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

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<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]''.
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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