Series Systems RBD - Revision history

Kate Racaza at 15:51, 20 August 2015

2015-08-20T15:51:28Z

Kate Racaza at 17:36, 3 August 2015

2015-08-03T17:36:34Z

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 {{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]]
-'''Analytical Proof'''
+Both results are within 0.2% error. More accurate results may be obtained via simulation if the number of simulations is increased.
 -->

Kate Racaza: Created page with '{{Reference Example|{{Banner BlockSim Reference Examples}}}} This example validates the results for series systems in BlockSim's analytical and simulation diagrams. {{Reference_…'

2015-07-31T16:27:51Z

Created page with '{{Reference Example|{{Banner BlockSim Reference Examples}}}} This example validates the results for series systems in BlockSim's analytical and simulation diagrams. {{Reference_…'

New page

{{Reference Example|{{Banner BlockSim Reference Examples}}}}
This example validates the results for series systems in BlockSim's analytical and simulation diagrams.

{{Reference_Example_Heading1}}
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.

{{Reference_Example_Heading2}}

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.

{| {{table}}
!Components of the vehicle
!Number of failures, <math>\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
|}

{{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 × 10-4 failures per 1000 miles.

::<math>\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.

{{Reference_Example_Heading4|BlockSim}}

← Older revision		Revision as of 15:51, 20 August 2015
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	{{Reference Example\|{{Banner BlockSim Reference Examples}}}}		{{Reference Example\|{{Banner BlockSim Reference Examples}}}}
	This example validates the results for series systems in BlockSim's analytical and simulation diagrams.		This example validates the results for series systems in BlockSim's analytical and simulation diagrams.


	{{Reference_Example_Heading1}}		{{Reference_Example_Heading1}}
	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.		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.


	{{Reference_Example_Heading2}}		{{Reference_Example_Heading2}}
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	Then, the reliability at 36,000 miles is calculated as R(36,000) = exp(-16.75 × 10<sup>-4</sup> × 36) = 0.9415. The mean mileage to failure (MTTF) is obtained as MTTF = 1 / λ = 1 / 16.75 × 10-4 = 597,000 miles.		Then, the reliability at 36,000 miles is calculated as R(36,000) = exp(-16.75 × 10<sup>-4</sup> × 36) = 0.9415. The mean mileage to failure (MTTF) is obtained as MTTF = 1 / λ = 1 / 16.75 × 10<sup>-4</sup> = 597,000 miles.


	{{Reference_Example_Heading4\|BlockSim}}		{{Reference_Example_Heading4\|BlockSim}}
	~~<!--~~
	In BlockSim, the vehicle RBD is configured as shown below:		In BlockSim, the vehicle RBD is configured as shown below:

	[[Image:series_rbd.png\|center]]		[[Image:series_rbd.png\|center]]

	Each component is modeled using a 1-parameter exponential distribution with the given lambda values:
			Each component is modeled using a 1-parameter exponential distribution with the given lambda values. (If the exponential models show the mean times, choose '''Application Setup > Calculations ''' and then clear the '''Use mean time for the exponential distribution''' check box.):

	[[Image:series_models.png\|center]]		[[Image:series_models.png\|center]]


	''Analytical Proof'''		'''Analytical Proof'''

	In the QCP, the reliability at 36,000 miles is estimated to be 94.15%		In the QCP, the reliability at 36,000 miles is estimated to be 94.1482%

	[[Image:series_qcprel.png\|center\|500px]]		[[Image:series_qcprel.png\|center\|500px]]


	And the mean life (MTTF), which is the mileage to failure, is obtained as 596~~,729~~ miles.		And the mean life (MTTF), which is the mileage to failure, is obtained as 596.728891 miles.

	[[Image:series_qcpmttf.png\|center\|500px]]		[[Image:series_qcpmttf.png\|center\|500px]]
Line 62:		Line 65:


	The point reliability at 36,000 miles is calculated in the QCP as 94.26%.		The point reliability at 36,000 miles is calculated in the QCP as 94.2580%.

	[[Image:series_simqcprel.png\|center\|500px]]		[[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.		And the mean time to first failure (MTTFF), which is the mean mileage to first failure, is obtained as 595.880646 miles.

	[[Image:series_simqcpmttf.png\|center\|500px]]		[[Image:series_simqcpmttf.png\|center\|500px]]
Line 73:		Line 76:

	Both results are within 0.2% error. More accurate results may be obtained via simulation if the number of simulations is increased.		Both results are within 0.2% error. More accurate results may be obtained via simulation if the number of simulations is increased.
	~~-->~~