General Examples Using the Logistic Model

Logistic Model Example 5

Table 8.4 presents the reliabilities observed monthly for an automobile transmission that was tested for one year.

Find a Logistic reliability growth curve that best represents the data.
Plot it comparatively with the raw data.
If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99% be achieved?
If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of January the following year?

Table 8.4 - Reliability data

Month	Observed Reliability (%)
June	22
July	26
August	30
September	34
October	45
November	58
December	68
January	79
February	85
March	89
April	92
May	95

Solution to Logistic Model Example 5

Figure 8.7 shows the estimated parameters.
Figure 8.8 displays the Reliability vs. Time plot.
Using the QCP, Figure 8.9 displays when the reliability goal of 99% will be achieved.
Figure 8.10 shows the reliability at the end of January the following year (i.e. after 20 months of testing and development).

Figure 8.7: Entered data and the estimated Logistic parameters

Figure 8.8: Reliability vs. Time plot

Figure 8.9: When the reliability goal of 99% will be achieved

Figure 8.10: The reliability at the end of the following January (month = 20)

Logistic Model Example 6

Table 8.5 presents the results for a missile launch test. The test consisted of 20 attempts. If the missile launched, it was recorded as a success. If not, it was recorded as a failure. Note that, at this development stage, the test did not consider whether or not the target was destroyed.

Find a Logistic reliability growth curve that best represents the data.
Plot it comparatively with the raw data.
If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.5% with a 90% confidence level be achieved?
If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

Table 8.5 - Sequential success/failure data

Launch Number	Result
1	F
2	F
3	S
4	F
5	F
6	S
7	S
8	S
9	F
10	S
11	F
12	S
13	S
14	S
15	S
16	S
17	S
18	S
19	S
20	S

Solution to Logistic Model Example 6

Figure 8.11 shows the entered data and the estimated parameters.
Figure 8.12 displays the Reliability vs. Time plot.
Figure 8.13 displays when the reliability goal of 99.5% will be achieved with a 90% confidence level.
Figure 8.14 displays the reliability achieved after the 35th launch.

Figure 8.11: Entered data and the estimated Logistic parameters

Figure 8.12: Reliability vs. Time plot

Figure 8.13: When the reliability goal of 99.5% with a 90% confidence level will be achieved

Figure 8.14: The reliability at the end of the 35th launch

Logistic Model Example 7

Consider the data given for the missile launch test in Example 6. Now suppose that the engineers assigned failure modes to each failure and that the appropriate corrective actions were taken. Table 8.6 presents the data.

Find the Logistic reliability growth curve that best represents the data.
Plot it comparatively with the raw data.
If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.50% be achieved?
If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

Table 8.6 - Sequential success/failure data with modes

Launch Number	Result	Mode
1	F	2
2	F	1
3	S
4	F	3
5	F	3
6	S
7	S
8	S
9	F	2
10	S
11	F	1
12	S
13	S
14	S
15	S
16	S
17	S
18	S
19	S
20	S

Solution to Logistic Model Example 7

Figure 8.15 shows the estimated parameters.
Figure 8.16 displays the Reliability vs. Time plot.
Figure 8.17 displays when the reliability goal of 99.5% will be achieved.
Figure 8.18 displays the reliability after the 35th launch.

Figure 8.15: Entered data and the estimated Logistic parameters

Figure 8.16: Reliability vs. Time plot

Figure 8.17: Calculate when the reliability goal of 99.5% will be achieved

Figure 8.18: Calculate the reliability at the end of the 35th launch