 10-4 |
| Electrical | 5.5 x 10-5 |
| Chassis | 4.8 x 10-4 |
Result
Substituting the values of [math]\displaystyle{ \lambda_{1} }[/math], [math]\displaystyle{ \lambda_{2} }[/math], [math]\displaystyle{ \lambda_{3} }[/math], and [math]\displaystyle{ \lambda_{4} }[/math] into the equation (Equation 4.4 in the reference book) below, the lifetime of the vehicle is estimated to be 16.75 × 10-4 failures per 1000 miles.
Then, the reliability at 36,000 miles is calculated as R(36,000) = exp(-16.75 × 10-4 × 36) = 0.9415. The mean mileage to failure (MTTF) is obtained as MTTF = 1 / λ = 1 / 16.75 × 10-4 = 597,000 miles.
Results in BlockSim