K-out-of-n Systems - Revision history

Kate Racaza at 18:21, 31 July 2015

2015-07-31T18:21:14Z

Kate Racaza at 18:17, 31 July 2015

2015-07-31T18:17:34Z

← Older revision		Revision as of 18:17, 31 July 2015
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	The reliability of the web host after one year of continuous operation (8760 hours) is calculated in the QCP as 93.36%, which is the same as the result calculated in the reference book.		The reliability of the web host after one year of continuous operation (8760 hours) is calculated in the QCP as 93.36%, which is the same as the result calculated in the reference book.

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


	Mean time between failures (MTBF) is estimated to be 29,004 hours.		Mean time between failures (MTBF) is estimated to be 29,004 hours.

	[[Image:~~kn_qcpmtfbf~~.png\|center]]		[[Image:kn_qcpmtbf.png\|center\|500px]]


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	We can also estimate the results by using the simulation tool in BlockSim. The simulation settings are shown below.		We can also estimate the results by using the simulation tool in BlockSim. The simulation settings are shown below.

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


	The point reliability after 8760 hours of use is estimated to be 93.28%.		The point reliability after 8760 hours of use is estimated to be 93.28%.

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


	And the mean time to failure (MTTF) is estimated to be 29,105 hours.		And the mean time to failure (MTTF) is estimated to be 29,105 hours.

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

Kate Racaza: Created page with '{{DISPLAYTITLE:k-out-of-n Systems}}{{Reference Example|{{Banner BlockSim Reference Examples}}}} This example validates the results for ''k''-out-of-''n'' systems in BlockSim's an…'

2015-07-31T17:38:07Z

Created page with '{{DISPLAYTITLE:k-out-of-n Systems}}{{Reference Example|{{Banner BlockSim Reference Examples}}}} This example validates the results for ''k''-out-of-''n'' systems in BlockSim's an…'

New page

{{DISPLAYTITLE:k-out-of-n Systems}}{{Reference Example|{{Banner BlockSim Reference Examples}}}}
This example validates the results for ''k''-out-of-''n'' systems in BlockSim's analytical and simulation diagrams.

{{Reference_Example_Heading1}}

This data set is from example 4.6 on page 78 in the book ''Life Cycle Reliability Engineering'' by Dr. Guangbin Yang, John Wiley & Sons, 2007.

{{Reference_Example_Heading2}}

A web host has 5 independent and identical servers connected in parallel, and at least 3 of them must be operational for the web service to be operational. Each server has an exponential life distribution model with a lambda of 2.7 × 10-5 failures per hour. Mean time between failures (MTBF) and the reliability of the web host after one year of continuous operation are calculated.

{{Reference_Example_Heading3}}

It is assumed that the server is repaired immediately to a good-as-new condition if failed; therefore, the MTBF is the same as the MTTF and is calculated by using Equation 4.24 on page 78:

::<math>MTTF = \frac{1}{\lambda}\sum^{n}_{i=k}\frac{1}{i} = \frac{1}{2.7 \times 10^{-5}}\sum^{5}_{i=3}\frac{1}{i} = 2.9 \times 10^{4}\,\!</math>   hours

Since the time to failure is exponential, system reliability is calculated via Equation 4.23 on page 78 by substituting the given data as:

::<math>R(t) = \sum^{n}_{i=k}C^{i}_{5} e^{-\lambda i t} (1-e^{-\lambda t})^{n-i}\,\!</math>

::<math>R(8760) = \sum^{5}_{i=3}C^{i}_{5} e^{-2.7 \times 10^{-5} \times 8760i} (1-e^{-2.7 \times 10^{-5} \times 8760})^{5-i} = 0.9336\,\!</math>

{{Reference_Example_Heading4|BlockSim}}

In BlockSim, the server system RBD is configured as shown below.

[[Image:kn_rbd.png|center]]

Each server is modeled with an exponential distribution with a lambda of 2.7 × 10-5 failures per hour.

'''Analytical Proof'''

The reliability of the web host after one year of continuous operation (8760 hours) is calculated in the QCP as 93.36%, which is the same as the result calculated in the reference book.

[[Image:kn_qcprel.png|center]]

Mean time between failures (MTBF) is estimated to be 29,004 hours.

[[Image:kn_qcpmtfbf.png|center]]

'''Simulation Proof'''

We can also estimate the results by using the simulation tool in BlockSim. The simulation settings are shown below.

[[Image:kn_sim.png|center]]

The point reliability after 8760 hours of use is estimated to be 93.28%.

[[Image:kn_simqcprel.png|center]]

And the mean time to failure (MTTF) is estimated to be 29,105 hours.

[[Image:kn_simqcpmttf.png|center]]

← Older revision		Revision as of 18:21, 31 July 2015
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	Since the time to failure is exponential, system reliability is calculated via Equation 4.23 on page 78 by substituting the given data as:		Since the time to failure is exponential, system reliability is calculated via Equation 4.23 on page 78 by substituting the given data as:

	::<math>R(t) = \sum^{n}_{i=k}C^{i}_{5} e^{-\lambda i t} (1-e^{-\lambda t})^{n-i}\,\!</math>		::<math>R(t) = \sum^{n}_{i=k}C^{i}_{n} e^{-\lambda i t} (1-e^{-\lambda t})^{n-i}\,\!</math>

	::<math>R(8760) = \sum^{5}_{i=3}C^{i}_{5} e^{-2.7 \times 10^{-5} \times 8760i} (1-e^{-2.7 \times 10^{-5} \times 8760})^{5-i} = 0.9336\,\!</math>		::<math>R(8760) = \sum^{5}_{i=3}C^{i}_{5} e^{-2.7 \times 10^{-5} \times 8760i} (1-e^{-2.7 \times 10^{-5} \times 8760})^{5-i} = 0.9336\,\!</math>
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	Each server is modeled with an exponential distribution with a lambda of 2.7 × 10-5 failures per hour.		Each server is modeled with an exponential distribution with a lambda of 2.7 × 10<sup>-5</sup> failures per hour.


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	~~Mean~~ time between failures (MTBF) is estimated to be 29,004 hours.		The mean time between failures (MTBF) is estimated to be 29,004 hours.

	[[Image:kn_qcpmtbf.png\|center\|500px]]		[[Image:kn_qcpmtbf.png\|center\|500px]]
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	The point reliability after 8760 hours of use is estimated to be 93.28%.		The point reliability after 8760 hours of use is estimated to be 93.45%.

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


	And the mean time to failure (MTTF) is estimated to be 29,~~105~~ hours.		And the mean time to failure (MTTF) is estimated to be 29,048 hours.

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