Grouped per Configuration - Lloyd-Lipow Model: Difference between revisions

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<noinclude>{{Banner RGA Examples}}
<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Lloyd-Lipow|Reliability Growth and Repairable System Analysis Reference book]]''.
''This example appears in the [https://help.reliasoft.com/reference/reliability_growth_and_repairable_system_analysis Reliability growth reference]''.
</noinclude>
</noinclude>


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|15|| 14|| 12
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'''Solution'''
'''Solution'''
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<li>The figure below displays the entered data and the estimated Lloyd-Lipow parameters.
<li>The figure below displays the entered data and the estimated Lloyd-Lipow parameters.


[[Image:rga6.4.png|thumb|center|400px|Estimated Lloyd-Lipow parameters using MLE.]]
[[Image:rga6.4.png|center|600px]]
</li>
</li>
<li>The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.
<li>The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.
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<li>The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .
<li>The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .
   
   
[[Image:rga6.5.png|thumb|center|400px|Confidence bounds on the parameters.]]</li>
[[Image:rga6.5.png|center|450px]]</li>
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Latest revision as of 21:22, 18 September 2023

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This example appears in the Reliability growth reference.


A 15-stage reliability development test program was performed. The grouped per configuration data set is shown in the following table. Do the following:

  1. Fit the Lloyd-Lipow model to the data using MLE.
  2. What is the maximum reliability attained as the number of test stages approaches infinity?
  3. What is the maximum achievable reliability with a 90% confidence level?
Grouped per Configuration Data
Stage, [math]\displaystyle{ k\,\! }[/math] Number of Tests ([math]\displaystyle{ n_k\,\! }[/math]) Number of Successes ([math]\displaystyle{ S_k\,\! }[/math])
1 10 3
2 10 3
3 10 4
4 10 5
5 10 5
6 12 6
7 12 5
8 12 7
9 14 8
10 14 8
11 14 10
12 14 12
13 14 11
14 14 12
15 14 12

Solution

  1. The figure below displays the entered data and the estimated Lloyd-Lipow parameters.
    Rga6.4.png
  2. The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of [math]\displaystyle{ R\,\! }[/math]. Therefore, [math]\displaystyle{ R=0.7157\,\! }[/math].
  3. The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of [math]\displaystyle{ R\,\! }[/math] is equal to 0.6691 .
    Rga6.5.png