Reliability Data - Lloyd-Lipow Model

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This example appears in the Reliability Growth and Repairable System Analysis Reference book.

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.
   

   Estimated Lloyd-Lipow parameters using least squares.
2. The figure below displays Reliability vs. Time plot with 90% 2-sided confidence bounds.
   

   Reliability vs. Time plot with 90% 2-sided confidence bounds.
3. The next figure shows the number of months of testing required to achieve a reliability goal of 90%.
   

   Number of months required to achieve a reliability of 90%.
4. The figure below displays the reliability achieved after 30 months of testing.
   

   Maximum attainable reliability for a testing duration of 30 months.