A prototype of a system was tested with design changes incorporated during the test. A total of 12 failures occurred. The data set is given in Table 4.5.
Estimate the Duane parameters.
Plot the cumulative and instantaneous MTBF curves.
How many cumulative test and development hours are required to meet an instantaneous MTBF goal of 500 hours?
How many cumulative test and development hours are required to meet a cumulative MTBF goal of 500 hours?
Table 4.5 - Developmental Test data for Example 6
|
Figure 4.11 shows the data entered into RGA along with the estimated Duane parameters.
Figure 4.12 shows the cumulative and instantaneous MTBF curves.
Figure 4.13 shows the cumulative test and development hours needed for an instantaneous MTBF goal of 500 hours.
Figure 4.14 shows the cumulative test and development hours needed for a cumulative MTBF goal of 500 hours.
Figure 4.11: Entered data and the estimated Duane parameters
Figure 4.12: The cumulative and instantaneous MTBF curves
Figure 4.13: Test time for an instantaneous MTBF of 500 hours
Figure 4.14: Required test time for a cumulative MTBF of 500 hours
Two identical systems were tested. Any design changes made to improve the reliability of these systems were incorporated into both systems when any system failed. A total of 29 failures occurred. The data set is given in Table 4.6. Do the following:
Estimate the Duane parameters.
Assume both units are tested for an additional 100 hours each. How many failures do you expect in that period?
If testing/development were halted at this point, what would the reliability equation for this system be?
Table 4.6 - Developmental test data
|
Failure Number |
Failed Unit |
Test Time Unit 1 (hr) |
Test Time Unit 2 (hr) |
|
1 |
1 |
0.2 |
2.0 |
|
2 |
2 |
1.7 |
2.9 |
|
3 |
2 |
4.5 |
5.2 |
|
4 |
2 |
5.8 |
9.1 |
|
5 |
2 |
17.3 |
9.2 |
|
6 |
2 |
29.3 |
24.1 |
|
7 |
1 |
36.5 |
61.1 |
|
8 |
2 |
46.3 |
69.6 |
|
9 |
1 |
63.6 |
78.1 |
|
10 |
2 |
64.4 |
85.4 |
|
11 |
1 |
74.3 |
93.6 |
|
12 |
1 |
106.6 |
103 |
|
13 |
2 |
195.2 |
117 |
|
14 |
2 |
235.1 |
134.3 |
|
15 |
1 |
248.7 |
150.2 |
|
16 |
2 |
256.8 |
164.6 |
|
17 |
2 |
261.1 |
174.3 |
|
18 |
2 |
299.4 |
193.2 |
|
19 |
1 |
305.3 |
234.2 |
|
20 |
1 |
326.9 |
257.3 |
|
21 |
1 |
339.2 |
290.2 |
|
22 |
1 |
366.1 |
293.1 |
|
23 |
2 |
466.4 |
316.4 |
|
24 |
1 |
504 |
373.2 |
|
25 |
1 |
510 |
375.1 |
|
26 |
2 |
543.2 |
386.1 |
|
27 |
2 |
635.4 |
453.3 |
|
28 |
1 |
641.2 |
485.8 |
|
29 |
2 |
755.8 |
573.6 |
Figure 4.15 shows the data entered into RGA along with the estimated Duane parameters.
Figure 4.15: Entered data and the estimated parameters
The current accumulated
test time for both units is 1329.4 hr. If the process were to continue
for an additional combined time of 200 hr, the expected cumulative number
of failures at 
T =
1529.4 is 31.2695, as shown in Figure 4.16. At T = 1329.4, the expected
number of failures is 29.2004. Therefore, the expected number of failures
that would be observed over the additional 200 hr is equal to 
.
If testing/development were halted at
this point, the system failure intensity would be equal to the instantaneous
failure intensity at that time, or 
failures/hr.
See Figure 4.17. An exponential distribution can be assumed since the
value of the failure intensity at that instant in time is known. Therefore:
Weibull++ can be utilized (from within RGA) to provide a Reliability vs. Time plot. This is shown in Figure 4.18.
Figure 4.16: Calculate the expected cumulative number of failures at T = 1529.4
Figure 4.17: Calculate the instantaneous failure intensity at the end of the test
Figure 4.18: Reliability vs. Time plot
Given the Sequential data in the Table 4.7, do the following:
Estimate the Duane parameters.
What is the instantaneous MTBF at the end of the test?
How many additional test runs with a one-sided 90% confidence level are required to meet an instantaneous MTBF goal of 5 hours?
Table 4.7 - Sequential data for Duane Example 8
|
Figure 4.19 shows the data set entered into RGA along with the estimated Duane parameters.
The MTBF at the end of the test is equal to 4.5904 hours.
Figure 4.20 shows the
number of test runs with both one-sided confidence bounds at 90% confidence
level to achieve an instantaneous MTBF of 5 hours. Therefore, the number
of additional test runs required with a 90% confidence level is equal
to 
test runs.
Figure 4.19: Entered data and the estimated parameters
Figure 4.20: Number of test runs with a one-sided 90% confidence level required to meet an instantaneous MTBF goal of 5 hours
See Also:
Duane Model History and Development
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