Series Systems RBD: Difference between revisions

Revision as of 17:36, 3 August 2015

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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.

[math]\displaystyle{ \lambda = \sum_{i=1}^{n}\lambda_{i}\,\! }[/math]

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

@@ Line 24: / Line 24: @@
 {{Reference_Example_Heading3}}
-Substituting the values of <math>\lambda_{1}</math>, <math>\lambda_{2}</math>, <math>\lambda_{3}</math>, and <math>\lambda_{4}</math> into the equation (Equation 4.4 in the reference book) below, the lifetime of the vehicle is calculated as 16.75 × 10<sup>-4</sup> failures per 1000 miles.
+Substituting the values of <math>\lambda_{1}</math>, <math>\lambda_{2}</math>, <math>\lambda_{3}</math>, and <math>\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<sup>-4</sup> failures per 1000 miles.
 ::<math>\lambda = \sum_{i=1}^{n}\lambda_{i}\,\!</math>
@@ Line 35: / Line 34: @@
 {{Reference_Example_Heading4|BlockSim}}
 <!--
-In BlockSim, vehicle RBD is configured as shown below:
+In BlockSim, the vehicle RBD is configured as shown below:
 [[Image:series_rbd.png|center]]
+Each component is modeled using a 1-parameter exponential distribution with the given lambda values:
+[[Image:series_models.png|center]]
+''Analytical Proof'''
+In the QCP, the reliability at 36,000 miles is estimated to be 94.15%
+[[Image:series_qcprel.png|center|500px]]
+And the mean life (MTTF), which is the mileage to failure, is obtained as 596,729 miles.
+[[Image:series_qcpmttf.png|center|500px]]
+'''Simulation Proof'''
+We can also estimate the results by using the simulation tool in BlockSim. The simulation settings are shown below.
+[[Image:series_sim.png|center|500px]]
+The point reliability at 36,000 miles is calculated in the QCP as 94.26%.
+[[Image:series_simqcprel.png|center|500px]]
+And the mean time to first failure (MTTFF), which is the mean mileage to first failure, is obtained as 595,881 miles.
+[[Image:series_simqcpmttf.png|center|500px]]
-'''Analytical Proof'''
+Both results are within 0.2% error. More accurate results may be obtained via simulation if the number of simulations is increased.
 -->

Series Systems RBD: Difference between revisions

Revision as of 17:36, 3 August 2015

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