Repairable Systems Analysis Reference Example: Difference between revisions

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{{Reference Example|{{Banner RGA Reference_Examples}}}}
{{Reference Example|{{Banner RGA Reference_Examples}}|Repairable Systems Analysis}}
This example compares the results for a repairable systems analysis.  
This example validates the results for a repairable systems analysis in RGA.  




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Crow, L.H., ''Reliability Analysis for Complex Repairable Systems'', Reliability and Biometry: Statistical Analysis of Lifelength, pg. 385, 1974.
Crow, L.H., ''Reliability Analysis for Complex Repairable Systems'', Reliability and Biometry: Statistical Analysis of Lifelength, pg. 385, 1974.


For this example, the power law model parameters will be calculated.
For this example, the Power Law model parameters will be calculated.




Latest revision as of 18:26, 28 September 2015

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Repairable Systems Analysis

This example validates the results for a repairable systems analysis in RGA.


Reference Case

Crow, L.H., Reliability Analysis for Complex Repairable Systems, Reliability and Biometry: Statistical Analysis of Lifelength, pg. 385, 1974.

For this example, the Power Law model parameters will be calculated.


Data

The following table shows the data.

System 1 System 2 System 3
4.3 0.1 8.4
4.4 5.6 32.4
10.2 18.6 44.7
23.5 19.5 48.4
23.8 24.2 50.6
26.4 26.7 73.6
74 45.1 98.7
77.1 45.8 112.2
92.1 72.7 129.8
197.2 75.7 136
98.6 195.8
120.1
161.8
180.6
190.8
Simulated Data for 3 Systems with End Time = 200 hours


Result

The book has the following results:

Beta = 0.615, Lambda = 0.461


Results in RGA

Since [math]\displaystyle{ \,\!S_{1}=S_{2}=S_{3}=0 }[/math] and [math]\displaystyle{ \,\!T_{1}=T_{2}=T_{3}=200 }[/math] then the maximum likelihood estimates of [math]\displaystyle{ \,\!\hat{\beta} }[/math] and [math]\displaystyle{ \,\!\hat{\lambda } }[/math] are given by:


[math]\displaystyle{ \begin{align} \hat{\beta} =&\frac{\underset{q=1}{\overset{K}{\mathop \sum }}N_{q}}{\underset{q=1}{\overset{K}{\mathop \sum }}\,\underset{i=1}{\overset{N_{q}}{\mathop \sum }}\ln \left ( \frac{T}{X_{iq}} \right )}\\ \\ =&0.6153 \end{align}\,\! }[/math]


[math]\displaystyle{ \begin{align} \hat{\lambda }=&\frac{{\underset{q=1}{\overset{K}{\mathop \sum }}N_{q}}}{KT^{\hat{\beta }}}\\ \\ =&0.4605 \end{align}\,\! }[/math]


The model parameters are:

Repairable SystemS SIAM Results.png
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