Reliability Data - 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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#How many months of testing are required to achieve a reliability goal of 90%?
#How many months of testing are required to achieve a reliability goal of 90%?
#What is the attainable reliability if the maximum duration of testing is 30 months?
#What is the attainable reliability if the maximum duration of testing is 30 months?


{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Reliability Data'''
|+'''Reliability Data'''
!Time(months)
!Time (months)
!Reliability(%)
!Reliability (%)
|-
|-
|1|| 33.35
|1|| 33.35
Line 36: Line 35:
|10|| 92.10
|10|| 92.10
|}
|}


'''Solution'''
'''Solution'''
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<li>The next figure displays the estimated parameters.
<li>The next figure displays the estimated parameters.


[[Image:rga6.6.png|thumb|center|400px|Estimated Lloyd-Lipow parameters using least squares.]]
[[Image:rga6.6.png|center|600px]]
</li>
</li>
<li>The figure below displays Reliability vs. Time plot with 90% 2-sided confidence bounds.
<li>The figure below displays Reliability vs. Time plot with 90% 2-sided confidence bounds.


[[Image:rga6.7.png|thumb|center|400px|Reliability vs. Time plot with 90% 2-sided confidence bounds.]]
[[Image:rga6.7.png|center|450px]]
</li>
</li>
<li>The next figure shows the number of months of testing required to achieve a reliability goal of 90%.
<li>The next figure shows the number of months of testing required to achieve a reliability goal of 90%.


[[Image:rga6.8.png|thumb|center|400px|Number of months required to achieve a reliability of 90%.]]
[[Image:rga6.8.png|center|450px]]
</li>
</li>
<li>The figure below displays the reliability achieved after 30 months of testing.
<li>The figure below displays the reliability achieved after 30 months of testing.


[[Image:rga6.9.png|thumb|center|400px|Maximum attainable reliability for a testing duration of 30 months.]]
[[Image:rga6.9.png|center|450px]]
</li>
</li>
</ol>
</ol>

Latest revision as of 21:17, 18 September 2023

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This example appears in the Reliability growth reference.


Given the reliability data in the table below, do the following:

  1. Fit the Lloyd-Lipow model to the data using least squares analysis.
  2. Plot the Lloyd-Lipow reliability with 90% 2-sided confidence bounds.
  3. How many months of testing are required to achieve a reliability goal of 90%?
  4. What is the attainable reliability if the maximum duration of testing is 30 months?
Reliability Data
Time (months) Reliability (%)
1 33.35
2 42.50
3 58.02
4 68.50
5 74.20
6 80.00
7 82.30
8 89.50
9 91.00
10 92.10

Solution

  1. The next figure displays the estimated parameters.
    Rga6.6.png
  2. The figure below displays Reliability vs. Time plot with 90% 2-sided confidence bounds.
    Rga6.7.png
  3. The next figure shows the number of months of testing required to achieve a reliability goal of 90%.
    Rga6.8.png
  4. The figure below displays the reliability achieved after 30 months of testing.
    Rga6.9.png