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 [ | ''This example appears in the [https://help.reliasoft.com/reference/reliability_growth_and_repairable_system_analysis Reliability growth reference]''. | ||
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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 | [[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 | [[Image:rga6.5.png|center|450px]]</li> | ||
</ol> | </ol> | ||
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:
- Fit the Lloyd-Lipow model to the data using MLE.
- What is the maximum reliability attained as the number of test stages approaches infinity?
- What is the maximum achievable reliability with a 90% confidence level?
| 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
- The figure below displays the entered data and the estimated Lloyd-Lipow parameters.
- 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].
- 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 .
